|\^/|     Maple 18 (X86 64 WINDOWS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         printf("%s\n",str);
>     fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc

# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         printf("%s",str);
>     fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then printf("%s", str) end if
end proc

# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         print(label,str);
>     fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then print(label, str) end if
end proc

# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         if vallen = 4 then
>         printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
>         else
>         printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
>     fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        if vallen = 4 then
            printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
        else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
        end if
    end if
end proc

# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 0
>         if vallen = 5  then # if number 1
>             printf("%-30s = %-32d  %s\n",prelabel,value, postlabel);
>             else
>             printf("%-30s = %-32d  %s \n",prelabel,value, postlabel);
>         fi;# end if 1;
>     fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        if vallen = 5 then
            printf("%-30s = %-32d  %s\n", prelabel, value, postlabel)
        else printf("%-30s = %-32d  %s \n", prelabel, value, postlabel)
        end if
    end if
end proc

# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 0
>         print(prelabel,"[",elemnt,"]",value, postlabel);
>     fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        print(prelabel, "[", elemnt, "]", value, postlabel)
    end if
end proc

# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
>     global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
>     local  days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
>     fprintf(fd,"<td>");
>     if (secs_in >= 0)  then # if number 0
>         years_int  :=  int_trunc(secs_in / glob_sec_in_year);
>         sec_temp  :=  int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
>         days_int  :=  int_trunc(sec_temp / glob_sec_in_day) ;
>         sec_temp  :=  sec_temp mod int_trunc(glob_sec_in_day) ;
>         hours_int  :=  int_trunc(sec_temp / glob_sec_in_hour);
>         sec_temp  :=  sec_temp mod int_trunc(glob_sec_in_hour);
>         minutes_int  := int_trunc(sec_temp / glob_sec_in_minute);
>         sec_int  := sec_temp mod int_trunc(glob_sec_in_minute);
>         if  (years_int > 0)  then # if number 1
>             fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
>         elif
>         (days_int > 0)  then # if number 2
>             fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
>         elif
>         (hours_int > 0)  then # if number 3
>             fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
>         elif
>         (minutes_int > 0)  then # if number 4
>             fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
>         else
>             fprintf(fd,"%d Seconds",sec_int);
>         fi;# end if 4
>     else
>         fprintf(fd," 0.0 Seconds");
>     fi;# end if 3
>     fprintf(fd,"</td>\n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
    fprintf(fd, "<td>");
    if 0 <= secs_in then
        years_int := int_trunc(secs_in/glob_sec_in_year);
        sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
        days_int := int_trunc(sec_temp/glob_sec_in_day);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
        hours_int := int_trunc(sec_temp/glob_sec_in_hour);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
        minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
        sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
        if 0 < years_int then fprintf(fd,
            "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
            days_int, hours_int, minutes_int, sec_int)
        elif 0 < days_int then fprintf(fd,
            "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
            minutes_int, sec_int)
        elif 0 < hours_int then fprintf(fd,
            "%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
            sec_int)
        elif 0 < minutes_int then
            fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
        else fprintf(fd, "%d Seconds", sec_int)
        end if
    else fprintf(fd, " 0.0 Seconds")
    end if;
    fprintf(fd, "</td>\n")
end proc

# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
>     global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
>     local  days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
>     if (secs_in >= 0)  then # if number 3
>         years_int  :=  int_trunc(secs_in / glob_sec_in_year);
>         sec_temp  :=  (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
>         days_int  :=  int_trunc(sec_temp / glob_sec_in_day) ;
>         sec_temp  :=  (sec_temp mod int_trunc(glob_sec_in_day)) ;
>         hours_int  :=  int_trunc(sec_temp / glob_sec_in_hour);
>         sec_temp  :=  (sec_temp mod int_trunc(glob_sec_in_hour));
>         minutes_int  := int_trunc(sec_temp / glob_sec_in_minute);
>         sec_int  := (sec_temp mod int_trunc(glob_sec_in_minute));
>         if  (years_int > 0)  then # if number 4
>             printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
>         elif
>         (days_int > 0)  then # if number 5
>             printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
>         elif
>         (hours_int > 0)  then # if number 6
>             printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
>         elif
>         (minutes_int > 0)  then # if number 7
>             printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
>         else
>             printf(" = %d Seconds\n",sec_int);
>         fi;# end if 7
>     else
>         printf(" 0.0 Seconds\n");
>     fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
    if 0 <= secs_in then
        years_int := int_trunc(secs_in/glob_sec_in_year);
        sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
        days_int := int_trunc(sec_temp/glob_sec_in_day);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
        hours_int := int_trunc(sec_temp/glob_sec_in_hour);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
        minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
        sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
        if 0 < years_int then printf(
            " = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
            years_int, days_int, hours_int, minutes_int, sec_int)
        elif 0 < days_int then printf(
            " = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
            hours_int, minutes_int, sec_int)
        elif 0 < hours_int then printf(
            " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
            sec_int)
        elif 0 < minutes_int then
            printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
        else printf(" = %d Seconds\n", sec_int)
        end if
    else printf(" 0.0 Seconds\n")
    end if
end proc

# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
>     global ATS_MAX_TERMS;
>     local iii;
>     iii  := 1;
>     while (iii <= ATS_MAX_TERMS) do # do number 1
>         arr_a [iii] := glob__0;
>         iii  :=  iii + 1;
>     od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
    iii := 1;
    while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
    end do
end proc

# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
>     global ATS_MAX_TERMS;
>     local iii_ats, lll_ats,ma_ats, ret_ats;
>     ret_ats  := glob__0;
>     if (jjj_ats <=  mmm_ats)  then # if number 6
>         ma_ats  :=  mmm_ats + 1;
>         iii_ats  :=  jjj_ats;
>         while (iii_ats <= mmm_ats) do # do number 1
>             lll_ats  :=  ma_ats - iii_ats;
>             if ((lll_ats <= ATS_MAX_TERMS  and (iii_ats <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_ats  :=  ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
>             fi;# end if 7;
>             iii_ats  :=  iii_ats + 1;
>         od;# end do number 1
>     fi;# end if 6;
>     ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
    ret_ats := glob__0;
    if jjj_ats <= mmm_ats then
        ma_ats := mmm_ats + 1;
        iii_ats := jjj_ats;
        while iii_ats <= mmm_ats do
            lll_ats := ma_ats - iii_ats;
            if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
                ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
            end if;
            iii_ats := iii_ats + 1
        end do
    end if;
    ret_ats
end proc

# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
>     global ATS_MAX_TERMS;
>     local al_att, iii_att,lll_att, ma_att, ret_att;
>     ret_att  := glob__0;
>     if (jjj_att < mmm_att)  then # if number 6
>         ma_att  :=  mmm_att + 2;
>         iii_att  :=  jjj_att;
>         while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) )   do # do number 1
>             lll_att  :=  ma_att - iii_att;
>             al_att  :=  (lll_att - 1);
>             if ((lll_att <= ATS_MAX_TERMS  and (iii_att <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_att  :=   ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
>             fi;# end if 7;
>             iii_att  :=  iii_att + 1;
>         od;# end do number 1;
>         ret_att  :=  ret_att / c(mmm_att) ;
>     fi;# end if 6;
>     ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
    ret_att := glob__0;
    if jjj_att < mmm_att then
        ma_att := mmm_att + 2;
        iii_att := jjj_att;
        while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
            lll_att := ma_att - iii_att;
            al_att := lll_att - 1;
            if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
                ret_att :=
                ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
            end if;
            iii_att := iii_att + 1
        end do;
        ret_att := ret_att/c(mmm_att)
    end if;
    ret_att
end proc

# End Function number 12
# Begin Function number 13
> logditto := proc(file)
>     fprintf(file,"<td>");
>     fprintf(file,"ditto");
>     fprintf(file,"</td>");
> end;
logditto := proc(file)
    fprintf(file, "<td>"); fprintf(file, "ditto"); fprintf(file, "</td>")
end proc

# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
>     fprintf(file,"<td>");
>     fprintf(file,"%d",n);
>     fprintf(file,"</td>");
> end;
logitem_integer := proc(file, n)
    fprintf(file, "<td>"); fprintf(file, "%d", n); fprintf(file, "</td>")
end proc

# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
>     fprintf(file,"<td>");
>     fprintf(file,str);
>     fprintf(file,"</td>");
> end;
logitem_str := proc(file, str)
    fprintf(file, "<td>"); fprintf(file, str); fprintf(file, "</td>")
end proc

# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
>     global glob_small_float,glob_prec;
>     local good_digits;
>     fprintf(file,"<td>");
>     fprintf(file,"%d",glob_min_good_digits);
>     fprintf(file,"</td>");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
    fprintf(file, "<td>");
    fprintf(file, "%d", glob_min_good_digits);
    fprintf(file, "</td>")
end proc

# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
>     fprintf(file,revs);
> end;
           log_revs := proc(file, revs) fprintf(file, revs) end proc

# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
>     fprintf(file,"<td>");
>     fprintf(file,"%g",x);
>     fprintf(file,"</td>");
> end;
logitem_float := proc(file, x)
    fprintf(file, "<td>"); fprintf(file, "%g", x); fprintf(file, "</td>")
end proc

# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
>     global glob_h_reason;
>     fprintf(file,"<td>");
>     if (glob_h_reason  = 1) then # if number 6
>         fprintf(file,"Max H");
>     elif
>     (glob_h_reason = 2) then # if number 7
>         fprintf(file,"Display Interval");
>     elif
>     (glob_h_reason = 3) then # if number 8
>         fprintf(file,"Optimal");
>     elif
>     (glob_h_reason = 4) then # if number 9
>         fprintf(file,"Pole Accuracy");
>     elif
>     (glob_h_reason = 5) then # if number 10
>         fprintf(file,"Min H (Pole)");
>     elif
>     (glob_h_reason = 6) then # if number 11
>         fprintf(file,"Pole");
>     elif
>     (glob_h_reason = 7) then # if number 12
>         fprintf(file,"Opt Iter");
>     else
>         fprintf(file,"Impossible");
>     fi;# end if 12
>     fprintf(file,"</td>");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
    fprintf(file, "<td>");
    if glob_h_reason = 1 then fprintf(file, "Max H")
    elif glob_h_reason = 2 then fprintf(file, "Display Interval")
    elif glob_h_reason = 3 then fprintf(file, "Optimal")
    elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
    elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
    elif glob_h_reason = 6 then fprintf(file, "Pole")
    elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
    else fprintf(file, "Impossible")
    end if;
    fprintf(file, "</td>")
end proc

# End Function number 19
# Begin Function number 20
> logstart := proc(file)
>     fprintf(file,"<tr>");
> end;
             logstart := proc(file) fprintf(file, "<tr>") end proc

# End Function number 20
# Begin Function number 21
> logend := proc(file)
>     fprintf(file,"</tr>\n");
> end;
             logend := proc(file) fprintf(file, "</tr>\n") end proc

# End Function number 21
# Begin Function number 22
> chk_data := proc()
>     global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
>     local  errflag;
>     errflag  :=  false;
>     if (glob_max_iter < 2)  then # if number 12
>         omniout_str(ALWAYS,"Illegal max_iter");
>         errflag  :=  true;
>     fi;# end if 12;
>     if (errflag)   then # if number 12
>         quit;
>     fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
    errflag := false;
    if glob_max_iter < 2 then
        omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
    end if;
    if errflag then quit end if
end proc

# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
>     global glob_small_float;
>     local ms2, rrr, sec_left, sub1, sub2;
>     ;
>     ms2 := c(clock_sec2);
>     sub1 := c(t_end2-t_start2);
>     sub2 := c(t2-t_start2);
>     if (sub1 = glob__0)  then # if number 12
>         sec_left := glob__0;
>     else
>         if (sub2 > glob__0)  then # if number 13
>             rrr := (sub1/sub2);
>             sec_left  := rrr * c(ms2) - c(ms2);
>         else
>             sec_left  := glob__0;
>         fi;# end if 13
>     fi;# end if 12;
>     sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
    ms2 := c(clock_sec2);
    sub1 := c(t_end2 - t_start2);
    sub2 := c(t2 - t_start2);
    if sub1 = glob__0 then sec_left := glob__0
    else
        if glob__0 < sub2 then
            rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
        else sec_left := glob__0
        end if
    end if;
    sec_left
end proc

# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
>     global glob_small_float;
>     local rrr, sub1, sub2;
>     sub1  :=  (t_end2-t_start2);
>     sub2  :=  (t2-t_start2);
>     if (sub2 > glob_small_float)  then # if number 12
>         rrr  :=  (glob__100*sub2)/sub1;
>     else
>         rrr  :=  0.0;
>     fi;# end if 12;
>     rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
    sub1 := t_end2 - t_start2;
    sub2 := t2 - t_start2;
    if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
    else rrr := 0.
    end if;
    rrr
end proc

# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (float_abs(term2) > glob__0)  then # if number 12
>         ret :=  float_abs(term1 * glob_h / term2);
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
    if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM ORDER ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (float_abs(term2) > glob__0)  then # if number 12
>         ret := glob__1 +  float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
    if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
        c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 26
# Begin Function number 27
> c := proc(in_val)
>     #To Force Conversion when needed
>     local ret;
>     ret := evalf(in_val);
>     ret;
>     #End Conversion
> end;
        c := proc(in_val) local ret; ret := evalf(in_val); ret end proc

# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret,temp;
>     temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
>     if (float_abs(temp) > glob__0)  then # if number 12
>         ret := float_abs((term2*glob_h*term1)/(temp));
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
    temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
         - term1*term3*c(last_no) + term1*term3);
    if glob__0 < float_abs(temp) then
        ret := float_abs(term2*glob_h*term1/temp)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM ORDER ANALYSIS
>     local ret;
>     ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
>     ret;
>     #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
    ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
         - glob__4*term2*term2*c(last_no) + glob__4*term2*term2
         + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
        /(term2*term2*c(last_no) - glob__2*term2*term2
         - term1*term3*c(last_no) + term1*term3));
    ret
end proc

# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
>     #TOP SIX TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float,glob_six_term_ord_save;
>     local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
>     if ((term5  <> glob__0) and (term4  <> glob__0) and (term3  <> glob__0) and  (term2  <> glob__0) and (term1  <> glob__0)) then # if number 12
>         rm0 := term6/term5;
>         rm1 := term5/term4;
>         rm2 := term4/term3;
>         rm3 := term3/term2;
>         rm4 := term2/term1;
>         nr1 :=  c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
>         nr2 :=  c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
>         dr1 :=  glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
>         dr2 :=  glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
>         ds1 :=  glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
>         ds2 :=  glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
>         if ((float_abs(nr1 * dr2 - nr2 * dr1)  =  glob__0)  or  (float_abs(dr1) = glob__0))  then # if number 13
>             rad_c :=  glob_larger_float;
>             ord_no :=  glob_larger_float;
>         else
>             if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0)  then # if number 14
>                 rcs :=  ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
>                 #(Manuels)  rcs  :=  (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
>                 ord_no :=  (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
>                 if (float_abs(rcs)  <> glob__0)  then # if number 15
>                     if (rcs > glob__0)  then # if number 16
>                         rad_c  :=  sqrt(rcs) * float_abs(glob_h);
>                     else
>                         rad_c  :=  glob_larger_float;
>                         ord_no :=  glob_larger_float;
>                     fi;# end if 16
>                 else
>                     rad_c :=  glob_larger_float;
>                     ord_no :=  glob_larger_float;
>                 fi;# end if 15
>             else
>                 rad_c :=  glob_larger_float;
>                 ord_no :=  glob_larger_float;
>             fi;# end if 14
>         fi;# end if 13
>     else
>         rad_c :=  glob_larger_float;
>         ord_no :=  glob_larger_float;
>     fi;# end if 12;
>     glob_six_term_ord_save :=  ord_no;
>     rad_c;
>     #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
    if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
    term2 <> glob__0 and term1 <> glob__0 then
        rm0 := term6/term5;
        rm1 := term5/term4;
        rm2 := term4/term3;
        rm3 := term3/term2;
        rm4 := term2/term1;
        nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
             + c(last_no - 3)*rm2;
        nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
             + c(last_no - 4)*rm3;
        dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
        dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
        ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
        ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
        if
        float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
        then rad_c := glob_larger_float; ord_no := glob_larger_float
        else
            if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
                rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
                ord_no :=
                    (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
                if float_abs(rcs) <> glob__0 then
                    if glob__0 < rcs then
                        rad_c := sqrt(rcs)*float_abs(glob_h)
                    else
                        rad_c := glob_larger_float;
                        ord_no := glob_larger_float
                    end if
                else
                    rad_c := glob_larger_float; ord_no := glob_larger_float
                end if
            else rad_c := glob_larger_float; ord_no := glob_larger_float
            end if
        end if
    else rad_c := glob_larger_float; ord_no := glob_larger_float
    end if;
    glob_six_term_ord_save := ord_no;
    rad_c
end proc

# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
>     global glob_six_term_ord_save;
>     #TOP SIX TERM ORDER ANALYSIS
>     #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
>     glob_six_term_ord_save;
>     #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
    glob_six_term_ord_save
end proc

# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
>     ret := nnn!;
>     ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
         factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc

# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
>     global ATS_MAX_TERMS,array_fact_1;
>     local ret;
>     if (nnn <= ATS_MAX_TERMS) then # if number 12
>         if (array_fact_1[nnn] = 0) then # if number 13
>             ret := factorial_2(nnn);
>             array_fact_1[nnn] := ret;
>         else
>             ret := array_fact_1[nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
    if nnn <= ATS_MAX_TERMS then
        if array_fact_1[nnn] = 0 then
            ret := factorial_2(nnn); array_fact_1[nnn] := ret
        else ret := array_fact_1[nnn]
        end if
    else ret := factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
>     global ATS_MAX_TERMS,array_fact_2;
>     local ret;
>     if ((nnn <= ATS_MAX_TERMS)  and  (mmm <= ATS_MAX_TERMS)) then # if number 12
>         if (array_fact_2[mmm,nnn] = 0) then # if number 13
>             ret := factorial_1(mmm)/factorial_1(nnn);
>             array_fact_2[mmm,nnn] := ret;
>         else
>             ret := array_fact_2[mmm,nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(mmm)/factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
    if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
        if array_fact_2[mmm, nnn] = 0 then
            ret := factorial_1(mmm)/factorial_1(nnn);
            array_fact_2[mmm, nnn] := ret
        else ret := array_fact_2[mmm, nnn]
        end if
    else ret := factorial_2(mmm)/factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
>     (mmm);
> end;
                      convfloat := proc(mmm) mmm end proc

# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
>     time();
> end;
                 elapsed_time_seconds := proc() time() end proc

# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
>     abs(x);
> end;
                      float_abs := proc(x) abs(x) end proc

# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
>     x^y;
> end;
                        expt := proc(x, y) x^y end proc

# End Function number 38
# Begin Function number 39
> neg := proc(x)
>     -x;
> end;
                           neg := proc(x) -x end proc

# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
>     trunc(x);
> end;
                     int_trunc := proc(x) trunc(x) end proc

# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
>     local desired_abs_gbl_error,range,estimated_steps,step_error;
>     global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
>     omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
>     desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
>     omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
>     omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
>     omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
>     range := (x_end - x_start);
>     omniout_float(ALWAYS,"range",32,range,32,"");
>     estimated_steps := range / estimated_h;
>     omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
>     step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
>     omniout_float(ALWAYS,"step_error",32,step_error,32,"");
>     (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
    omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
        glob_desired_digits_correct, 32, "");
    desired_abs_gbl_error :=
        expt(glob__10, c(-glob_desired_digits_correct))*
        c(float_abs(c(estimated_answer)));
    omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
    omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
        ;
    omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
        desired_abs_gbl_error, 32, "");
    range := x_end - x_start;
    omniout_float(ALWAYS, "range", 32, range, 32, "");
    estimated_steps := range/estimated_h;
    omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
    step_error := c(float_abs(desired_abs_gbl_error)/(
        sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
    omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
    step_error
end proc

# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y2 := proc(x)
> return(sin(c(x)));
> end;
               exact_soln_y2 := proc(x) return sin(c(x)) end proc

> exact_soln_y2p := proc(x)
> return( cos(c(x)));
> end;
              exact_soln_y2p := proc(x) return cos(c(x)) end proc

> exact_soln_y2pp := proc(x)
> return( neg( sin(c(x))));
> end;
           exact_soln_y2pp := proc(x) return neg(sin(c(x))) end proc

> exact_soln_y1 := proc(x)
> return( cos(c(x)));
> end;
               exact_soln_y1 := proc(x) return cos(c(x)) end proc

#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
>     local rad_given;
>     global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 1
>         rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) +  array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
>         omniout_float(ALWAYS,"Radius of convergence (given) for eq  1           ",4,rad_given,4," ");
>         omniout_float(ALWAYS,"Order of pole (given)                             ",4,array_given_ord_poles[1,1],4," ");
>         if (rad_given < glob_least_given_sing)  then # if number 2
>             glob_least_given_sing :=  rad_given;
>         fi;# end if 2;
>     elif
>     (glob_type_given_pole = 3) then # if number 2
>         omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
>     elif
>     (glob_type_given_pole = 5) then # if number 3
>         omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
>     else
>         omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
>     fi;# end if 3;
>     if (array_rad_test_poles[1,1] < glob_large_float)  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq  1      ",4,array_rad_test_poles[1,1],4," ");
>         if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
>             glob_least_ratio_sing := array_rad_test_poles[1,1];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (ratio test)                        ",4, array_ord_test_poles[1,1],4," ");
>     else
>         omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
>     fi;# end if 3;
>     if ((array_rad_test_poles[1,2] >  glob__small) and (array_rad_test_poles[1,2] < glob_large_float))  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1  ",4,array_rad_test_poles[1,2],4," ");
>         if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
>             glob_least_3_sing := array_rad_test_poles[1,2];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (three term test)                   ",4, array_ord_test_poles[1,2],4," ");
>     else
>         omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
>     fi;# end if 3;
>     if ((array_rad_test_poles[1,3] >  glob__small) and (array_rad_test_poles[1,3] < glob_large_float))  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1    ",4,array_rad_test_poles[1,3],4," ");
>         if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
>             glob_least_6_sing := array_rad_test_poles[1,3];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (six term test)                     ",4, array_ord_test_poles[1,3],4," ");
>     else
>         omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
>     fi;# end if 3
>     ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 3
>         rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) +  array_given_rad_poles[2,2] * array_given_rad_poles[2,2]);
>         omniout_float(ALWAYS,"Radius of convergence (given) for eq  2           ",4,rad_given,4," ");
>         omniout_float(ALWAYS,"Order of pole (given)                             ",4,array_given_ord_poles[2,1],4," ");
>         if (rad_given < glob_least_given_sing)  then # if number 4
>             glob_least_given_sing :=  rad_given;
>         fi;# end if 4;
>     elif
>     (glob_type_given_pole = 3) then # if number 4
>         omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
>     elif
>     (glob_type_given_pole = 5) then # if number 5
>         omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
>     else
>         omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
>     fi;# end if 5;
>     if (array_rad_test_poles[2,1] < glob_large_float)  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq  2      ",4,array_rad_test_poles[2,1],4," ");
>         if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6
>             glob_least_ratio_sing := array_rad_test_poles[2,1];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (ratio test)                        ",4, array_ord_test_poles[2,1],4," ");
>     else
>         omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
>     fi;# end if 5;
>     if ((array_rad_test_poles[2,2] >  glob__small) and (array_rad_test_poles[2,2] < glob_large_float))  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2  ",4,array_rad_test_poles[2,2],4," ");
>         if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6
>             glob_least_3_sing := array_rad_test_poles[2,2];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (three term test)                   ",4, array_ord_test_poles[2,2],4," ");
>     else
>         omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
>     fi;# end if 5;
>     if ((array_rad_test_poles[2,3] >  glob__small) and (array_rad_test_poles[2,3] < glob_large_float))  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2    ",4,array_rad_test_poles[2,3],4," ");
>         if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6
>             glob_least_6_sing := array_rad_test_poles[2,3];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (six term test)                     ",4, array_ord_test_poles[2,3],4," ");
>     else
>         omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
>     fi;# end if 5
>     ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
    if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
        rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
            (array_x[1] - array_given_rad_poles[1, 1])
             + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
        omniout_float(ALWAYS,
            "Radius of convergence (given) for eq  1           ", 4,
            rad_given, 4, " ");
        omniout_float(ALWAYS,
            "Order of pole (given)                             ", 4,
            array_given_ord_poles[1, 1], 4, " ");
        if rad_given < glob_least_given_sing then
            glob_least_given_sing := rad_given
        end if
    elif glob_type_given_pole = 3 then
        omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
    elif glob_type_given_pole = 5 then
        omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
    else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
    end if;
    if array_rad_test_poles[1, 1] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (ratio test) for eq  1      ", 4,
            array_rad_test_poles[1, 1], 4, " ");
        if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
            glob_least_ratio_sing := array_rad_test_poles[1, 1]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (ratio test)                        ", 4,
            array_ord_test_poles[1, 1], 4, " ")
    else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
    end if;
    if glob__small < array_rad_test_poles[1, 2] and
    array_rad_test_poles[1, 2] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (three term test) for eq 1  ", 4,
            array_rad_test_poles[1, 2], 4, " ");
        if array_rad_test_poles[1, 2] < glob_least_3_sing then
            glob_least_3_sing := array_rad_test_poles[1, 2]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (three term test)                   ", 4,
            array_ord_test_poles[1, 2], 4, " ")
    else omniout_str(ALWAYS,
        "NO REAL POLE (three term test) for Equation 1")
    end if;
    if glob__small < array_rad_test_poles[1, 3] and
    array_rad_test_poles[1, 3] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (six term test) for eq 1    ", 4,
            array_rad_test_poles[1, 3], 4, " ");
        if array_rad_test_poles[1, 3] < glob_least_6_sing then
            glob_least_6_sing := array_rad_test_poles[1, 3]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (six term test)                     ", 4,
            array_ord_test_poles[1, 3], 4, " ")
    else omniout_str(ALWAYS,
        "NO COMPLEX POLE (six term test) for Equation 1")
    end if;
    if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
        rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])*
            (array_x[1] - array_given_rad_poles[2, 1])
             + array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]);
        omniout_float(ALWAYS,
            "Radius of convergence (given) for eq  2           ", 4,
            rad_given, 4, " ");
        omniout_float(ALWAYS,
            "Order of pole (given)                             ", 4,
            array_given_ord_poles[2, 1], 4, " ");
        if rad_given < glob_least_given_sing then
            glob_least_given_sing := rad_given
        end if
    elif glob_type_given_pole = 3 then
        omniout_str(ALWAYS, "NO POLE (given) for Equation 2")
    elif glob_type_given_pole = 5 then
        omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
    else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
    end if;
    if array_rad_test_poles[2, 1] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (ratio test) for eq  2      ", 4,
            array_rad_test_poles[2, 1], 4, " ");
        if array_rad_test_poles[2, 1] < glob_least_ratio_sing then
            glob_least_ratio_sing := array_rad_test_poles[2, 1]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (ratio test)                        ", 4,
            array_ord_test_poles[2, 1], 4, " ")
    else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
    end if;
    if glob__small < array_rad_test_poles[2, 2] and
    array_rad_test_poles[2, 2] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (three term test) for eq 2  ", 4,
            array_rad_test_poles[2, 2], 4, " ");
        if array_rad_test_poles[2, 2] < glob_least_3_sing then
            glob_least_3_sing := array_rad_test_poles[2, 2]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (three term test)                   ", 4,
            array_ord_test_poles[2, 2], 4, " ")
    else omniout_str(ALWAYS,
        "NO REAL POLE (three term test) for Equation 2")
    end if;
    if glob__small < array_rad_test_poles[2, 3] and
    array_rad_test_poles[2, 3] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (six term test) for eq 2    ", 4,
            array_rad_test_poles[2, 3], 4, " ");
        if array_rad_test_poles[2, 3] < glob_least_6_sing then
            glob_least_6_sing := array_rad_test_poles[2, 3]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (six term test)                     ", 4,
            array_ord_test_poles[2, 3], 4, " ")
    else omniout_str(ALWAYS,
        "NO COMPLEX POLE (six term test) for Equation 2")
    end if
end proc

# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
>     local ret;
>     if (xf > x0) then # if number 5
>         ret := glob__1;
>     else
>         ret := glob__m1;
>     fi;# end if 5;
>     ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
    if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc

# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local min_size;
>     min_size := glob_estimated_size_answer;
>     if (float_abs(array_y2[1]) < min_size) then # if number 5
>         min_size := float_abs(array_y2[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     if (float_abs(array_y1[1]) < min_size) then # if number 5
>         min_size := float_abs(array_y1[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     if (min_size < glob__1) then # if number 5
>         min_size := glob__1;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    min_size := glob_estimated_size_answer;
    if float_abs(array_y2[1]) < min_size then
        min_size := float_abs(array_y2[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if float_abs(array_y1[1]) < min_size then
        min_size := float_abs(array_y1[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if min_size < glob__1 then
        min_size := glob__1;
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    min_size
end proc

# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     max_estimated_step_error  := glob__small;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
>     est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 5
>         max_estimated_step_error := est_tmp;
>     fi;# end if 5;
>     est_tmp := float_abs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 5
>         max_estimated_step_error := est_tmp;
>     fi;# end if 5;
>     omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
>     max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    max_estimated_step_error := glob__small;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
    est_tmp := float_abs(array_y2[no_terms - 3]
         + array_y2[no_terms - 2]*hn_div_ho
         + array_y2[no_terms - 1]*hn_div_ho_2
         + array_y2[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    est_tmp := float_abs(array_y1[no_terms - 3]
         + array_y1[no_terms - 2]*hn_div_ho
         + array_y1[no_terms - 1]*hn_div_ho_2
         + array_y1[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    omniout_float(ALWAYS, "max_estimated_step_error", 32,
        max_estimated_step_error, 32, "");
    max_estimated_step_error
end proc

# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
>     fi;# end if 5;
>     if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
>         array_max_est_error[1] := c(est_tmp);
>     fi;# end if 5
>     ;
>     est_tmp := c(float_abs(array_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
>     fi;# end if 5;
>     if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
>         array_max_est_error[2] := c(est_tmp);
>     fi;# end if 5
>     ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    est_tmp := c(float_abs(array_y2[no_terms - 3]))
         + c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
    end if;
    if c(array_max_est_error[1]) <= c(est_tmp) then
        array_max_est_error[1] := c(est_tmp)
    end if;
    est_tmp := c(float_abs(array_y1[no_terms - 3]))
         + c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
    end if;
    if c(array_max_est_error[2]) <= c(est_tmp) then
        array_max_est_error[2] := c(est_tmp)
    end if
end proc

# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local ret;
>     if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 5
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 5;
>     return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    if glob_check_sign*glob_next_display - glob_h/glob__10 <=
    glob_check_sign*array_x[1] then ret := true
    else ret := false
    end if;
    return ret
end proc

# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
>     #TOP DISPLAY ALOT
>     if (reached_interval())  then # if number 5
>         if (iter >= 0)  then # if number 6
>             ind_var := array_x[1];
>             omniout_float(ALWAYS,"x[1]                             ",33,ind_var,20," ");
>             closed_form_val_y := evalf(exact_soln_y2(ind_var));
>             omniout_float(ALWAYS,"y2[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y2[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y2[1] (numeric)                  ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 7
>                 relerr := abserr*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 8
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 7;
>             if (glob_good_digits < glob_min_good_digits) then # if number 7
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 7;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 7;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 7
>                 est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 8
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[1] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 7
>                 array_1st_rel_error[1] := relerr;
>             else
>                 array_last_rel_error[1] := relerr;
>             fi;# end if 7;
>             array_est_rel_error[1] := est_rel_err;
>             omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>             omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>             omniout_int(INFO,"Desired digits                   ",32,glob_desired_digits_correct,4," ");
>             omniout_int(INFO,"Estimated correct digits         ",32,glob_est_digits,4," ");
>             omniout_int(INFO,"Correct digits                   ",32,glob_good_digits,4," ")
>             ;
>             omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>             ;
>             closed_form_val_y := evalf(exact_soln_y1(ind_var));
>             omniout_float(ALWAYS,"y1[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y1[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y1[1] (numeric)                  ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 7
>                 relerr := abserr*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 8
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 7;
>             if (glob_good_digits < glob_min_good_digits) then # if number 7
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 7;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 7;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 7
>                 est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 8
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[2] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 7
>                 array_1st_rel_error[2] := relerr;
>             else
>                 array_last_rel_error[2] := relerr;
>             fi;# end if 7;
>             array_est_rel_error[2] := est_rel_err;
>             omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>             omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>             omniout_int(INFO,"Desired digits                   ",32,glob_desired_digits_correct,4," ");
>             omniout_int(INFO,"Estimated correct digits         ",32,glob_est_digits,4," ");
>             omniout_int(INFO,"Correct digits                   ",32,glob_good_digits,4," ")
>             ;
>             omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>         fi;# end if 6;
>         #BOTTOM DISPLAY ALOT
>     fi;# end if 5;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    if reached_interval() then
        if 0 <= iter then
            ind_var := array_x[1];
            omniout_float(ALWAYS, "x[1]                             ", 33,
                ind_var, 20, " ");
            closed_form_val_y := evalf(exact_soln_y2(ind_var));
            omniout_float(ALWAYS, "y2[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y2[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y2[1] (numeric)                  ", 33,
                numeric_val, 20, " ");
            if c(glob_prec) < c(float_abs(closed_form_val_y)) then
                relerr := abserr*glob__100/float_abs(closed_form_val_y);
                if c(glob_prec) < c(relerr) then
                    glob_good_digits := -int_trunc(log10(c(relerr))) + 3
                else glob_good_digits := Digits
                end if
            else relerr := glob__m1; glob_good_digits := -16
            end if;
            if glob_good_digits < glob_min_good_digits then
                glob_min_good_digits := glob_good_digits
            end if;
            if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
            then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
            end if;
            if glob_prec < evalf(float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[1]*100.0*
                    sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val))
                    ;
                if glob_prec < evalf(est_rel_err) then
                    glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
                else glob_est_digits := Digits
                end if
            else relerr := glob__m1; glob_est_digits := -16
            end if;
            array_est_digits[1] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[1] := relerr
            else array_last_rel_error[1] := relerr
            end if;
            array_est_rel_error[1] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ");
            closed_form_val_y := evalf(exact_soln_y1(ind_var));
            omniout_float(ALWAYS, "y1[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y1[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y1[1] (numeric)                  ", 33,
                numeric_val, 20, " ");
            if c(glob_prec) < c(float_abs(closed_form_val_y)) then
                relerr := abserr*glob__100/float_abs(closed_form_val_y);
                if c(glob_prec) < c(relerr) then
                    glob_good_digits := -int_trunc(log10(c(relerr))) + 3
                else glob_good_digits := Digits
                end if
            else relerr := glob__m1; glob_good_digits := -16
            end if;
            if glob_good_digits < glob_min_good_digits then
                glob_min_good_digits := glob_good_digits
            end if;
            if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
            then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
            end if;
            if glob_prec < evalf(float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[2]*100.0*
                    sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val))
                    ;
                if glob_prec < evalf(est_rel_err) then
                    glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
                else glob_est_digits := Digits
                end if
            else relerr := glob__m1; glob_est_digits := -16
            end if;
            array_est_digits[2] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[2] := relerr
            else array_last_rel_error[2] := relerr
            end if;
            array_est_rel_error[2] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ")
        end if
    end if
end proc

# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>     #TOP PROGRESS REPORT
>     clock_sec1   := elapsed_time_seconds();
>     total_clock_sec   :=  (clock_sec1) - (glob_orig_start_sec);
>     glob_clock_sec   :=  (clock_sec1) - (glob_clock_start_sec);
>     left_sec   :=  (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
>     expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h)  ,( clock_sec1) - (glob_orig_start_sec));
>     opt_clock_sec   := ( clock_sec1) - (glob_optimal_clock_start_sec);
>     glob_optimal_expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
>     glob_total_exp_sec   := glob_optimal_expect_sec + c(total_clock_sec);
>     percent_done   :=  comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
>     glob_percent_done := percent_done;
>     omniout_str_noeol(INFO,"Total Elapsed Time              ");
>     omniout_timestr((total_clock_sec));
>     omniout_str_noeol(INFO,"Elapsed Time(since restart)     ");
>     omniout_timestr((glob_clock_sec));
>     if (c(percent_done) < glob__100)  then # if number 5
>         omniout_str_noeol(INFO,"Expected Time Remaining         ");
>         omniout_timestr((expect_sec));
>         omniout_str_noeol(INFO,"Optimized Time Remaining        ");
>         omniout_timestr((glob_optimal_expect_sec));
>         omniout_str_noeol(INFO,"Expected Total Time             ");
>         omniout_timestr((glob_total_exp_sec));
>     fi;# end if 5;
>     omniout_str_noeol(INFO,"Time to Timeout                 ");
>     omniout_timestr((left_sec));
>     omniout_float(INFO,    "Percent Done                    ",33,percent_done,4,"%");
>     #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    clock_sec1 := elapsed_time_seconds();
    total_clock_sec := clock_sec1 - glob_orig_start_sec;
    glob_clock_sec := clock_sec1 - glob_clock_start_sec;
    left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
    expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
        clock_sec1 - glob_orig_start_sec);
    opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
    glob_optimal_expect_sec :=
        comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
        ;
    glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
    percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
    glob_percent_done := percent_done;
    omniout_str_noeol(INFO, "Total Elapsed Time              ");
    omniout_timestr(total_clock_sec);
    omniout_str_noeol(INFO, "Elapsed Time(since restart)     ");
    omniout_timestr(glob_clock_sec);
    if c(percent_done) < glob__100 then
        omniout_str_noeol(INFO, "Expected Time Remaining         ");
        omniout_timestr(expect_sec);
        omniout_str_noeol(INFO, "Optimized Time Remaining        ");
        omniout_timestr(glob_optimal_expect_sec);
        omniout_str_noeol(INFO, "Expected Total Time             ");
        omniout_timestr(glob_total_exp_sec)
    end if;
    omniout_str_noeol(INFO, "Time to Timeout                 ");
    omniout_timestr(left_sec);
    omniout_float(INFO, "Percent Done                    ", 33,
        percent_done, 4, "%")
end proc

# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14,  rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
>     #TOP CHECK FOR POLE
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,1] :=  glob_larger_float;
>     array_ord_test_poles[1,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 3 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 5;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 6
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 7
>             found_sing := 0;
>         fi;# end if 7;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 7
>         if (rad_c  < array_rad_test_poles[1,1]) then # if number 8
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[1,1] := rad_c;
>             array_ord_test_poles[1,1] := tmp_ord;
>         fi;# end if 8;
>     fi;# end if 7;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,1] :=  glob_larger_float;
>     array_ord_test_poles[2,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 7;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 8
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 9
>             found_sing := 0;
>         fi;# end if 9;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 9
>         if (rad_c  < array_rad_test_poles[2,1]) then # if number 10
>             array_rad_test_poles[2,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[2,1] := rad_c;
>             array_ord_test_poles[2,1] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test2
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,2] :=  glob_larger_float;
>     array_ord_test_poles[1,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 3 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 9;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 10
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 11
>             found_sing := 0;
>         fi;# end if 11;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 11
>         if (rad_c  < array_rad_test_poles[1,2]) then # if number 12
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 13
>                 glob_min_pole_est := rad_c;
>             fi;# end if 13;
>             array_ord_test_poles[1,2] := tmp_ord;
>         fi;# end if 12;
>     fi;# end if 11;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,2] :=  glob_larger_float;
>     array_ord_test_poles[2,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 11;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 12
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 13
>             found_sing := 0;
>         fi;# end if 13;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 13
>         if (rad_c  < array_rad_test_poles[2,2]) then # if number 14
>             array_rad_test_poles[2,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[2,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 15
>                 glob_min_pole_est := rad_c;
>             fi;# end if 15;
>             array_ord_test_poles[2,2] := tmp_ord;
>         fi;# end if 14;
>     fi;# end if 13;
>     #BOTTOM general radius test2
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,3] :=  glob_larger_float;
>     array_ord_test_poles[1,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 3 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 13;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 14
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 15
>             found_sing := 0;
>         fi;# end if 15;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 15
>         if (rad_c  < array_rad_test_poles[1,3]) then # if number 16
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 17
>                 glob_min_pole_est := rad_c;
>             fi;# end if 17;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 16;
>     fi;# end if 15;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,3] :=  glob_larger_float;
>     array_ord_test_poles[2,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 15;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 16
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 17
>             found_sing := 0;
>         fi;# end if 17;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 17
>         if (rad_c  < array_rad_test_poles[2,3]) then # if number 18
>             array_rad_test_poles[2,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[2,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 19
>                 glob_min_pole_est := rad_c;
>             fi;# end if 19;
>             array_ord_test_poles[2,3] := tmp_ord;
>         fi;# end if 18;
>     fi;# end if 17;
>     #BOTTOM general radius test2
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
>         h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
>         omniout_str(ALWAYS,"SETTING H FOR POLE");
>         glob_h_reason := 6;
>         if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 18;
>         term := 1;
>         ratio := c(1.0);
>         while (term <= ATS_MAX_TERMS)  do # do number 1
>             array_y2[term] := array_y2[term]* ratio;
>             array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             array_y1[term] := array_y1[term]* ratio;
>             array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             ratio := ratio * h_new / float_abs(glob_h);
>             term := term + 1;
>         od;# end do number 1;
>         glob_h := h_new;
>     fi;# end if 17;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 17
>         display_poles();
>     fi;# end if 17
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 1] := glob_larger_float;
    array_ord_test_poles[1, 1] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 13;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
            array_y2_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 1] then
            array_rad_test_poles[1, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[1, 1] := rad_c;
            array_ord_test_poles[1, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 1] := glob_larger_float;
    array_ord_test_poles[2, 1] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y1_higher[1, last_no - 1],
            array_y1_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 1] then
            array_rad_test_poles[2, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y1_higher[1, last_no - 1],
                array_y1_higher[1, last_no], last_no);
            array_rad_test_poles[2, 1] := rad_c;
            array_ord_test_poles[2, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 2] := glob_larger_float;
    array_ord_test_poles[1, 2] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 13;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 2] then
            array_rad_test_poles[1, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y2_higher[1, last_no - 2],
                array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[1, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 2] := glob_larger_float;
    array_ord_test_poles[2, 2] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 2] then
            array_rad_test_poles[2, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y1_higher[1, last_no - 2],
                array_y1_higher[1, last_no - 1],
                array_y1_higher[1, last_no], last_no);
            array_rad_test_poles[2, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 3] := glob_larger_float;
    array_ord_test_poles[1, 3] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 13;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
            array_y2_higher[1, last_no - 4],
            array_y2_higher[1, last_no - 3],
            array_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 3] then
            array_rad_test_poles[1, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y2_higher[1, last_no - 5],
                array_y2_higher[1, last_no - 4],
                array_y2_higher[1, last_no - 3],
                array_y2_higher[1, last_no - 2],
                array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[1, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 3] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 3] := glob_larger_float;
    array_ord_test_poles[2, 3] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y1_higher[1, last_no - 5],
            array_y1_higher[1, last_no - 4],
            array_y1_higher[1, last_no - 3],
            array_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 3] then
            array_rad_test_poles[2, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y1_higher[1, last_no - 5],
                array_y1_higher[1, last_no - 4],
                array_y1_higher[1, last_no - 3],
                array_y1_higher[1, last_no - 2],
                array_y1_higher[1, last_no - 1],
                array_y1_higher[1, last_no], last_no);
            array_rad_test_poles[2, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 3] := tmp_ord
        end if
    end if;
    if
    float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
    then
        h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
        omniout_str(ALWAYS, "SETTING H FOR POLE");
        glob_h_reason := 6;
        if glob_check_sign*h_new < glob_check_sign*glob_min_h then
            omniout_str(ALWAYS, "SETTING H FOR MIN H");
            h_new := glob_min_h;
            glob_h_reason := 5
        end if;
        term := 1;
        ratio := c(1.0);
        while term <= ATS_MAX_TERMS do
            array_y2[term] := array_y2[term]*ratio;
            array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            array_y1[term] := array_y1[term]*ratio;
            array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            ratio := ratio*h_new/float_abs(glob_h);
            term := term + 1
        end do;
        glob_h := h_new
    end if;
    if reached_interval() then display_poles() end if
end proc

# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre cos 1 $eq_no = 1
>     array_tmp1[1] :=  cos(array_x[1]);
>     array_tmp1_g[1] :=  sin(array_x[1]);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[1] :=  neg(array_tmp1[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,4]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[1]) * (expt((glob_h) , c(3))) * c(factorial_3(0,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[4] := temporary;
>                 array_y2_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[2,3] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y2_higher[3,2] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y2_higher[4,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[1] :=  neg(array_y2[1]);
>     #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,2]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[2] := temporary;
>                 array_y1_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y1_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
>     array_tmp1[2] := neg(array_tmp1_g[1]) * array_x[2] / c(1);
>     array_tmp1_g[2] := array_tmp1[1] * array_x[2] / c(1);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[2] :=  neg(array_tmp1[2]);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp3[2] := array_tmp2[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,5]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[2]) * (expt((glob_h) , c(3))) * c(factorial_3(1,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[5] := temporary;
>                 array_y2_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[2,4] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[3,3] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y2_higher[4,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[2] :=  neg(array_y2[2]);
>     #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,3]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[3] := temporary;
>                 array_y1_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y1_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
>     array_tmp1[3] := neg(array_tmp1_g[2]) * array_x[2] / c(2);
>     array_tmp1_g[3] := array_tmp1[2] * array_x[2] / c(2);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[3] :=  neg(array_tmp1[3]);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp3[3] := array_tmp2[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,6]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[3]) * (expt((glob_h) , c(3))) * c(factorial_3(2,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[6] := temporary;
>                 array_y2_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_higher[2,5] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[3,4] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[4,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[3] :=  neg(array_y2[3]);
>     #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[4] := temporary;
>                 array_y1_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y1_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
>     array_tmp1[4] := neg(array_tmp1_g[3]) * array_x[2] / c(3);
>     array_tmp1_g[4] := array_tmp1[3] * array_x[2] / c(3);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[4] :=  neg(array_tmp1[4]);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp3[4] := array_tmp2[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,7]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[4]) * (expt((glob_h) , c(3))) * c(factorial_3(3,6));
>             if (7 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[7] := temporary;
>                 array_y2_higher[1,7] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(6);
>             array_y2_higher[2,6] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_higher[3,5] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[4,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[4] :=  neg(array_y2[4]);
>     #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[5] := temporary;
>                 array_y1_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y1_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
>     array_tmp1[5] := neg(array_tmp1_g[4]) * array_x[2] / c(4);
>     array_tmp1_g[5] := array_tmp1[4] * array_x[2] / c(4);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[5] :=  neg(array_tmp1[5]);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp3[5] := array_tmp2[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,8]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[5]) * (expt((glob_h) , c(3))) * c(factorial_3(4,7));
>             if (8 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[8] := temporary;
>                 array_y2_higher[1,8] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(7);
>             array_y2_higher[2,7] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(6);
>             array_y2_higher[3,6] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_higher[4,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[5] :=  neg(array_y2[5]);
>     #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[6] := temporary;
>                 array_y1_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y1_higher[2,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #END ATOMHDR5
>     #BEGIN OUTFILE3
>     #Top Atomall While Loop-- outfile3
>     while (kkk <= ATS_MAX_TERMS) do # do number 1
>         #END OUTFILE3
>         #BEGIN OUTFILE4
>         #emit cos LINEAR $eq_no = 1
>         array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1]) * array_x[2] / c(kkk - 1);
>         array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1);
>         #emit neg FULL $eq_no = 1
>         array_tmp2[kkk] := neg(array_tmp1[kkk]);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp3[kkk] := array_tmp2[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 3;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y2_set_initial[1,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y2[kkk + order_d] := c(temporary);
>                 array_y2_higher[1,kkk + order_d] := c(temporary);
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
>                     if (adj3 <= order_d + 1) then # if number 3
>                         if (adj2 > 0) then # if number 4
>                             temporary := c(temporary) / c(glob_h) * c(adj2);
>                         else
>                             temporary := c(temporary);
>                         fi;# end if 4;
>                         array_y2_higher[adj3,term] := c(temporary);
>                     fi;# end if 3;
>                     term  := term - 1;
>                     adj2 := adj2 - 1;
>                     adj3 := adj3 + 1;
>                 od;# end do number 1
>             fi;# end if 2
>         fi;# end if 1;
>         #emit neg FULL $eq_no = 2
>         array_tmp5[kkk] := neg(array_y2[kkk]);
>         #emit assign $eq_no = 2
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y1_set_initial[2,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y1[kkk + order_d] := c(temporary);
>                 array_y1_higher[1,kkk + order_d] := c(temporary);
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
>                     if (adj3 <= order_d + 1) then # if number 3
>                         if (adj2 > 0) then # if number 4
>                             temporary := c(temporary) / c(glob_h) * c(adj2);
>                         else
>                             temporary := c(temporary);
>                         fi;# end if 4;
>                         array_y1_higher[adj3,term] := c(temporary);
>                     fi;# end if 3;
>                     term  := term - 1;
>                     adj2 := adj2 - 1;
>                     adj3 := adj3 + 1;
>                 od;# end do number 1
>             fi;# end if 2
>         fi;# end if 1;
>         kkk   :=  kkk + 1;
>     od;# end do number 1;
>     #BOTTOM ATOMALL
>     #END OUTFILE4
>     #BEGIN OUTFILE5
>     #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    array_tmp1[1] := cos(array_x[1]);
    array_tmp1_g[1] := sin(array_x[1]);
    array_tmp2[1] := neg(array_tmp1[1]);
    array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
    if not array_y2_set_initial[1, 4] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[1])*expt(glob_h, c(3))*c(factorial_3(0, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y2[4] := temporary;
                array_y2_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[2, 3] := c(temporary);
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y2_higher[3, 2] := c(temporary);
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y2_higher[4, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp5[1] := neg(array_y2[1]);
    if not array_y1_set_initial[2, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y1[2] := temporary;
                array_y1_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y1_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := neg(array_tmp1_g[1])*array_x[2]/c(1);
    array_tmp1_g[2] := array_tmp1[1]*array_x[2]/c(1);
    array_tmp2[2] := neg(array_tmp1[2]);
    array_tmp3[2] := array_tmp2[2];
    if not array_y2_set_initial[1, 5] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[2])*expt(glob_h, c(3))*c(factorial_3(1, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y2[5] := temporary;
                array_y2_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[2, 4] := c(temporary);
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[3, 3] := c(temporary);
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y2_higher[4, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp5[2] := neg(array_y2[2]);
    if not array_y1_set_initial[2, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y1[3] := temporary;
                array_y1_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y1_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp1[3] := neg(array_tmp1_g[2])*array_x[2]/c(2);
    array_tmp1_g[3] := array_tmp1[2]*array_x[2]/c(2);
    array_tmp2[3] := neg(array_tmp1[3]);
    array_tmp3[3] := array_tmp2[3];
    if not array_y2_set_initial[1, 6] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[3])*expt(glob_h, c(3))*c(factorial_3(2, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y2[6] := temporary;
                array_y2_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[2, 5] := c(temporary);
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[3, 4] := c(temporary);
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[4, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp5[3] := neg(array_y2[3]);
    if not array_y1_set_initial[2, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y1[4] := temporary;
                array_y1_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y1_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp1[4] := neg(array_tmp1_g[3])*array_x[2]/c(3);
    array_tmp1_g[4] := array_tmp1[3]*array_x[2]/c(3);
    array_tmp2[4] := neg(array_tmp1[4]);
    array_tmp3[4] := array_tmp2[4];
    if not array_y2_set_initial[1, 7] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[4])*expt(glob_h, c(3))*c(factorial_3(3, 6));
            if 7 <= ATS_MAX_TERMS then
                array_y2[7] := temporary;
                array_y2_higher[1, 7] := temporary
            end if;
            temporary := c(temporary)*c(6)/c(glob_h);
            array_y2_higher[2, 6] := c(temporary);
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[3, 5] := c(temporary);
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[4, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp5[4] := neg(array_y2[4]);
    if not array_y1_set_initial[2, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y1[5] := temporary;
                array_y1_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y1_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp1[5] := neg(array_tmp1_g[4])*array_x[2]/c(4);
    array_tmp1_g[5] := array_tmp1[4]*array_x[2]/c(4);
    array_tmp2[5] := neg(array_tmp1[5]);
    array_tmp3[5] := array_tmp2[5];
    if not array_y2_set_initial[1, 8] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[5])*expt(glob_h, c(3))*c(factorial_3(4, 7));
            if 8 <= ATS_MAX_TERMS then
                array_y2[8] := temporary;
                array_y2_higher[1, 8] := temporary
            end if;
            temporary := c(temporary)*c(7)/c(glob_h);
            array_y2_higher[2, 7] := c(temporary);
            temporary := c(temporary)*c(6)/c(glob_h);
            array_y2_higher[3, 6] := c(temporary);
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[4, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    array_tmp5[5] := neg(array_y2[5]);
    if not array_y1_set_initial[2, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y1[6] := temporary;
                array_y1_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y1_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1])*array_x[2]/c(kkk - 1)
            ;
        array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
        array_tmp2[kkk] := neg(array_tmp1[kkk]);
        array_tmp3[kkk] := array_tmp2[kkk];
        order_d := 3;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y2_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y2[kkk + order_d] := c(temporary);
                array_y2_higher[1, kkk + order_d] := c(temporary);
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
                do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then
                            temporary := c(temporary)*c(adj2)/c(glob_h)
                        else temporary := c(temporary)
                        end if;
                        array_y2_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        array_tmp5[kkk] := neg(array_y2[kkk]);
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y1_set_initial[2, kkk + order_d] then
                temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y1[kkk + order_d] := c(temporary);
                array_y1_higher[1, kkk + order_d] := c(temporary);
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
                do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then
                            temporary := c(temporary)*c(adj2)/c(glob_h)
                        else temporary := c(temporary)
                        end if;
                        array_y1_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        kkk := kkk + 1
    end do
end proc

# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
>     #BEGIN OUTFIEMAIN
>     local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
>     term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
>     rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
>     x_start,x_end
>     ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
>     global
>     ALWAYS,
>     INFO,
>     DEBUGL,
>     DEBUGMASSIVE,
>     glob_iolevel,
>     glob_yes_pole,
>     glob_no_pole,
>     glob_not_given,
>     glob_no_sing_tests,
>     glob_ratio_test,
>     glob_three_term_test,
>     glob_six_term_test,
>     glob_log_10,
>     #Top Generate Globals Decl
>     MAX_UNCHANGED,
>     glob__small,
>     glob_small_float,
>     glob_smallish_float,
>     glob_large_float,
>     glob_larger_float,
>     glob__m2,
>     glob__m1,
>     glob__0,
>     glob__1,
>     glob__2,
>     glob__3,
>     glob__4,
>     glob__5,
>     glob__8,
>     glob__10,
>     glob__100,
>     glob__pi,
>     glob__0_5,
>     glob__0_8,
>     glob__m0_8,
>     glob__0_25,
>     glob__0_125,
>     glob_prec,
>     glob_check_sign,
>     glob_desired_digits_correct,
>     glob_max_estimated_step_error,
>     glob_ratio_of_radius,
>     glob_percent_done,
>     glob_total_exp_sec,
>     glob_optimal_expect_sec,
>     glob_estimated_size_answer,
>     glob_almost_1,
>     glob_clock_sec,
>     glob_clock_start_sec,
>     glob_disp_incr,
>     glob_h,
>     glob_diff_rc_fm,
>     glob_diff_rc_fmm1,
>     glob_diff_rc_fmm2,
>     glob_diff_ord_fm,
>     glob_diff_ord_fmm1,
>     glob_diff_ord_fmm2,
>     glob_six_term_ord_save,
>     glob_guess_error_rc,
>     glob_guess_error_ord,
>     glob_least_given_sing,
>     glob_least_ratio_sing,
>     glob_least_3_sing,
>     glob_least_6_sing,
>     glob_last_good_h,
>     glob_max_h,
>     glob_min_h,
>     glob_display_interval,
>     glob_abserr,
>     glob_relerr,
>     glob_min_pole_est,
>     glob_max_rel_trunc_err,
>     glob_max_trunc_err,
>     glob_max_hours,
>     glob_optimal_clock_start_sec,
>     glob_optimal_start,
>     glob_upper_ratio_limit,
>     glob_lower_ratio_limit,
>     glob_max_sec,
>     glob_orig_start_sec,
>     glob_normmax,
>     glob_max_minutes,
>     glob_next_display,
>     glob_est_digits,
>     glob_subiter_method,
>     glob_html_log,
>     glob_min_good_digits,
>     glob_good_digits,
>     glob_min_apfp_est_good_digits,
>     glob_apfp_est_good_digits,
>     glob_max_opt_iter,
>     glob_dump,
>     glob_djd_debug,
>     glob_display_flag,
>     glob_djd_debug2,
>     glob_h_reason,
>     glob_sec_in_minute,
>     glob_min_in_hour,
>     glob_hours_in_day,
>     glob_days_in_year,
>     glob_sec_in_hour,
>     glob_sec_in_day,
>     glob_sec_in_year,
>     glob_not_yet_finished,
>     glob_initial_pass,
>     glob_not_yet_start_msg,
>     glob_reached_optimal_h,
>     glob_optimal_done,
>     glob_type_given_pole,
>     glob_optimize,
>     glob_look_poles,
>     glob_dump_closed_form,
>     glob_max_iter,
>     glob_no_eqs,
>     glob_unchanged_h_cnt,
>     glob_warned,
>     glob_warned2,
>     glob_start,
>     glob_iter,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_3,
>     array_const_0D0,
>     array_const_1,
>     #END CONST
>     array_y2_init,
>     array_y1_init,
>     array_norms,
>     array_fact_1,
>     array_1st_rel_error,
>     array_last_rel_error,
>     array_est_rel_error,
>     array_max_est_error,
>     array_type_pole,
>     array_type_real_pole,
>     array_type_complex_pole,
>     array_est_digits,
>     array_y2,
>     array_x,
>     array_y1,
>     array_tmp0,
>     array_tmp1_g,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_m1,
>     array_y2_higher,
>     array_y2_higher_work,
>     array_y2_higher_work2,
>     array_y2_set_initial,
>     array_y1_higher,
>     array_y1_higher_work,
>     array_y1_higher_work2,
>     array_y1_set_initial,
>     array_given_rad_poles,
>     array_given_ord_poles,
>     array_rad_test_poles,
>     array_ord_test_poles,
>     array_fact_2,
>     ATS_MAX_TERMS,
>     glob_last;
>     ATS_MAX_TERMS := 40;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=40;
>     #END BLOCK 1
>     #END FIRST INPUT BLOCK
>     #START OF INITS AFTER INPUT BLOCK
>     glob_html_log := true;
>     #END OF INITS AFTER INPUT BLOCK
>     # before generate arrays
>     array_y2_init:= Array(0..(40),[]);
>     array_y1_init:= Array(0..(40),[]);
>     array_norms:= Array(0..(40),[]);
>     array_fact_1:= Array(0..(40),[]);
>     array_1st_rel_error:= Array(0..(3),[]);
>     array_last_rel_error:= Array(0..(3),[]);
>     array_est_rel_error:= Array(0..(3),[]);
>     array_max_est_error:= Array(0..(3),[]);
>     array_type_pole:= Array(0..(3),[]);
>     array_type_real_pole:= Array(0..(3),[]);
>     array_type_complex_pole:= Array(0..(3),[]);
>     array_est_digits:= Array(0..(3),[]);
>     array_y2:= Array(0..(40),[]);
>     array_x:= Array(0..(40),[]);
>     array_y1:= Array(0..(40),[]);
>     array_tmp0:= Array(0..(40),[]);
>     array_tmp1_g:= Array(0..(40),[]);
>     array_tmp1:= Array(0..(40),[]);
>     array_tmp2:= Array(0..(40),[]);
>     array_tmp3:= Array(0..(40),[]);
>     array_tmp4:= Array(0..(40),[]);
>     array_tmp5:= Array(0..(40),[]);
>     array_m1:= Array(0..(40),[]);
>     array_y2_higher := Array(0..(4) ,(0..40+ 1),[]);
>     array_y2_higher_work := Array(0..(4) ,(0..40+ 1),[]);
>     array_y2_higher_work2 := Array(0..(4) ,(0..40+ 1),[]);
>     array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]);
>     array_y1_higher := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
>     array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
>     array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
>     array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
>     array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
>     array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
>     # before generate constants
>     # before generate globals definition
>     #Top Generate Globals Definition
>     #Bottom Generate Globals Deninition
>     # before generate const definition
>     # before arrays initialized
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y2_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y1_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_fact_1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_1st_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_last_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_est_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_max_est_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_real_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_complex_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_est_digits[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1_g[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp5[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_m1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=4) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=4) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=4) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_higher_work2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_set_initial[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher_work2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_set_initial[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_rad_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_ord_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_rad_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_ord_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=40) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y2);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_y1);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1_g);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5);
>     zero_ats_ar(array_m1);
>     zero_ats_ar(array_const_3);
>     array_const_3[1]   := c(3);
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := c(0.0);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := c(1);
>     zero_ats_ar(array_m1);
>     array_m1[1]   := glob__m1;
>     #END SYMBOLS INITIALIZATED
>     # before generate factorials init
>     #Initing Factorial Tables
>     iiif := 0;
>     while (iiif <= ATS_MAX_TERMS) do # do number 1
>         jjjf := 0;
>         while (jjjf <= ATS_MAX_TERMS) do # do number 2
>             array_fact_1[iiif] := 0;
>             array_fact_2[iiif,jjjf] := 0;
>             jjjf := jjjf + 1;
>         od;# end do number 2;
>         iiif := iiif + 1;
>     od;# end do number 1;
>     #Done Initing Factorial Table
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     glob_iolevel := 5;
>     glob_yes_pole := 4;
>     glob_no_pole := 3;
>     glob_not_given := 0;
>     glob_no_sing_tests := 4;
>     glob_ratio_test := 1;
>     glob_three_term_test := 2;
>     glob_six_term_test := 3;
>     glob_log_10 := log(c(10.0));
>     MAX_UNCHANGED := 10;
>     glob__small := c(0.1e-50);
>     glob_small_float := c(0.1e-50);
>     glob_smallish_float := c(0.1e-60);
>     glob_large_float := c(1.0e100);
>     glob_larger_float := c(1.1e100);
>     glob__m2 := c(-2);
>     glob__m1 := c(-1);
>     glob__0 := c(0);
>     glob__1 := c(1);
>     glob__2 := c(2);
>     glob__3 := c(3);
>     glob__4 := c(4);
>     glob__5 := c(5);
>     glob__8 := c(8);
>     glob__10 := c(10);
>     glob__100 := c(100);
>     glob__pi := c(0.0);
>     glob__0_5 := c(0.5);
>     glob__0_8 := c(0.8);
>     glob__m0_8 := c(-0.8);
>     glob__0_25 := c(0.25);
>     glob__0_125 := c(0.125);
>     glob_prec := c(1.0e-16);
>     glob_check_sign := c(1.0);
>     glob_desired_digits_correct := c(8.0);
>     glob_max_estimated_step_error := c(0.0);
>     glob_ratio_of_radius := c(0.1);
>     glob_percent_done := c(0.0);
>     glob_total_exp_sec := c(0.1);
>     glob_optimal_expect_sec := c(0.1);
>     glob_estimated_size_answer := c(100.0);
>     glob_almost_1 := c(0.9990);
>     glob_clock_sec := c(0.0);
>     glob_clock_start_sec := c(0.0);
>     glob_disp_incr := c(0.1);
>     glob_h := c(0.1);
>     glob_diff_rc_fm := c(0.1);
>     glob_diff_rc_fmm1 := c(0.1);
>     glob_diff_rc_fmm2 := c(0.1);
>     glob_diff_ord_fm := c(0.1);
>     glob_diff_ord_fmm1 := c(0.1);
>     glob_diff_ord_fmm2 := c(0.1);
>     glob_six_term_ord_save := c(0.1);
>     glob_guess_error_rc := c(0.1);
>     glob_guess_error_ord := c(0.1);
>     glob_least_given_sing := c(9.9e200);
>     glob_least_ratio_sing := c(9.9e200);
>     glob_least_3_sing := c(9.9e100);
>     glob_least_6_sing := c(9.9e100);
>     glob_last_good_h := c(0.1);
>     glob_max_h := c(0.1);
>     glob_min_h := c(0.000001);
>     glob_display_interval := c(0.1);
>     glob_abserr := c(0.1e-10);
>     glob_relerr := c(0.1e-10);
>     glob_min_pole_est := c(0.1e+10);
>     glob_max_rel_trunc_err := c(0.1e-10);
>     glob_max_trunc_err := c(0.1e-10);
>     glob_max_hours := c(0.0);
>     glob_optimal_clock_start_sec := c(0.0);
>     glob_optimal_start := c(0.0);
>     glob_upper_ratio_limit := c(1.0001);
>     glob_lower_ratio_limit := c(0.9999);
>     glob_max_sec := c(10000.0);
>     glob_orig_start_sec := c(0.0);
>     glob_normmax := c(0.0);
>     glob_max_minutes := c(0.0);
>     glob_next_display := c(0.0);
>     glob_est_digits := 1;
>     glob_subiter_method := 3;
>     glob_html_log := true;
>     glob_min_good_digits := 99999;
>     glob_good_digits := 0;
>     glob_min_apfp_est_good_digits := 99999;
>     glob_apfp_est_good_digits := 0;
>     glob_max_opt_iter := 10;
>     glob_dump := false;
>     glob_djd_debug := true;
>     glob_display_flag := true;
>     glob_djd_debug2 := true;
>     glob_h_reason := 0;
>     glob_sec_in_minute := 60 ;
>     glob_min_in_hour := 60;
>     glob_hours_in_day := 24;
>     glob_days_in_year := 365;
>     glob_sec_in_hour := 3600;
>     glob_sec_in_day := 86400;
>     glob_sec_in_year := 31536000;
>     glob_not_yet_finished := true;
>     glob_initial_pass := true;
>     glob_not_yet_start_msg := true;
>     glob_reached_optimal_h := false;
>     glob_optimal_done := false;
>     glob_type_given_pole := 0;
>     glob_optimize := false;
>     glob_look_poles := false;
>     glob_dump_closed_form := false;
>     glob_max_iter := 1000;
>     glob_no_eqs := 0;
>     glob_unchanged_h_cnt := 0;
>     glob_warned := false;
>     glob_warned2 := false;
>     glob_start := 0;
>     glob_iter := 0;
>     # before generate set diff initial
>     array_y2_set_initial[1,1] := true;
>     array_y2_set_initial[1,2] := true;
>     array_y2_set_initial[1,3] := true;
>     array_y2_set_initial[1,4] := false;
>     array_y2_set_initial[1,5] := false;
>     array_y2_set_initial[1,6] := false;
>     array_y2_set_initial[1,7] := false;
>     array_y2_set_initial[1,8] := false;
>     array_y2_set_initial[1,9] := false;
>     array_y2_set_initial[1,10] := false;
>     array_y2_set_initial[1,11] := false;
>     array_y2_set_initial[1,12] := false;
>     array_y2_set_initial[1,13] := false;
>     array_y2_set_initial[1,14] := false;
>     array_y2_set_initial[1,15] := false;
>     array_y2_set_initial[1,16] := false;
>     array_y2_set_initial[1,17] := false;
>     array_y2_set_initial[1,18] := false;
>     array_y2_set_initial[1,19] := false;
>     array_y2_set_initial[1,20] := false;
>     array_y2_set_initial[1,21] := false;
>     array_y2_set_initial[1,22] := false;
>     array_y2_set_initial[1,23] := false;
>     array_y2_set_initial[1,24] := false;
>     array_y2_set_initial[1,25] := false;
>     array_y2_set_initial[1,26] := false;
>     array_y2_set_initial[1,27] := false;
>     array_y2_set_initial[1,28] := false;
>     array_y2_set_initial[1,29] := false;
>     array_y2_set_initial[1,30] := false;
>     array_y2_set_initial[1,31] := false;
>     array_y2_set_initial[1,32] := false;
>     array_y2_set_initial[1,33] := false;
>     array_y2_set_initial[1,34] := false;
>     array_y2_set_initial[1,35] := false;
>     array_y2_set_initial[1,36] := false;
>     array_y2_set_initial[1,37] := false;
>     array_y2_set_initial[1,38] := false;
>     array_y2_set_initial[1,39] := false;
>     array_y2_set_initial[1,40] := false;
>     array_y1_set_initial[2,1] := true;
>     array_y1_set_initial[2,2] := false;
>     array_y1_set_initial[2,3] := false;
>     array_y1_set_initial[2,4] := false;
>     array_y1_set_initial[2,5] := false;
>     array_y1_set_initial[2,6] := false;
>     array_y1_set_initial[2,7] := false;
>     array_y1_set_initial[2,8] := false;
>     array_y1_set_initial[2,9] := false;
>     array_y1_set_initial[2,10] := false;
>     array_y1_set_initial[2,11] := false;
>     array_y1_set_initial[2,12] := false;
>     array_y1_set_initial[2,13] := false;
>     array_y1_set_initial[2,14] := false;
>     array_y1_set_initial[2,15] := false;
>     array_y1_set_initial[2,16] := false;
>     array_y1_set_initial[2,17] := false;
>     array_y1_set_initial[2,18] := false;
>     array_y1_set_initial[2,19] := false;
>     array_y1_set_initial[2,20] := false;
>     array_y1_set_initial[2,21] := false;
>     array_y1_set_initial[2,22] := false;
>     array_y1_set_initial[2,23] := false;
>     array_y1_set_initial[2,24] := false;
>     array_y1_set_initial[2,25] := false;
>     array_y1_set_initial[2,26] := false;
>     array_y1_set_initial[2,27] := false;
>     array_y1_set_initial[2,28] := false;
>     array_y1_set_initial[2,29] := false;
>     array_y1_set_initial[2,30] := false;
>     array_y1_set_initial[2,31] := false;
>     array_y1_set_initial[2,32] := false;
>     array_y1_set_initial[2,33] := false;
>     array_y1_set_initial[2,34] := false;
>     array_y1_set_initial[2,35] := false;
>     array_y1_set_initial[2,36] := false;
>     array_y1_set_initial[2,37] := false;
>     array_y1_set_initial[2,38] := false;
>     array_y1_set_initial[2,39] := false;
>     array_y1_set_initial[2,40] := false;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 40;
>     glob_iolevel := INFO;
>     # set default block
>     #Write Set Defaults
>     glob_orig_start_sec   :=  elapsed_time_seconds();
>     glob_display_flag   :=   true;
>     glob_no_eqs   := 2;
>     glob_iter   :=  -1;
>     opt_iter   :=  -1;
>     glob_max_iter   :=  50000;
>     glob_max_hours   :=  (0.0);
>     glob_max_minutes   :=  (15.0);
>     omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
>     omniout_str(ALWAYS,"##############temp/mtest4postode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
>     omniout_str(ALWAYS,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=40;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(0.1);");
>     omniout_str(ALWAYS,"x_end := c(5.0);");
>     omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
>     omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
>     omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
>     omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 3;");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
>     omniout_str(ALWAYS,"glob_look_poles:=true;");
>     omniout_str(ALWAYS,"glob_h:=c(0.005);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
>     omniout_str(ALWAYS,"return(sin(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
>     omniout_str(ALWAYS,"return( cos(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
>     omniout_str(ALWAYS,"return( neg( sin(c(x))));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
>     omniout_str(ALWAYS,"return( cos(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(0.1);
>     x_end := c(5.0);
>     array_y1_init[0 + 1] := exact_soln_y1(x_start);
>     array_y2_init[0 + 1] := exact_soln_y2(x_start);
>     array_y2_init[1 + 1] := exact_soln_y2p(x_start);
>     array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
>     glob_look_poles := true;
>     glob_type_given_pole := 3;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=8;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=3;
>     glob_max_iter:=100000;
>     glob_upper_ratio_limit:=c(1.0000001);
>     glob_lower_ratio_limit:=c(0.9999999);
>     glob_look_poles:=true;
>     glob_h:=c(0.005);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(x_start,x_end));
>     glob__pi := arccos(glob__m1);
>     glob_prec = expt(10.0,c(-Digits));
>     if (glob_optimize)  then # if number 17
>         #BEGIN OPTIMIZE CODE
>         omniout_str(ALWAYS,"START of Optimize");
>         #Start Series -- INITIALIZE FOR OPTIMIZE
>         found_h := false;
>         glob_min_pole_est :=  glob_larger_float;
>         last_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         glob_min_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_max_h := float_abs(glob_max_h) * glob_check_sign;
>         glob_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
>         display_max := c(x_end) - c(x_start)/glob__10;
>         if ((glob_display_interval) > (display_max)) then # if number 18
>             glob_display_interval := c(display_max);
>         fi;# end if 18;
>         chk_data();
>         min_value := glob_larger_float;
>         est_answer := est_size_answer();
>         opt_iter := 1;
>         est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>         omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>         estimated_step_error  := glob_small_float;
>         while ((opt_iter <= 100) and ( not found_h)) do # do number 1
>             omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
>             array_x[1]   := c(x_start);
>             array_x[2]   :=  c(glob_h);
>             glob_next_display := c(x_start);
>             order_diff := 3;
>             #Start Series array_y2
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             rows   :=  order_diff;
>             r_order   :=  1;
>             while (r_order <= rows) do # do number 2
>                 term_no   :=  1;
>                 while (term_no <= (rows - r_order + 1)) do # do number 3
>                     it  := term_no + r_order - 1;
>                     if (term_no < ATS_MAX_TERMS) then # if number 18
>                         array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 18;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             order_diff := 1;
>             #Start Series array_y1
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             rows   :=  order_diff;
>             r_order   :=  1;
>             while (r_order <= rows) do # do number 2
>                 term_no   :=  1;
>                 while (term_no <= (rows - r_order + 1)) do # do number 3
>                     it  := term_no + r_order - 1;
>                     if (term_no < ATS_MAX_TERMS) then # if number 18
>                         array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 18;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             if (glob_subiter_method  =  1 ) then # if number 18
>                 atomall();
>             elif
>             (glob_subiter_method  =  2 ) then # if number 19
>                 subiter := 1;
>                 while (subiter <= 4) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 4 + ATS_MAX_TERMS) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             fi;# end if 19;
>             if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19
>                 omniout_str(ALWAYS,"SETTING H FOR MIN H");
>                 glob_h := glob_check_sign * float_abs(glob_min_h);
>                 glob_h_reason := 1;
>                 found_h := true;
>             fi;# end if 19;
>             if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19
>                 omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>                 glob_h_reason := 2;
>                 glob_h := glob_display_interval;
>                 found_h := true;
>             fi;# end if 19;
>             if (glob_look_poles)  then # if number 19
>                 check_for_pole();
>             fi;# end if 19;
>             if ( not found_h) then # if number 19
>                 est_answer := est_size_answer();
>                 est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>                 omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>                 estimated_step_error := test_suggested_h();
>                 omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
>                 if (estimated_step_error < est_needed_step_err) then # if number 20
>                     omniout_str(ALWAYS,"Double H and LOOP");
>                     glob_h := glob_h*glob__2;
>                 else
>                     omniout_str(ALWAYS,"Found H for OPTIMAL");
>                     found_h := true;
>                     glob_h_reason := 3;
>                     glob_h := glob_h/glob__2;
>                 fi;# end if 20;
>             fi;# end if 19;
>             opt_iter := opt_iter + 1;
>         od;# end do number 1;
>         if (( not found_h) and (opt_iter = 1)) then # if number 19
>             omniout_str(ALWAYS,"Beginning glob_h too large.");
>             found_h := false;
>         fi;# end if 19;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19
>             omniout_str(ALWAYS,"SETTING H FOR MAX H");
>             glob_h := glob_check_sign * float_abs(glob_max_h);
>             glob_h_reason := 1;
>             found_h := true;
>         fi;# end if 19;
>     else
>         found_h := true;
>         glob_h := glob_h * glob_check_sign;
>     fi;# end if 18;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 18
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 18;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 18
>         omniout_str(ALWAYS,"START of Soultion");
>         #Start Series -- INITIALIZE FOR SOLUTION
>         array_x[1]   := c(x_start);
>         array_x[2]   :=  c(glob_h);
>         glob_next_display := c(x_start);
>         glob_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         order_diff := 3;
>         #Start Series array_y2
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>             term_no   :=  term_no + 1;
>         od;# end do number 1;
>         rows   :=  order_diff;
>         r_order   :=  1;
>         while (r_order <= rows) do # do number 1
>             term_no   :=  1;
>             while (term_no <= (rows - r_order + 1)) do # do number 2
>                 it  := term_no + r_order - 1;
>                 if (term_no < ATS_MAX_TERMS) then # if number 19
>                     array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 19;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         order_diff := 1;
>         #Start Series array_y1
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>             term_no   :=  term_no + 1;
>         od;# end do number 1;
>         rows   :=  order_diff;
>         r_order   :=  1;
>         while (r_order <= rows) do # do number 1
>             term_no   :=  1;
>             while (term_no <= (rows - r_order + 1)) do # do number 2
>                 it  := term_no + r_order - 1;
>                 if (term_no < ATS_MAX_TERMS) then # if number 19
>                     array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 19;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         current_iter   :=  1;
>         glob_clock_start_sec   := elapsed_time_seconds();
>         glob_clock_sec   :=  elapsed_time_seconds();
>         glob_iter   :=  0;
>         omniout_str(DEBUGL," ");
>         glob_reached_optimal_h   :=  true;
>         glob_optimal_clock_start_sec := elapsed_time_seconds();
>         while ((glob_iter < glob_max_iter)  and (glob_check_sign * array_x[1] < glob_check_sign * x_end )  and  (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
>             #left paren 0001C
>             if (reached_interval()) then # if number 19
>                 omniout_str(INFO," ");
>                 omniout_str(INFO,"TOP MAIN SOLVE Loop");
>             fi;# end if 19;
>             glob_iter   :=  glob_iter + 1;
>             glob_clock_sec   := elapsed_time_seconds();
>             track_estimated_error();
>             if (glob_subiter_method  =  1 ) then # if number 19
>                 atomall();
>             elif
>             (glob_subiter_method  =  2 ) then # if number 20
>                 subiter := 1;
>                 while (subiter <= 4) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 4 + ATS_MAX_TERMS) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             fi;# end if 20;
>             track_estimated_error();
>             display_alot(current_iter);
>             if (glob_look_poles)  then # if number 20
>                 check_for_pole();
>             fi;# end if 20;
>             if (reached_interval()) then # if number 20
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 20;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y2;
>             order_diff  := 4;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y2
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 4;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 4;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 3;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 3;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 3;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 3;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 3;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 3;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 4;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 4;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 3;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 3;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #END SUM AND ADJUST EQ =1
>             #END PART 1
>             #START PART 2  MOVE TERMS to REGULAR Array
>             term_no := ATS_MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_y2[term_no] := array_y2_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
>                     ord := ord + 1;
>                 od;# end do number 3;
>                 term_no   :=  term_no - 1;
>             od;# end do number 2;
>             #END PART 2 HEVE MOVED TERMS to REGULAR Array
>             #Jump Series array_y1;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =2
>             #sum_and_adjust array_y1
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #END SUM AND ADJUST EQ =2
>             #END PART 1
>             #START PART 2  MOVE TERMS to REGULAR Array
>             term_no := ATS_MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_y1[term_no] := array_y1_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
>                     ord := ord + 1;
>                 od;# end do number 3;
>                 term_no   :=  term_no - 1;
>             od;# end do number 2;
>             #END PART 2 HEVE MOVED TERMS to REGULAR Array
>             ;
>         od;# end do number 1;#right paren 0001C
>         omniout_str(ALWAYS,"Finished!");
>         if (glob_iter >= glob_max_iter)  then # if number 20
>             omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
>         fi;# end if 20;
>         if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec  )) then # if number 20
>             omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
>         fi;# end if 20;
>         glob_clock_sec   := elapsed_time_seconds();
>         omniout_str(INFO,"diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
>         omniout_str(INFO,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(x_start,x_end);
>         if (glob_html_log)  then # if number 20
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2015-05-02T21:38:04-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"mtest4.ode.txt\">mtest4</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ")
>             ;
>             logitem_float(html_log_file,x_start)
>             ;
>             logitem_float(html_log_file,x_end)
>             ;
>             logitem_float(html_log_file,array_x[1])
>             ;
>             logitem_float(html_log_file,glob_h)
>             ;
>             logitem_h_reason(html_log_file)
>             ;
>             logitem_integer(html_log_file,Digits)
>             ;
>             ;
>             logitem_float(html_log_file,glob_desired_digits_correct)
>             ;
>             if (array_est_digits[1] <> -16) then # if number 21
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             if (glob_min_good_digits <> -16) then # if number 21
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             if (glob_good_digits <> -16) then # if number 21
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_integer(html_log_file,ATS_MAX_TERMS)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 21
>                 logitem_str(html_log_file,"Not Given")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 22
>                 logitem_str(html_log_file,"No Solution")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 23
>                 logitem_str(html_log_file,"Some Pole")
>                 ;
>                 logitem_str(html_log_file,"????")
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 24
>                 logitem_str(html_log_file,"No Pole")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 25
>                 logitem_str(html_log_file,"Real Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 26
>                 logitem_str(html_log_file,"Complex Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             fi;# end if 26;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_ratio_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             if (glob_least_3_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_3_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             if (glob_least_6_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_6_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             logitem_integer(html_log_file,glob_iter)
>             ;
>             logitem_time(html_log_file,(glob_clock_sec))
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 26
>                 logitem_time(html_log_file,(glob_total_exp_sec))
>                 ;
>                 0;
>             else
>                 logitem_str(html_log_file,"Done")
>                 ;
>                 0;
>             fi;# end if 26;
>             log_revs(html_log_file,"<td> 308.maple.seems.ok </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.mtest4.mxt.txt\">mtest4 diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.mtest4.mxt.txt\">mtest4 maple results</a>")
>             ;
>             logitem_str(html_log_file,"OK")
>             ;
>             logend(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logitem_str(html_log_file,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ")
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             ;
>             logditto(html_log_file)
>             ;
>             if (array_est_digits[2] <> -16) then # if number 26
>                 logitem_integer(html_log_file,array_est_digits[2])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             if (glob_min_good_digits <> -16) then # if number 26
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             if (glob_good_digits <> -16) then # if number 26
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logditto(html_log_file)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 26
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 27
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 28
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 29
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 30
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 31
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_3_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_6_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 31
>                 logditto(html_log_file)
>                 ;
>                 0;
>             else
>                 logditto(html_log_file)
>                 ;
>                 0;
>             fi;# end if 31;
>             logditto(html_log_file);
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logend(html_log_file)
>             ;
>             ;
>         fi;# end if 30;
>         if (glob_html_log)  then # if number 30
>             fclose(html_log_file);
>         fi;# end if 30
>         ;
>         ;;
>     fi;# end if 29
>     #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    ATS_MAX_TERMS := 40;
    Digits := 32;
    max_terms := 40;
    glob_html_log := true;
    array_y2_init := Array(0 .. 40, []);
    array_y1_init := Array(0 .. 40, []);
    array_norms := Array(0 .. 40, []);
    array_fact_1 := Array(0 .. 40, []);
    array_1st_rel_error := Array(0 .. 3, []);
    array_last_rel_error := Array(0 .. 3, []);
    array_est_rel_error := Array(0 .. 3, []);
    array_max_est_error := Array(0 .. 3, []);
    array_type_pole := Array(0 .. 3, []);
    array_type_real_pole := Array(0 .. 3, []);
    array_type_complex_pole := Array(0 .. 3, []);
    array_est_digits := Array(0 .. 3, []);
    array_y2 := Array(0 .. 40, []);
    array_x := Array(0 .. 40, []);
    array_y1 := Array(0 .. 40, []);
    array_tmp0 := Array(0 .. 40, []);
    array_tmp1_g := Array(0 .. 40, []);
    array_tmp1 := Array(0 .. 40, []);
    array_tmp2 := Array(0 .. 40, []);
    array_tmp3 := Array(0 .. 40, []);
    array_tmp4 := Array(0 .. 40, []);
    array_tmp5 := Array(0 .. 40, []);
    array_m1 := Array(0 .. 40, []);
    array_y2_higher := Array(0 .. 4, 0 .. 41, []);
    array_y2_higher_work := Array(0 .. 4, 0 .. 41, []);
    array_y2_higher_work2 := Array(0 .. 4, 0 .. 41, []);
    array_y2_set_initial := Array(0 .. 3, 0 .. 41, []);
    array_y1_higher := Array(0 .. 2, 0 .. 41, []);
    array_y1_higher_work := Array(0 .. 2, 0 .. 41, []);
    array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []);
    array_y1_set_initial := Array(0 .. 3, 0 .. 41, []);
    array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
    array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
    array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
    array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
    array_fact_2 := Array(0 .. 40, 0 .. 41, []);
    term := 1;
    while term <= 40 do array_y2_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_y1_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do
        array_last_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
    term := 1;
    while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_y2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_y1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 4 do
        term := 1;
        while term <= 40 do
            array_y2_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 4 do
        term := 1;
        while term <= 40 do
            array_y2_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 4 do
        term := 1;
        while term <= 40 do
            array_y2_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 40 do
            array_y2_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 40 do
            array_y1_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 3 do
            array_given_rad_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 3 do
            array_given_ord_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 4 do
            array_rad_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 4 do
            array_ord_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 40 do
        term := 1;
        while term <= 40 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y2);
    zero_ats_ar(array_x);
    zero_ats_ar(array_y1);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1_g);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5);
    zero_ats_ar(array_m1);
    zero_ats_ar(array_const_3);
    array_const_3[1] := c(3);
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := c(0.);
    zero_ats_ar(array_const_1);
    array_const_1[1] := c(1);
    zero_ats_ar(array_m1);
    array_m1[1] := glob__m1;
    iiif := 0;
    while iiif <= ATS_MAX_TERMS do
        jjjf := 0;
        while jjjf <= ATS_MAX_TERMS do
            array_fact_1[iiif] := 0;
            array_fact_2[iiif, jjjf] := 0;
            jjjf := jjjf + 1
        end do;
        iiif := iiif + 1
    end do;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := 5;
    glob_yes_pole := 4;
    glob_no_pole := 3;
    glob_not_given := 0;
    glob_no_sing_tests := 4;
    glob_ratio_test := 1;
    glob_three_term_test := 2;
    glob_six_term_test := 3;
    glob_log_10 := log(c(10.0));
    MAX_UNCHANGED := 10;
    glob__small := c(0.1*10^(-50));
    glob_small_float := c(0.1*10^(-50));
    glob_smallish_float := c(0.1*10^(-60));
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob__m2 := c(-2);
    glob__m1 := c(-1);
    glob__0 := c(0);
    glob__1 := c(1);
    glob__2 := c(2);
    glob__3 := c(3);
    glob__4 := c(4);
    glob__5 := c(5);
    glob__8 := c(8);
    glob__10 := c(10);
    glob__100 := c(100);
    glob__pi := c(0.);
    glob__0_5 := c(0.5);
    glob__0_8 := c(0.8);
    glob__m0_8 := c(-0.8);
    glob__0_25 := c(0.25);
    glob__0_125 := c(0.125);
    glob_prec := c(0.10*10^(-15));
    glob_check_sign := c(1.0);
    glob_desired_digits_correct := c(8.0);
    glob_max_estimated_step_error := c(0.);
    glob_ratio_of_radius := c(0.1);
    glob_percent_done := c(0.);
    glob_total_exp_sec := c(0.1);
    glob_optimal_expect_sec := c(0.1);
    glob_estimated_size_answer := c(100.0);
    glob_almost_1 := c(0.9990);
    glob_clock_sec := c(0.);
    glob_clock_start_sec := c(0.);
    glob_disp_incr := c(0.1);
    glob_h := c(0.1);
    glob_diff_rc_fm := c(0.1);
    glob_diff_rc_fmm1 := c(0.1);
    glob_diff_rc_fmm2 := c(0.1);
    glob_diff_ord_fm := c(0.1);
    glob_diff_ord_fmm1 := c(0.1);
    glob_diff_ord_fmm2 := c(0.1);
    glob_six_term_ord_save := c(0.1);
    glob_guess_error_rc := c(0.1);
    glob_guess_error_ord := c(0.1);
    glob_least_given_sing := c(0.99*10^201);
    glob_least_ratio_sing := c(0.99*10^201);
    glob_least_3_sing := c(0.99*10^101);
    glob_least_6_sing := c(0.99*10^101);
    glob_last_good_h := c(0.1);
    glob_max_h := c(0.1);
    glob_min_h := c(0.1*10^(-5));
    glob_display_interval := c(0.1);
    glob_abserr := c(0.1*10^(-10));
    glob_relerr := c(0.1*10^(-10));
    glob_min_pole_est := c(0.1*10^10);
    glob_max_rel_trunc_err := c(0.1*10^(-10));
    glob_max_trunc_err := c(0.1*10^(-10));
    glob_max_hours := c(0.);
    glob_optimal_clock_start_sec := c(0.);
    glob_optimal_start := c(0.);
    glob_upper_ratio_limit := c(1.0001);
    glob_lower_ratio_limit := c(0.9999);
    glob_max_sec := c(10000.0);
    glob_orig_start_sec := c(0.);
    glob_normmax := c(0.);
    glob_max_minutes := c(0.);
    glob_next_display := c(0.);
    glob_est_digits := 1;
    glob_subiter_method := 3;
    glob_html_log := true;
    glob_min_good_digits := 99999;
    glob_good_digits := 0;
    glob_min_apfp_est_good_digits := 99999;
    glob_apfp_est_good_digits := 0;
    glob_max_opt_iter := 10;
    glob_dump := false;
    glob_djd_debug := true;
    glob_display_flag := true;
    glob_djd_debug2 := true;
    glob_h_reason := 0;
    glob_sec_in_minute := 60;
    glob_min_in_hour := 60;
    glob_hours_in_day := 24;
    glob_days_in_year := 365;
    glob_sec_in_hour := 3600;
    glob_sec_in_day := 86400;
    glob_sec_in_year := 31536000;
    glob_not_yet_finished := true;
    glob_initial_pass := true;
    glob_not_yet_start_msg := true;
    glob_reached_optimal_h := false;
    glob_optimal_done := false;
    glob_type_given_pole := 0;
    glob_optimize := false;
    glob_look_poles := false;
    glob_dump_closed_form := false;
    glob_max_iter := 1000;
    glob_no_eqs := 0;
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_start := 0;
    glob_iter := 0;
    array_y2_set_initial[1, 1] := true;
    array_y2_set_initial[1, 2] := true;
    array_y2_set_initial[1, 3] := true;
    array_y2_set_initial[1, 4] := false;
    array_y2_set_initial[1, 5] := false;
    array_y2_set_initial[1, 6] := false;
    array_y2_set_initial[1, 7] := false;
    array_y2_set_initial[1, 8] := false;
    array_y2_set_initial[1, 9] := false;
    array_y2_set_initial[1, 10] := false;
    array_y2_set_initial[1, 11] := false;
    array_y2_set_initial[1, 12] := false;
    array_y2_set_initial[1, 13] := false;
    array_y2_set_initial[1, 14] := false;
    array_y2_set_initial[1, 15] := false;
    array_y2_set_initial[1, 16] := false;
    array_y2_set_initial[1, 17] := false;
    array_y2_set_initial[1, 18] := false;
    array_y2_set_initial[1, 19] := false;
    array_y2_set_initial[1, 20] := false;
    array_y2_set_initial[1, 21] := false;
    array_y2_set_initial[1, 22] := false;
    array_y2_set_initial[1, 23] := false;
    array_y2_set_initial[1, 24] := false;
    array_y2_set_initial[1, 25] := false;
    array_y2_set_initial[1, 26] := false;
    array_y2_set_initial[1, 27] := false;
    array_y2_set_initial[1, 28] := false;
    array_y2_set_initial[1, 29] := false;
    array_y2_set_initial[1, 30] := false;
    array_y2_set_initial[1, 31] := false;
    array_y2_set_initial[1, 32] := false;
    array_y2_set_initial[1, 33] := false;
    array_y2_set_initial[1, 34] := false;
    array_y2_set_initial[1, 35] := false;
    array_y2_set_initial[1, 36] := false;
    array_y2_set_initial[1, 37] := false;
    array_y2_set_initial[1, 38] := false;
    array_y2_set_initial[1, 39] := false;
    array_y2_set_initial[1, 40] := false;
    array_y1_set_initial[2, 1] := true;
    array_y1_set_initial[2, 2] := false;
    array_y1_set_initial[2, 3] := false;
    array_y1_set_initial[2, 4] := false;
    array_y1_set_initial[2, 5] := false;
    array_y1_set_initial[2, 6] := false;
    array_y1_set_initial[2, 7] := false;
    array_y1_set_initial[2, 8] := false;
    array_y1_set_initial[2, 9] := false;
    array_y1_set_initial[2, 10] := false;
    array_y1_set_initial[2, 11] := false;
    array_y1_set_initial[2, 12] := false;
    array_y1_set_initial[2, 13] := false;
    array_y1_set_initial[2, 14] := false;
    array_y1_set_initial[2, 15] := false;
    array_y1_set_initial[2, 16] := false;
    array_y1_set_initial[2, 17] := false;
    array_y1_set_initial[2, 18] := false;
    array_y1_set_initial[2, 19] := false;
    array_y1_set_initial[2, 20] := false;
    array_y1_set_initial[2, 21] := false;
    array_y1_set_initial[2, 22] := false;
    array_y1_set_initial[2, 23] := false;
    array_y1_set_initial[2, 24] := false;
    array_y1_set_initial[2, 25] := false;
    array_y1_set_initial[2, 26] := false;
    array_y1_set_initial[2, 27] := false;
    array_y1_set_initial[2, 28] := false;
    array_y1_set_initial[2, 29] := false;
    array_y1_set_initial[2, 30] := false;
    array_y1_set_initial[2, 31] := false;
    array_y1_set_initial[2, 32] := false;
    array_y1_set_initial[2, 33] := false;
    array_y1_set_initial[2, 34] := false;
    array_y1_set_initial[2, 35] := false;
    array_y1_set_initial[2, 36] := false;
    array_y1_set_initial[2, 37] := false;
    array_y1_set_initial[2, 38] := false;
    array_y1_set_initial[2, 39] := false;
    array_y1_set_initial[2, 40] := false;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 40;
    glob_iolevel := INFO;
    glob_orig_start_sec := elapsed_time_seconds();
    glob_display_flag := true;
    glob_no_eqs := 2;
    glob_iter := -1;
    opt_iter := -1;
    glob_max_iter := 50000;
    glob_max_hours := 0.;
    glob_max_minutes := 15.0;
    omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
    omniout_str(ALWAYS,
        "##############temp/mtest4postode.ode#################");
    omniout_str(ALWAYS,
        "diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
    omniout_str(ALWAYS, "diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ")
        ;
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=40;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(0.1);");
    omniout_str(ALWAYS, "x_end := c(5.0);");
    omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
    omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
    omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
        ;
    omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
        ;
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 3;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
    omniout_str(ALWAYS, "glob_look_poles:=true;");
    omniout_str(ALWAYS, "glob_h:=c(0.005);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
    omniout_str(ALWAYS, "return(sin(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
    omniout_str(ALWAYS, "return( cos(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
    omniout_str(ALWAYS, "return( neg( sin(c(x))));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
    omniout_str(ALWAYS, "return( cos(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(0.1);
    x_end := c(5.0);
    array_y1_init[1] := exact_soln_y1(x_start);
    array_y2_init[1] := exact_soln_y2(x_start);
    array_y2_init[2] := exact_soln_y2p(x_start);
    array_y2_init[3] := exact_soln_y2pp(x_start);
    glob_look_poles := true;
    glob_type_given_pole := 3;
    glob_desired_digits_correct := 8;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000;
    glob_upper_ratio_limit := c(1.0000001);
    glob_lower_ratio_limit := c(0.9999999);
    glob_look_poles := true;
    glob_h := c(0.005);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(x_start, x_end));
    glob__pi := arccos(glob__m1);
    glob_prec = expt(10.0, c(-Digits));
    if glob_optimize then
        omniout_str(ALWAYS, "START of Optimize");
        found_h := false;
        glob_min_pole_est := glob_larger_float;
        last_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        glob_min_h := float_abs(glob_min_h)*glob_check_sign;
        glob_max_h := float_abs(glob_max_h)*glob_check_sign;
        glob_h := float_abs(glob_min_h)*glob_check_sign;
        glob_display_interval :=
            c(float_abs(c(glob_display_interval))*glob_check_sign);
        display_max := c(x_end) - c(x_start)/glob__10;
        if display_max < glob_display_interval then
            glob_display_interval := c(display_max)
        end if;
        chk_data();
        min_value := glob_larger_float;
        est_answer := est_size_answer();
        opt_iter := 1;
        est_needed_step_err :=
            estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
            ;
        omniout_float(ALWAYS, "est_needed_step_err", 32,
            est_needed_step_err, 16, "");
        estimated_step_error := glob_small_float;
        while opt_iter <= 100 and not found_h do
            omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
            array_x[1] := c(x_start);
            array_x[2] := c(glob_h);
            glob_next_display := c(x_start);
            order_diff := 3;
            term_no := 1;
            while term_no <= order_diff do
                array_y2[term_no] := array_y2_init[term_no]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1));
                term_no := term_no + 1
            end do;
            rows := order_diff;
            r_order := 1;
            while r_order <= rows do
                term_no := 1;
                while term_no <= rows - r_order + 1 do
                    it := term_no + r_order - 1;
                    if term_no < ATS_MAX_TERMS then
                        array_y2_higher[r_order, term_no] :=
                        array_y2_init[it]*expt(glob_h, c(term_no - 1))/
                        c(factorial_1(term_no - 1))
                    end if;
                    term_no := term_no + 1
                end do;
                r_order := r_order + 1
            end do;
            order_diff := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y1[term_no] := array_y1_init[term_no]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1));
                term_no := term_no + 1
            end do;
            rows := order_diff;
            r_order := 1;
            while r_order <= rows do
                term_no := 1;
                while term_no <= rows - r_order + 1 do
                    it := term_no + r_order - 1;
                    if term_no < ATS_MAX_TERMS then
                        array_y1_higher[r_order, term_no] :=
                        array_y1_init[it]*expt(glob_h, c(term_no - 1))/
                        c(factorial_1(term_no - 1))
                    end if;
                    term_no := term_no + 1
                end do;
                r_order := r_order + 1
            end do;
            if glob_subiter_method = 1 then atomall()
            elif glob_subiter_method = 2 then
                subiter := 1;
                while subiter <= 4 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 4 + ATS_MAX_TERMS do
                    atomall(); subiter := subiter + 1
                end do
            end if;
            if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
                omniout_str(ALWAYS, "SETTING H FOR MIN H");
                glob_h := float_abs(glob_min_h)*glob_check_sign;
                glob_h_reason := 1;
                found_h := true
            end if;
            if
            glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
            then
                omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
                glob_h_reason := 2;
                glob_h := glob_display_interval;
                found_h := true
            end if;
            if glob_look_poles then check_for_pole() end if;
            if not found_h then
                est_answer := est_size_answer();
                est_needed_step_err := estimated_needed_step_error(x_start,
                    x_end, glob_h, est_answer);
                omniout_float(ALWAYS, "est_needed_step_err", 32,
                    est_needed_step_err, 16, "");
                estimated_step_error := test_suggested_h();
                omniout_float(ALWAYS, "estimated_step_error", 32,
                    estimated_step_error, 32, "");
                if estimated_step_error < est_needed_step_err then
                    omniout_str(ALWAYS, "Double H and LOOP");
                    glob_h := glob_h*glob__2
                else
                    omniout_str(ALWAYS, "Found H for OPTIMAL");
                    found_h := true;
                    glob_h_reason := 3;
                    glob_h := glob_h/glob__2
                end if
            end if;
            opt_iter := opt_iter + 1
        end do;
        if not found_h and opt_iter = 1 then
            omniout_str(ALWAYS, "Beginning glob_h too large.");
            found_h := false
        end if;
        if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
            omniout_str(ALWAYS, "SETTING H FOR MAX H");
            glob_h := float_abs(glob_max_h)*glob_check_sign;
            glob_h_reason := 1;
            found_h := true
        end if
    else found_h := true; glob_h := glob_check_sign*glob_h
    end if;
    if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
    end if;
    if found_h then
        omniout_str(ALWAYS, "START of Soultion");
        array_x[1] := c(x_start);
        array_x[2] := c(glob_h);
        glob_next_display := c(x_start);
        glob_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        order_diff := 3;
        term_no := 1;
        while term_no <= order_diff do
            array_y2[term_no] := array_y2_init[term_no]*
                expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
            term_no := term_no + 1
        end do;
        rows := order_diff;
        r_order := 1;
        while r_order <= rows do
            term_no := 1;
            while term_no <= rows - r_order + 1 do
                it := term_no + r_order - 1;
                if term_no < ATS_MAX_TERMS then
                    array_y2_higher[r_order, term_no] := array_y2_init[it]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1))
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y1[term_no] := array_y1_init[term_no]*
                expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
            term_no := term_no + 1
        end do;
        rows := order_diff;
        r_order := 1;
        while r_order <= rows do
            term_no := 1;
            while term_no <= rows - r_order + 1 do
                it := term_no + r_order - 1;
                if term_no < ATS_MAX_TERMS then
                    array_y1_higher[r_order, term_no] := array_y1_init[it]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1))
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        current_iter := 1;
        glob_clock_start_sec := elapsed_time_seconds();
        glob_clock_sec := elapsed_time_seconds();
        glob_iter := 0;
        omniout_str(DEBUGL, " ");
        glob_reached_optimal_h := true;
        glob_optimal_clock_start_sec := elapsed_time_seconds();
        while glob_iter < glob_max_iter and
        glob_check_sign*array_x[1] < glob_check_sign*x_end and
        glob_clock_sec - glob_orig_start_sec < glob_max_sec do
            if reached_interval() then
                omniout_str(INFO, " ");
                omniout_str(INFO, "TOP MAIN SOLVE Loop")
            end if;
            glob_iter := glob_iter + 1;
            glob_clock_sec := elapsed_time_seconds();
            track_estimated_error();
            if glob_subiter_method = 1 then atomall()
            elif glob_subiter_method = 2 then
                subiter := 1;
                while subiter <= 4 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 4 + ATS_MAX_TERMS do
                    atomall(); subiter := subiter + 1
                end do
            end if;
            track_estimated_error();
            display_alot(current_iter);
            if glob_look_poles then check_for_pole() end if;
            if reached_interval() then glob_next_display :=
                glob_next_display + glob_display_interval
            end if;
            array_x[1] := array_x[1] + glob_h;
            array_x[2] := glob_h;
            order_diff := 4;
            ord := 4;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 4;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 3;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 3;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 3;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 3;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 4;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 4;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            term_no := ATS_MAX_TERMS;
            while 1 <= term_no do
                array_y2[term_no] := array_y2_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y2_higher[ord, term_no] :=
                        array_y2_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            term_no := ATS_MAX_TERMS;
            while 1 <= term_no do
                array_y1[term_no] := array_y1_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y1_higher[ord, term_no] :=
                        array_y1_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do
        end do;
        omniout_str(ALWAYS, "Finished!");
        if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
            "Maximum Iterations Reached before Solution Completed!")
        end if;
        if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
        then omniout_str(ALWAYS,
            "Maximum Time Reached before Solution Completed!")
        end if;
        glob_clock_sec := elapsed_time_seconds();
        omniout_str(INFO,
            "diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
        omniout_str(INFO,
            "diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
        omniout_int(INFO, "Iterations                      ", 32, glob_iter,
            4, " ");
        prog_report(x_start, x_end);
        if glob_html_log then
            logstart(html_log_file);
            logitem_str(html_log_file, "2015-05-02T21:38:04-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"mtest4.ode.txt\">mtest4</a>");
            logitem_str(html_log_file, "diff  (  y2  ,  x  ,  3  )   =  n\
                eg (  cos  (  x  )   )  ; ");
            logitem_float(html_log_file, x_start);
            logitem_float(html_log_file, x_end);
            logitem_float(html_log_file, array_x[1]);
            logitem_float(html_log_file, glob_h);
            logitem_h_reason(html_log_file);
            logitem_integer(html_log_file, Digits);
            logitem_float(html_log_file, glob_desired_digits_correct);
            if array_est_digits[1] <> -16 then
                logitem_integer(html_log_file, array_est_digits[1])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_min_good_digits <> -16 then
                logitem_integer(html_log_file, glob_min_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_good_digits <> -16 then
                logitem_integer(html_log_file, glob_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            logitem_integer(html_log_file, ATS_MAX_TERMS);
            if glob_type_given_pole = 0 then
                logitem_str(html_log_file, "Not Given");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 4 then
                logitem_str(html_log_file, "No Solution");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 5 then
                logitem_str(html_log_file, "Some Pole");
                logitem_str(html_log_file, "????")
            elif glob_type_given_pole = 3 then
                logitem_str(html_log_file, "No Pole");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 1 then
                logitem_str(html_log_file, "Real Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            elif glob_type_given_pole = 2 then
                logitem_str(html_log_file, "Complex Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_ratio_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_3_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_3_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_6_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_6_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            logitem_integer(html_log_file, glob_iter);
            logitem_time(html_log_file, glob_clock_sec);
            if c(glob_percent_done) < glob__100 then
                logitem_time(html_log_file, glob_total_exp_sec); 0
            else logitem_str(html_log_file, "Done"); 0
            end if;
            log_revs(html_log_file, "<td> 308.maple.seems.ok </td>");
            logitem_str(html_log_file,
                "<a href=\"diffeq.mtest4.mxt.txt\">mtest4 diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.mtest4.mxt.txt\\
                ">mtest4 maple results</a>");
            logitem_str(html_log_file, "OK");
            logend(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logitem_str(html_log_file,
                "diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            if array_est_digits[2] <> -16 then
                logitem_integer(html_log_file, array_est_digits[2])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_min_good_digits <> -16 then
                logitem_integer(html_log_file, glob_min_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_good_digits <> -16 then
                logitem_integer(html_log_file, glob_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            logditto(html_log_file);
            if glob_type_given_pole = 0 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 4 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 5 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 3 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 1 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 2 then
                logditto(html_log_file); logditto(html_log_file)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            if glob_least_3_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            if glob_least_6_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            logditto(html_log_file);
            logditto(html_log_file);
            if c(glob_percent_done) < glob__100 then
                logditto(html_log_file); 0
            else logditto(html_log_file); 0
            end if;
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logend(html_log_file)
        end if;
        if glob_html_log then fclose(html_log_file) end if
    end if
end proc

# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest4postode.ode#################
diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; 
diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0);
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
glob_look_poles := true;







glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.005);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y2 := proc(x)
return(sin(c(x)));
end;
exact_soln_y2p := proc(x)
return( cos(c(x)));
end;
exact_soln_y2pp := proc(x)
return( neg( sin(c(x))));
end;
exact_soln_y1 := proc(x)
return( cos(c(x)));
end;

#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0.1                                          
y2[1] (closed_form)               = 0.099833416646828152306814198410622          
y2[1] (numeric)                   = 0.099833416646828152306814198410622          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.99500416527802576609556198780387           
y1[1] (numeric)                   = 0.99500416527802576609556198780387           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.09933                                      
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.09933                                      
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.11                                         
y2[1] (closed_form)               = 0.10977830083717480866494949008345           
y2[1] (numeric)                   = 0.10977830083717480866494949008345           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.99395609795669685035783961141985           
y1[1] (numeric)                   = 0.99395609795669685035783961141985           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1091                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1091                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=42.2MB, alloc=40.3MB, time=0.50
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y2[1] (closed_form)               = 0.11971220728891935996735061427097           
y2[1] (numeric)                   = 0.11971220728891935996735061427096           
absolute error                    = 1e-32                                        
relative error                    = 8.3533669844258284979015712551952e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.99280863585386625224809816785763           
y1[1] (numeric)                   = 0.99280863585386625224809816785763           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1189                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1189                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=83.1MB, alloc=40.3MB, time=0.95
x[1]                              = 0.13                                         
y2[1] (closed_form)               = 0.12963414261969485954120581070831           
y2[1] (numeric)                   = 0.1296341426196948595412058107083            
absolute error                    = 1e-32                                        
relative error                    = 7.7140171546756812170269282105596e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.99156189371478803959451217115181           
y1[1] (numeric)                   = 0.99156189371478803959451217115181           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1285                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1285                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y2[1] (closed_form)               = 0.13954311464423648171798835170537           
y2[1] (numeric)                   = 0.13954311464423648171798835170536           
absolute error                    = 1e-32                                        
relative error                    = 7.1662439422359760118370861820459e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.9902159962126371718989482270114            
y1[1] (numeric)                   = 0.99021599621263717189894822701139           
absolute error                    = 1e-32                                        
relative error                    = 1.0098806763623134088645046107846e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1382                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1382                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=124.0MB, alloc=40.3MB, time=1.39
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y2[1] (closed_form)               = 0.14943813247359922149772543868764           
y2[1] (numeric)                   = 0.14943813247359922149772543868763           
absolute error                    = 1e-32                                        
relative error                    = 6.6917324477182351442239330191831e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.98877107793604228673498099865434           
y1[1] (numeric)                   = 0.98877107793604228673498099865433           
absolute error                    = 1e-32                                        
relative error                    = 1.0113564426736640909001707623026e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1478                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1478                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.16                                         
y2[1] (closed_form)               = 0.15931820661424596331146315968599           
y2[1] (numeric)                   = 0.15931820661424596331146315968598           
absolute error                    = 1e-32                                        
relative error                    = 6.2767465266620801847879838388932e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.98722728337562694904095252401834           
y1[1] (numeric)                   = 0.98722728337562694904095252401833           
absolute error                    = 1e-32                                        
relative error                    = 1.0129379696443348809827832796951e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1573                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1573                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=165.0MB, alloc=40.3MB, time=1.81
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y2[1] (closed_form)               = 0.16918234906699601015762437667085           
y2[1] (numeric)                   = 0.16918234906699601015762437667084           
absolute error                    = 1e-32                                        
relative error                    = 5.9107820970378013996445405978410e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.9855847669095607091719299902125            
y1[1] (numeric)                   = 0.98558476690956070917192999021249           
absolute error                    = 1e-32                                        
relative error                    = 1.0146260713176810517259565757587e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1667                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1667                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=40.3MB, time=2.25
x[1]                              = 0.18                                         
y2[1] (closed_form)               = 0.17902957342582417834180273969921           
y2[1] (numeric)                   = 0.17902957342582417834180273969919           
absolute error                    = 2e-32                                        
relative error                    = 1.1171338688513622729724627056286e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.98384369278812141459271602461153           
y1[1] (numeric)                   = 0.98384369278812141459271602461152           
absolute error                    = 1e-32                                        
relative error                    = 1.0164216199486862747130581631310e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1761                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1761                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y2[1] (closed_form)               = 0.18885889497650057799285115298131           
y2[1] (numeric)                   = 0.18885889497650057799285115298129           
absolute error                    = 2e-32                                        
relative error                    = 1.0589916880795352137385106331563e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.98200423511727031896787750418991           
y1[1] (numeric)                   = 0.9820042351172703189678775041899            
absolute error                    = 1e-32                                        
relative error                    = 1.0183255471200494754242006144117e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1855                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1855                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=246.8MB, alloc=40.3MB, time=2.70
x[1]                              = 0.2                                          
y2[1] (closed_form)               = 0.19866933079506121545941262711839           
y2[1] (numeric)                   = 0.19866933079506121545941262711837           
absolute error                    = 2e-32                                        
relative error                    = 1.0066979095344688404852192735052e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.98006657784124163112419651674817           
y1[1] (numeric)                   = 0.98006657784124163112419651674815           
absolute error                    = 2e-32                                        
relative error                    = 2.0406776898823853795848655536984e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1947                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1947                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y2[1] (closed_form)               = 0.20845989984609957060871242622764           
y2[1] (numeric)                   = 0.20845989984609957060871242622762           
absolute error                    = 2e-32                                        
relative error                    = 9.5941713561051650286610360041111e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.97803091472414824491613856809935           
y1[1] (numeric)                   = 0.97803091472414824491613856809933           
absolute error                    = 2e-32                                        
relative error                    = 2.0449251346662147048928172331590e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2039                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2039                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=287.8MB, alloc=40.3MB, time=3.13
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y2[1] (closed_form)               = 0.21822962308086931995179100545701           
y2[1] (numeric)                   = 0.21822962308086931995179100545699           
absolute error                    = 2e-32                                        
relative error                    = 9.1646586369205260847741515811431e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.9758974493306054894060229810447            
y1[1] (numeric)                   = 0.97589744933060548940602298104468           
absolute error                    = 2e-32                                        
relative error                    = 2.0493956628043799138079078336661e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.213                                        
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.213                                        
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y2[1] (closed_form)               = 0.22797752353518839540461721236007           
y2[1] (numeric)                   = 0.22797752353518839540461721236005           
absolute error                    = 2e-32                                        
relative error                    = 8.7727946553086380590737800475623e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.9736663950053748369677306480716            
y1[1] (numeric)                   = 0.97366639500537483696773064807158           
absolute error                    = 2e-32                                        
relative error                    = 2.0540916378129283103479982790132e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.222                                        
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.222                                        
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=328.8MB, alloc=40.3MB, time=3.56
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y2[1] (closed_form)               = 0.23770262642713458836079208448982           
y2[1] (numeric)                   = 0.23770262642713458836079208448979           
absolute error                    = 3e-32                                        
relative error                    = 1.2620811326708754783327609528026e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.97133797485202960492617524696338           
y1[1] (numeric)                   = 0.97133797485202960492617524696336           
absolute error                    = 2e-32                                        
relative error                    = 2.0590155556356924532169806326108e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2309                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2309                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=369.6MB, alloc=40.3MB, time=4.00
x[1]                              = 0.25                                         
y2[1] (closed_form)               = 0.24740395925452292959684870484939           
y2[1] (numeric)                   = 0.24740395925452292959684870484937           
absolute error                    = 2e-32                                        
relative error                    = 8.0839450024421421456663986661157e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.96891242171064478414459544949419           
y1[1] (numeric)                   = 0.96891242171064478414459544949417           
absolute error                    = 2e-32                                        
relative error                    = 2.0641700479687712887968986959752e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2397                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2397                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y2[1] (closed_form)               = 0.25708055189215509735338846436522           
y2[1] (numeric)                   = 0.2570805518921550973533884643652            
absolute error                    = 2e-32                                        
relative error                    = 7.7796627760430395166796951595015e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.96638997813451322555821764645006           
y1[1] (numeric)                   = 0.96638997813451322555821764645004           
absolute error                    = 2e-32                                        
relative error                    = 2.0695578857934069896806022235888e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2484                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2484                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=410.5MB, alloc=40.3MB, time=4.44
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y2[1] (closed_form)               = 0.26673143668883112873228652102054           
y2[1] (numeric)                   = 0.26673143668883112873228652102052           
absolute error                    = 2e-32                                        
relative error                    = 7.4981787854770183285159541145525e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.9637708963658905130162327094922            
y1[1] (numeric)                   = 0.96377089636589051301623270949218           
absolute error                    = 2e-32                                        
relative error                    = 2.0751819831263203029860610091120e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2571                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2571                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y2[1] (closed_form)               = 0.27635564856411373331966955845785           
y2[1] (numeric)                   = 0.27635564856411373331966955845783           
absolute error                    = 2e-32                                        
relative error                    = 7.2370512793625986778199431345201e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.96105543831077094792459005359648           
y1[1] (numeric)                   = 0.96105543831077094792459005359645           
absolute error                    = 3e-32                                        
relative error                    = 3.1215681014958341269871433717793e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2656                                       
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2656                                       
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=451.4MB, alloc=40.3MB, time=4.88
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y2[1] (closed_form)               = 0.28595222510483553268394020550437           
y2[1] (numeric)                   = 0.28595222510483553268394020550435           
absolute error                    = 2e-32                                        
relative error                    = 6.9941753356413362511977804562376e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.95824387551269716807012477793186           
y1[1] (numeric)                   = 0.95824387551269716807012477793183           
absolute error                    = 3e-32                                        
relative error                    = 3.1307270274958815875575117459817e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.274                                        
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.274                                        
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=492.4MB, alloc=40.3MB, time=5.31
x[1]                              = 0.3                                          
y2[1] (closed_form)               = 0.29552020666133957510532074568503           
y2[1] (numeric)                   = 0.29552020666133957510532074568501           
absolute error                    = 2e-32                                        
relative error                    = 6.7677267236482451699209531029548e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.95533648912560601964231022756805           
y1[1] (numeric)                   = 0.95533648912560601964231022756802           
absolute error                    = 3e-32                                        
relative error                    = 3.1402548046142568027983725367611e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2823                                       
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2823                                       
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y2[1] (closed_form)               = 0.30505863644344350156564332395896           
y2[1] (numeric)                   = 0.30505863644344350156564332395894           
absolute error                    = 2e-32                                        
relative error                    = 6.5561166315997449231716170028411e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.95233356988571339784280543620221           
y1[1] (numeric)                   = 0.95233356988571339784280543620218           
absolute error                    = 3e-32                                        
relative error                    = 3.1501567254003454991181714712254e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2905                                       
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2905                                       
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=533.4MB, alloc=40.3MB, time=5.75
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y2[1] (closed_form)               = 0.31456656061611776666175754341715           
y2[1] (numeric)                   = 0.31456656061611776666175754341713           
absolute error                    = 2e-32                                        
relative error                    = 6.3579548826892185779101948190767e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.94923541808244086757530727376609           
y1[1] (numeric)                   = 0.94923541808244086757530727376607           
absolute error                    = 2e-32                                        
relative error                    = 2.1069588870168985639438319667824e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2986                                       
Order of pole (three term test)                    = 32.9                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2986                                       
Order of pole (three term test)                    = 32.1                                         
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y2[1] (closed_form)               = 0.32404302839486834670019569617022           
y2[1] (numeric)                   = 0.3240430283948683467001956961702            
absolute error                    = 2e-32                                        
relative error                    = 6.1720198391766192553401291655113e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.94604234352838697152941057836621           
y1[1] (numeric)                   = 0.94604234352838697152941057836619           
absolute error                    = 2e-32                                        
relative error                    = 2.1140702778067438027024493873384e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3066                                       
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3066                                       
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=574.4MB, alloc=40.3MB, time=6.19
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y2[1] (closed_form)               = 0.33348709214081439678177148703079           
y2[1] (numeric)                   = 0.33348709214081439678177148703077           
absolute error                    = 2e-32                                        
relative error                    = 5.9972336175323486457095648899769e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.94275466552834622850264406002658           
y1[1] (numeric)                   = 0.94275466552834622850264406002656           
absolute error                    = 2e-32                                        
relative error                    = 2.1214426967371662405875655244569e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3144                                       
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3144                                       
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=615.3MB, alloc=40.3MB, time=6.62
x[1]                              = 0.35                                         
y2[1] (closed_form)               = 0.34289780745545134918963490691763           
y2[1] (numeric)                   = 0.34289780745545134918963490691762           
absolute error                    = 1e-32                                        
relative error                    = 2.9163207762123651254623362878160e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.93937271284737892003503235730367           
y1[1] (numeric)                   = 0.93937271284737892003503235730365           
absolute error                    = 2e-32                                        
relative error                    = 2.1290803667669901168485265931351e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3221                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3221                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y2[1] (closed_form)               = 0.35227423327508997684991343592073           
y2[1] (numeric)                   = 0.35227423327508997684991343592072           
absolute error                    = 1e-32                                        
relative error                    = 2.8386975416936122006164386118430e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.93589682367793485835091236812474           
y1[1] (numeric)                   = 0.93589682367793485835091236812472           
absolute error                    = 2e-32                                        
relative error                    = 2.1369876992853746943292352547215e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3297                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3297                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=656.3MB, alloc=40.3MB, time=7.06
x[1]                              = 0.37                                         
y2[1] (closed_form)               = 0.36161543196496197803729246912715           
y2[1] (numeric)                   = 0.36161543196496197803729246912714           
absolute error                    = 1e-32                                        
relative error                    = 2.7653687083157807533417226558039e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.93232734560603442320381290449088           
y1[1] (numeric)                   = 0.93232734560603442320381290449085           
absolute error                    = 3e-32                                        
relative error                    = 3.2177539510545304667223695003417e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3371                                       
Order of pole (three term test)                    = 32.87                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3371                                       
Order of pole (three term test)                    = 32.13                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y2[1] (closed_form)               = 0.3709204694129826718454854663492            
y2[1] (numeric)                   = 0.37092046941298267184548546634919           
absolute error                    = 1e-32                                        
relative error                    = 2.6959957253979436816714191021694e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.92866463557651024949253080772456           
y1[1] (numeric)                   = 0.92866463557651024949253080772453           
absolute error                    = 3e-32                                        
relative error                    = 3.2304449691223736164771359091780e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3445                                       
Order of pole (three term test)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3445                                       
Order of pole (three term test)                    = 32.14                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=697.3MB, alloc=40.3MB, time=7.50
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y2[1] (closed_form)               = 0.38018841512316142823118209784716           
y2[1] (numeric)                   = 0.38018841512316142823118209784715           
absolute error                    = 1e-32                                        
relative error                    = 2.6302747801403985480132266333003e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.9249090598573130414506767528811            
y1[1] (numeric)                   = 0.92490905985731304145067675288107           
absolute error                    = 3e-32                                        
relative error                    = 3.2435621297328561309123155040867e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3516                                       
Order of pole (three term test)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3516                                       
Order of pole (three term test)                    = 32.14                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y2[1] (closed_form)               = 0.38941834230865049166631175679571           
y2[1] (numeric)                   = 0.38941834230865049166631175679569           
absolute error                    = 2e-32                                        
relative error                    = 5.1358649110955661406893745933922e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.9210609940028850827985267320518            
y1[1] (numeric)                   = 0.92106099400288508279852673205177           
absolute error                    = 3e-32                                        
relative error                    = 3.2571132851497161093417898654763e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3587                                       
Order of pole (three term test)                    = 32.85                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3587                                       
Order of pole (three term test)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=738.4MB, alloc=40.3MB, time=7.94
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y2[1] (closed_form)               = 0.39860932798442289359379764005114           
y2[1] (numeric)                   = 0.39860932798442289359379764005113           
absolute error                    = 1e-32                                        
relative error                    = 2.5087220237833436499711227821204e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.91712082281660510547564205827702           
y1[1] (numeric)                   = 0.91712082281660510547564205827699           
absolute error                    = 3e-32                                        
relative error                    = 3.2711066256096818058852601338495e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3656                                       
Order of pole (three term test)                    = 32.84                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3656                                       
Order of pole (three term test)                    = 32.16                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=779.2MB, alloc=40.3MB, time=8.38
x[1]                              = 0.42                                         
y2[1] (closed_form)               = 0.40776045305957018597278715808634           
y2[1] (numeric)                   = 0.40776045305957018597278715808633           
absolute error                    = 1e-32                                        
relative error                    = 2.4524202690492617941281881910421e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.91308894031230827243608878966567           
y1[1] (numeric)                   = 0.91308894031230827243608878966564           
absolute error                    = 3e-32                                        
relative error                    = 3.2855506923278419507281472471636e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3723                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3723                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.43                                         
y2[1] (closed_form)               = 0.41687080242921076621691867262457           
y2[1] (numeric)                   = 0.41687080242921076621691867262456           
absolute error                    = 1e-32                                        
relative error                    = 2.3988247537912204016753349059711e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.90896574967488512247591047766345           
y1[1] (numeric)                   = 0.90896574967488512247591047766342           
absolute error                    = 3e-32                                        
relative error                    = 3.3004543912386432879141980383694e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3789                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3789                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=820.3MB, alloc=40.3MB, time=8.81
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y2[1] (closed_form)               = 0.42593946506599960276972075077992           
y2[1] (numeric)                   = 0.42593946506599960276972075077991           
absolute error                    = 1e-32                                        
relative error                    = 2.3477514576984533151673776707192e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.90475166321996341716553738899837           
y1[1] (numeric)                   = 0.90475166321996341716553738899834           
absolute error                    = 3e-32                                        
relative error                    = 3.3158270075162485340432559605432e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3854                                       
Order of pole (three term test)                    = 32.82                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3854                                       
Order of pole (three term test)                    = 32.18                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y2[1] (closed_form)               = 0.4349655341112302104208442462319            
y2[1] (numeric)                   = 0.43496553411123021042084424623189           
absolute error                    = 1e-32                                        
relative error                    = 2.2990327315089707901082775564880e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.90044710235267692166884061148645           
y1[1] (numeric)                   = 0.90044710235267692166884061148641           
absolute error                    = 4e-32                                        
relative error                    = 4.4422376278949091537778426840465e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3917                                       
Order of pole (three term test)                    = 32.81                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3917                                       
Order of pole (three term test)                    = 32.19                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=861.2MB, alloc=40.3MB, time=9.26
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y2[1] (closed_form)               = 0.4439481069655197652415136439289            
y2[1] (numeric)                   = 0.44394810696551976524151364392889           
absolute error                    = 1e-32                                        
relative error                    = 2.2525155177149280283966705837029e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.89605249752552524253638990350041           
y1[1] (numeric)                   = 0.89605249752552524253638990350037           
absolute error                    = 4e-32                                        
relative error                    = 4.4640241626981846569305767420374e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3978                                       
Order of pole (three term test)                    = 32.8                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3978                                       
Order of pole (three term test)                    = 32.2                                         
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=902.2MB, alloc=40.3MB, time=9.70
x[1]                              = 0.47                                         
y2[1] (closed_form)               = 0.45288628537906829070327480039641           
y2[1] (numeric)                   = 0.4528862853790682907032748003964            
absolute error                    = 1e-32                                        
relative error                    = 2.2080597984171557468192953787381e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.89156828819532893645401927653339           
y1[1] (numeric)                   = 0.89156828819532893645401927653335           
absolute error                    = 4e-32                                        
relative error                    = 4.4864763058100843474145178207608e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4038                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4038                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y2[1] (closed_form)               = 0.46177917554148288913664294258864           
y2[1] (numeric)                   = 0.46177917554148288913664294258863           
absolute error                    = 1e-32                                        
relative error                    = 2.1655372372030389639513622541410e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.88699492277928419439995483115874           
y1[1] (numeric)                   = 0.8869949227792841943999548311587            
absolute error                    = 4e-32                                        
relative error                    = 4.5096086767515149712194737237426e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4096                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4096                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=943.2MB, alloc=40.3MB, time=10.14
x[1]                              = 0.49                                         
y2[1] (closed_form)               = 0.47062588817115803618135833718796           
y2[1] (numeric)                   = 0.47062588817115803618135833718795           
absolute error                    = 1e-32                                        
relative error                    = 2.1248299873302300619495400683509e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.88233285861012149570546815913666           
y1[1] (numeric)                   = 0.88233285861012149570546815913661           
absolute error                    = 5e-32                                        
relative error                    = 5.6667956443061153295944927691598e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4152                                       
Order of pole (three term test)                    = 32.78                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4152                                       
Order of pole (three term test)                    = 32.22                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y2[1] (closed_form)               = 0.47942553860420300027328793521557           
y2[1] (numeric)                   = 0.47942553860420300027328793521556           
absolute error                    = 1e-32                                        
relative error                    = 2.0858296429334881857725016754593e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.87758256189037271611628158260383           
y1[1] (numeric)                   = 0.87758256189037271611628158260378           
absolute error                    = 5e-32                                        
relative error                    = 5.6974696366227456115666388410247e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4207                                       
Order of pole (three term test)                    = 32.77                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4207                                       
Order of pole (three term test)                    = 32.23                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=984.2MB, alloc=40.3MB, time=10.58
 
TOP MAIN SOLVE Loop
x[1]                              = 0.51                                         
y2[1] (closed_form)               = 0.48817724688290749450013023767457           
y2[1] (numeric)                   = 0.48817724688290749450013023767456           
absolute error                    = 1e-32                                        
relative error                    = 2.0484363136241303362488879428417e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.87274450764575126310580847357551           
y1[1] (numeric)                   = 0.87274450764575126310580847357546           
absolute error                    = 5e-32                                        
relative error                    = 5.7290535273462986668964966498672e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4261                                       
Order of pole (three term test)                    = 32.76                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4261                                       
Order of pole (three term test)                    = 32.24                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1025.1MB, alloc=40.3MB, time=11.02
x[1]                              = 0.52                                         
y2[1] (closed_form)               = 0.49688013784373671433445894254775           
y2[1] (numeric)                   = 0.49688013784373671433445894254774           
absolute error                    = 1e-32                                        
relative error                    = 2.0125578058716625443726996547782e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.86781917967764990038784757198851           
y1[1] (numeric)                   = 0.86781917967764990038784757198847           
absolute error                    = 4e-32                                        
relative error                    = 4.6092551232686443368576751445101e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4312                                       
Order of pole (three term test)                    = 32.75                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4312                                       
Order of pole (three term test)                    = 32.25                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.53                                         
y2[1] (closed_form)               = 0.50553334120484696181366102246608           
y2[1] (numeric)                   = 0.50553334120484696181366102246606           
absolute error                    = 2e-32                                        
relative error                    = 3.9562177941287967485404135352677e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.8628070705147610118066950185642            
y1[1] (numeric)                   = 0.86280707051476101180669501856416           
absolute error                    = 4e-32                                        
relative error                    = 4.6360306222497135844330941005581e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4362                                       
Order of pole (three term test)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4362                                       
Order of pole (three term test)                    = 32.26                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1066.1MB, alloc=40.3MB, time=11.45
x[1]                              = 0.54                                         
y2[1] (closed_form)               = 0.51413599165311310467728068295824           
y2[1] (numeric)                   = 0.51413599165311310467728068295822           
absolute error                    = 2e-32                                        
relative error                    = 3.8900213804704756779805487539004e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.8577086813638241425379687789178            
y1[1] (numeric)                   = 0.85770868136382414253796877891775           
absolute error                    = 5e-32                                        
relative error                    = 5.8294851254736135436021303533814e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.441                                        
Order of pole (three term test)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.441                                        
Order of pole (three term test)                    = 32.26                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.55                                         
y2[1] (closed_form)               = 0.52268722893065916778837810775729           
y2[1] (numeric)                   = 0.52268722893065916778837810775727           
absolute error                    = 2e-32                                        
relative error                    = 3.8263800783724990896847033647784e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.85252452205950574280498179761777           
y1[1] (numeric)                   = 0.85252452205950574280498179761773           
absolute error                    = 4e-32                                        
relative error                    = 4.6919471481440884579598873330178e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4456                                       
Order of pole (three term test)                    = 32.73                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4456                                       
Order of pole (three term test)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1107.2MB, alloc=40.3MB, time=11.89
 
TOP MAIN SOLVE Loop
x[1]                              = 0.56                                         
y2[1] (closed_form)               = 0.53118619792088340385186944111203           
y2[1] (numeric)                   = 0.53118619792088340385186944111201           
absolute error                    = 2e-32                                        
relative error                    = 3.7651580704246507747019089774180e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.84725511101341612609452550386632           
y1[1] (numeric)                   = 0.84725511101341612609452550386628           
absolute error                    = 4e-32                                        
relative error                    = 4.7211282033052979112875903141288e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4501                                       
Order of pole (three term test)                    = 32.72                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4501                                       
Order of pole (three term test)                    = 32.28                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.57                                         
y2[1] (closed_form)               = 0.53963204873396924099446349307883           
y2[1] (numeric)                   = 0.53963204873396924099446349307881           
absolute error                    = 2e-32                                        
relative error                    = 3.7062290957184623024167079069551e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.84190097516226874013375636391601           
y1[1] (numeric)                   = 0.84190097516226874013375636391597           
absolute error                    = 4e-32                                        
relative error                    = 4.7511525915848196455412108507539e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4543                                       
Order of pole (three term test)                    = 32.71                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4543                                       
Order of pole (three term test)                    = 32.29                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1148.2MB, alloc=40.3MB, time=12.33
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y2[1] (closed_form)               = 0.54802393679187355618269605957646           
y2[1] (numeric)                   = 0.54802393679187355618269605957644           
absolute error                    = 2e-32                                        
relative error                    = 3.6494756263895684248521951304792e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.83646264991518693465788732805002           
y1[1] (numeric)                   = 0.83646264991518693465788732804998           
absolute error                    = 4e-32                                        
relative error                    = 4.7820425698691743007856700863157e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4584                                       
Order of pole (three term test)                    = 32.7                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4584                                       
Order of pole (three term test)                    = 32.3                                         
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1189.1MB, alloc=40.3MB, time=12.77
x[1]                              = 0.59                                         
y2[1] (closed_form)               = 0.55636102291278377572254337887577           
y2[1] (numeric)                   = 0.55636102291278377572254337887575           
absolute error                    = 2e-32                                        
relative error                    = 3.5947881279122672250783008540811e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.83094067910016349524799652249068           
y1[1] (numeric)                   = 0.83094067910016349524799652249064           
absolute error                    = 4e-32                                        
relative error                    = 4.8138213721004153966458006838632e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4623                                       
Order of pole (three term test)                    = 32.69                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4623                                       
Order of pole (three term test)                    = 32.31                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y2[1] (closed_form)               = 0.56464247339503535720094544565866           
y2[1] (numeric)                   = 0.56464247339503535720094544565864           
absolute error                    = 2e-32                                        
relative error                    = 3.5420643933754507467492242142109e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.82533561490967829724095249895538           
y1[1] (numeric)                   = 0.82533561490967829724095249895533           
absolute error                    = 5e-32                                        
relative error                    = 6.0581415725615835230727756068620e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.466                                        
Order of pole (three term test)                    = 32.68                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.466                                        
Order of pole (three term test)                    = 32.32                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1230.1MB, alloc=40.3MB, time=13.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.61                                         
y2[1] (closed_form)               = 0.57286746010048126119097603216272           
y2[1] (numeric)                   = 0.57286746010048126119097603216271           
absolute error                    = 1e-32                                        
relative error                    = 1.7456044716252507362706331249149e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.81964801784547951790074657865482           
y1[1] (numeric)                   = 0.81964801784547951790074657865478           
absolute error                    = 4e-32                                        
relative error                    = 4.8801435651785863726751115353567e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4695                                       
Order of pole (three term test)                    = 32.67                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4695                                       
Order of pole (three term test)                    = 32.33                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.62                                         
y2[1] (closed_form)               = 0.58103516053730507584296322758221           
y2[1] (numeric)                   = 0.58103516053730507584296322758221           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.8138784566625339286839996543607            
y1[1] (numeric)                   = 0.81387845666253392868399965436066           
absolute error                    = 4e-32                                        
relative error                    = 4.9147387638232542407396460859407e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4729                                       
Order of pole (three term test)                    = 32.66                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4729                                       
Order of pole (three term test)                    = 32.34                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1271.1MB, alloc=40.3MB, time=13.64
 
TOP MAIN SOLVE Loop
x[1]                              = 0.63                                         
y2[1] (closed_form)               = 0.58914475794226951311811209079462           
y2[1] (numeric)                   = 0.58914475794226951311811209079462           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.80802750831215187252370896577706           
y1[1] (numeric)                   = 0.80802750831215187252370896577702           
absolute error                    = 4e-32                                        
relative error                    = 4.9503265159318639291276460728563e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.476                                        
Order of pole (three term test)                    = 32.65                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.476                                        
Order of pole (three term test)                    = 32.35                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1312.1MB, alloc=40.3MB, time=14.08
x[1]                              = 0.64                                         
y2[1] (closed_form)               = 0.59719544136239205188354623920793           
y2[1] (numeric)                   = 0.59719544136239205188354623920793           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.80209575788429261358611077926032           
y1[1] (numeric)                   = 0.80209575788429261358611077926029           
absolute error                    = 3e-32                                        
relative error                    = 3.7402018032275505131295999732792e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.479                                        
Order of pole (three term test)                    = 32.64                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.479                                        
Order of pole (three term test)                    = 32.36                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y2[1] (closed_form)               = 0.60518640573603956037252167860594           
y2[1] (numeric)                   = 0.60518640573603956037252167860594           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.79608379854905582891760457067991           
y1[1] (numeric)                   = 0.79608379854905582891760457067987           
absolute error                    = 4e-32                                        
relative error                    = 5.0245966659419639546597112310993e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4818                                       
Order of pole (three term test)                    = 32.63                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4818                                       
Order of pole (three term test)                    = 32.37                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1353.1MB, alloc=40.3MB, time=14.51
x[1]                              = 0.66                                         
y2[1] (closed_form)               = 0.6131168519734337886151454793963            
y2[1] (numeric)                   = 0.6131168519734337886151454793963            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.78999223149736509278381709123024           
y1[1] (numeric)                   = 0.78999223149736509278381709123021           
absolute error                    = 3e-32                                        
relative error                    = 3.7975056973835648093528520531170e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4844                                       
Order of pole (three term test)                    = 32.62                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4844                                       
Order of pole (three term test)                    = 32.38                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.67                                         
y2[1] (closed_form)               = 0.62098598703655968035744391412659           
y2[1] (numeric)                   = 0.6209859870365596803574439141266            
absolute error                    = 1e-32                                        
relative error                    = 1.6103422957612188443809399991484e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.78382166588084928530294214483812           
y1[1] (numeric)                   = 0.78382166588084928530294214483808           
absolute error                    = 4e-32                                        
relative error                    = 5.1032016262332433676423520268335e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4867                                       
Order of pole (three term test)                    = 32.61                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4867                                       
Order of pole (three term test)                    = 32.39                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1394.1MB, alloc=40.3MB, time=14.95
 
TOP MAIN SOLVE Loop
x[1]                              = 0.68                                         
y2[1] (closed_form)               = 0.62879302401846851370417818742025           
y2[1] (numeric)                   = 0.62879302401846851370417818742026           
absolute error                    = 1e-32                                        
relative error                    = 1.5903484323175770922409669273103e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.77757271875092793718239408404432           
y1[1] (numeric)                   = 0.77757271875092793718239408404428           
absolute error                    = 4e-32                                        
relative error                    = 5.1442134009350189706756638572067e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4889                                       
Order of pole (three term test)                    = 32.6                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4889                                       
Order of pole (three term test)                    = 32.4                                         
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.69                                         
y2[1] (closed_form)               = 0.63653718222196794023742920700872           
y2[1] (numeric)                   = 0.63653718222196794023742920700874           
absolute error                    = 2e-32                                        
relative error                    = 3.1420002725034476796470444715189e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.77124601499710660197353931549777           
y1[1] (numeric)                   = 0.77124601499710660197353931549773           
absolute error                    = 4e-32                                        
relative error                    = 5.1864125353244209058170869571309e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
memory used=1435.2MB, alloc=40.3MB, time=15.39
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4909                                       
Order of pole (three term test)                    = 32.59                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4909                                       
Order of pole (three term test)                    = 32.41                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y2[1] (closed_form)               = 0.64421768723769105367261435139872           
y2[1] (numeric)                   = 0.64421768723769105367261435139874           
absolute error                    = 2e-32                                        
relative error                    = 3.1045406539142078239799472819099e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.76484218728448842625585999019186           
y1[1] (numeric)                   = 0.76484218728448842625585999019183           
absolute error                    = 3e-32                                        
relative error                    = 3.9223777792007816096240185059160e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4927                                       
Order of pole (three term test)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4927                                       
Order of pole (three term test)                    = 32.42                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1476.0MB, alloc=40.3MB, time=15.83
x[1]                              = 0.71                                         
y2[1] (closed_form)               = 0.65183377102153668121012797285284           
y2[1] (numeric)                   = 0.65183377102153668121012797285286           
absolute error                    = 2e-32                                        
relative error                    = 3.0682669246572677397779021813019e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.75836187599050816654145794413955           
y1[1] (numeric)                   = 0.75836187599050816654145794413952           
absolute error                    = 3e-32                                        
relative error                    = 3.9558950614199238795892040788314e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4943                                       
Order of pole (three term test)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4943                                       
Order of pole (three term test)                    = 32.42                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y2[1] (closed_form)               = 0.65938467197147315361800383264817           
y2[1] (numeric)                   = 0.65938467197147315361800383264819           
absolute error                    = 2e-32                                        
relative error                    = 3.0331308642954406714238078312097e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.75180572914089497944548696225195           
y1[1] (numeric)                   = 0.75180572914089497944548696225192           
absolute error                    = 3e-32                                        
relative error                    = 3.9903925757897140473302837309239e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4957                                       
Order of pole (three term test)                    = 32.57                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4957                                       
Order of pole (three term test)                    = 32.43                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1517.0MB, alloc=40.3MB, time=16.28
 
TOP MAIN SOLVE Loop
x[1]                              = 0.73                                         
y2[1] (closed_form)               = 0.66686963500369787373259413076153           
y2[1] (numeric)                   = 0.66686963500369787373259413076155           
absolute error                    = 2e-32                                        
relative error                    = 2.9990869204727094153192585309935e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.74517440234487038879013215855033           
y1[1] (numeric)                   = 0.74517440234487038879013215855031           
absolute error                    = 2e-32                                        
relative error                    = 2.6839354568628756191548285450706e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4969                                       
Order of pole (three term test)                    = 32.56                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4969                                       
Order of pole (three term test)                    = 32.44                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.74                                         
y2[1] (closed_form)               = 0.67428791162814506748388115760817           
y2[1] (numeric)                   = 0.67428791162814506748388115760819           
absolute error                    = 2e-32                                        
relative error                    = 2.9660920291018889736796600468598e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.73846855872958790979142456069883           
y1[1] (numeric)                   = 0.7384685587295879097914245606988            
absolute error                    = 3e-32                                        
relative error                    = 4.0624613797519017638912438848657e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4979                                       
Order of pole (three term test)                    = 32.55                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4979                                       
Order of pole (three term test)                    = 32.45                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1558.1MB, alloc=40.3MB, time=16.72
 
TOP MAIN SOLVE Loop
x[1]                              = 0.75                                         
y2[1] (closed_form)               = 0.68163876002333416673324195277989           
y2[1] (numeric)                   = 0.68163876002333416673324195277991           
absolute error                    = 2e-32                                        
relative error                    = 2.9341054489500202339451566590895e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.73168886887382088631183875300008           
y1[1] (numeric)                   = 0.73168886887382088631183875300005           
absolute error                    = 3e-32                                        
relative error                    = 4.1001033740166784056452059804705e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4987                                       
Order of pole (three term test)                    = 32.54                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4987                                       
Order of pole (three term test)                    = 32.46                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1599.0MB, alloc=40.3MB, time=17.16
x[1]                              = 0.76                                         
y2[1] (closed_form)               = 0.68892144511055133914775563876973           
y2[1] (numeric)                   = 0.68892144511055133914775563876974           
absolute error                    = 1e-32                                        
relative error                    = 1.4515443046478685727207698547603e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.72483601074090517233968836666701           
y1[1] (numeric)                   = 0.72483601074090517233968836666698           
absolute error                    = 3e-32                                        
relative error                    = 4.1388672134728679855610360531458e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4994                                       
Order of pole (three term test)                    = 32.53                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4994                                       
Order of pole (three term test)                    = 32.47                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y2[1] (closed_form)               = 0.69613523862735674701988373445221           
y2[1] (numeric)                   = 0.69613523862735674701988373445223           
absolute error                    = 2e-32                                        
relative error                    = 2.8730049694706029924906087380248e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.71791066961094336337129056532434           
y1[1] (numeric)                   = 0.71791066961094336337129056532432           
absolute error                    = 2e-32                                        
relative error                    = 2.7858619249716097277693846674882e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4998                                       
Order of pole (three term test)                    = 32.52                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4998                                       
Order of pole (three term test)                    = 32.48                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1640.0MB, alloc=40.3MB, time=17.59
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y2[1] (closed_form)               = 0.70327941920041018436789732511792           
y2[1] (numeric)                   = 0.70327941920041018436789732511795           
absolute error                    = 3e-32                                        
relative error                    = 4.2657298338274055159561119486760e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.71091353801227735721626502376456           
y1[1] (numeric)                   = 0.71091353801227735721626502376454           
absolute error                    = 2e-32                                        
relative error                    = 2.8132816342083224421967142135470e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.5                                          
Order of pole (three term test)                    = 32.51                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.5                                          
Order of pole (three term test)                    = 32.49                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.79                                         
y2[1] (closed_form)               = 0.7103532724176078098140288749692            
y2[1] (numeric)                   = 0.71035327241760780981402887496922           
absolute error                    = 2e-32                                        
relative error                    = 2.8155005089132960296161411393593e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.70384531565223609691278086108495           
y1[1] (numeric)                   = 0.70384531565223609691278086108493           
absolute error                    = 2e-32                                        
relative error                    = 2.8415334385605014942610583502002e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.5                                          
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.5                                          
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=1681.0MB, alloc=40.3MB, time=18.03
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y2[1] (closed_form)               = 0.71735609089952276162717461058139           
y2[1] (numeric)                   = 0.71735609089952276162717461058141           
absolute error                    = 2e-32                                        
relative error                    = 2.7880156387772723490049644522139e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.69670670934716542092074998164232           
y1[1] (numeric)                   = 0.6967067093471654209207499816423            
absolute error                    = 2e-32                                        
relative error                    = 2.8706483993444796009939048163257e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4998                                       
Order of pole (three term test)                    = 32.49                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4998                                       
Order of pole (three term test)                    = 32.51                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1721.9MB, alloc=40.3MB, time=18.47
x[1]                              = 0.81                                         
y2[1] (closed_form)               = 0.72428717437014251092817685251454           
y2[1] (numeric)                   = 0.72428717437014251092817685251457           
absolute error                    = 3e-32                                        
relative error                    = 4.1420034844726774493234715007737e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.6894984329517470175496392406801            
y1[1] (numeric)                   = 0.68949843295174701754963924068008           
absolute error                    = 2e-32                                        
relative error                    = 2.9006592392646749631796699844823e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4994                                       
Order of pole (three term test)                    = 32.48                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4994                                       
Order of pole (three term test)                    = 32.52                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y2[1] (closed_form)               = 0.73114582972689587938131336468772           
y2[1] (numeric)                   = 0.73114582972689587938131336468775           
absolute error                    = 3e-32                                        
relative error                    = 4.1031486169053125759982871356489e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.68222120728761355166655797843693           
y1[1] (numeric)                   = 0.68222120728761355166655797843691           
absolute error                    = 2e-32                                        
relative error                    = 2.9316004525154433989688989109211e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4988                                       
Order of pole (three term test)                    = 32.47                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4988                                       
Order of pole (three term test)                    = 32.53                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1763.0MB, alloc=40.3MB, time=18.91
x[1]                              = 0.83                                         
y2[1] (closed_form)               = 0.73793137110996271872858022613808           
y2[1] (numeric)                   = 0.73793137110996271872858022613811           
absolute error                    = 3e-32                                        
relative error                    = 4.0654187061969418647964719051794e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.67487576007126710211246291786445           
y1[1] (numeric)                   = 0.67487576007126710211246291786443           
absolute error                    = 2e-32                                        
relative error                    = 2.9635084238153691318662949969539e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.498                                        
Order of pole (three term test)                    = 32.46                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.498                                        
Order of pole (three term test)                    = 32.54                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.84                                         
y2[1] (closed_form)               = 0.74464311997085932125657267062965           
y2[1] (numeric)                   = 0.74464311997085932125657267062968           
absolute error                    = 3e-32                                        
relative error                    = 4.0287755564268172573986939741142e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.66746282584130811792267103687086           
y1[1] (numeric)                   = 0.66746282584130811792267103687083           
absolute error                    = 3e-32                                        
relative error                    = 4.4946323358437667727440878712148e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.497                                        
Order of pole (three term test)                    = 32.45                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.497                                        
Order of pole (three term test)                    = 32.55                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1804.1MB, alloc=40.3MB, time=19.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y2[1] (closed_form)               = 0.75128040514029270271207152423547           
y2[1] (numeric)                   = 0.7512804051402927027120715242355            
absolute error                    = 3e-32                                        
relative error                    = 3.9931828109369970737227756632712e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.65998314588498217039541602946147           
y1[1] (numeric)                   = 0.65998314588498217039541602946143           
absolute error                    = 4e-32                                        
relative error                    = 6.0607608314547710534814195485968e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4958                                       
Order of pole (three term test)                    = 32.44                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4958                                       
Order of pole (three term test)                    = 32.56                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.86                                         
y2[1] (closed_form)               = 0.75784256289527697229458872952865           
y2[1] (numeric)                   = 0.75784256289527697229458872952868           
absolute error                    = 3e-32                                        
relative error                    = 3.9586058462310953491664231397564e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.65243746816405184627203066422386           
y1[1] (numeric)                   = 0.65243746816405184627203066422382           
absolute error                    = 4e-32                                        
relative error                    = 6.1308557450814915427142438904032e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4944                                       
Order of pole (three term test)                    = 32.43                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4944                                       
Order of pole (three term test)                    = 32.57                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1845.1MB, alloc=40.3MB, time=19.78
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y2[1] (closed_form)               = 0.76432893702550507814480282372285           
y2[1] (numeric)                   = 0.76432893702550507814480282372289           
absolute error                    = 4e-32                                        
relative error                    = 5.2333488976180461258752970927359e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.64482654724000119477766380548283           
y1[1] (numeric)                   = 0.64482654724000119477766380548279           
absolute error                    = 4e-32                                        
relative error                    = 6.2032185509744842069896284561557e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4929                                       
Order of pole (three term test)                    = 32.42                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4929                                       
Order of pole (three term test)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=1886.2MB, alloc=40.3MB, time=20.22
x[1]                              = 0.88                                         
y2[1] (closed_form)               = 0.77073887889896929120964513075599           
y2[1] (numeric)                   = 0.77073887889896929120964513075603           
absolute error                    = 4e-32                                        
relative error                    = 5.1898251269147818752636115922543e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.63715114419858020801549860572209           
y1[1] (numeric)                   = 0.63715114419858020801549860572205           
absolute error                    = 4e-32                                        
relative error                    = 6.2779452511715561262689041684732e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4911                                       
Order of pole (three term test)                    = 32.41                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4911                                       
Order of pole (three term test)                    = 32.59                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.89                                         
y2[1] (closed_form)               = 0.77707174752682386549033371297318           
y2[1] (numeric)                   = 0.77707174752682386549033371297322           
absolute error                    = 4e-32                                        
relative error                    = 5.1475298294279105189678064921586e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.62941202657369688020355305738025           
y1[1] (numeric)                   = 0.62941202657369688020355305738021           
absolute error                    = 4e-32                                        
relative error                    = 6.3551375428503131562381386057661e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4891                                       
Order of pole (three term test)                    = 32.4                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4891                                       
Order of pole (three term test)                    = 32.6                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=1927.3MB, alloc=40.3MB, time=20.66
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y2[1] (closed_form)               = 0.78332690962748338846138231571355           
y2[1] (numeric)                   = 0.78332690962748338846138231571359           
absolute error                    = 4e-32                                        
relative error                    = 5.1064248538355819840625826089280e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.62160996827066445648471615140713           
y1[1] (numeric)                   = 0.62160996827066445648471615140709           
absolute error                    = 4e-32                                        
relative error                    = 6.4349032418641980520960514492256e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4869                                       
Order of pole (three term test)                    = 32.39                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4869                                       
Order of pole (three term test)                    = 32.61                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y2[1] (closed_form)               = 0.78950373968995041187895751787155           
y2[1] (numeric)                   = 0.78950373968995041187895751787159           
absolute error                    = 4e-32                                        
relative error                    = 5.0664737846217905315407947942791e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.61374574948881154652117822617468           
y1[1] (numeric)                   = 0.61374574948881154652117822617464           
absolute error                    = 4e-32                                        
relative error                    = 6.5173567447621389070714150901352e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4846                                       
Order of pole (three term test)                    = 32.38                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4846                                       
Order of pole (three term test)                    = 32.62                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1968.3MB, alloc=40.3MB, time=21.11
 
TOP MAIN SOLVE Loop
x[1]                              = 0.92                                         
y2[1] (closed_form)               = 0.79560162003636603026827610248162           
y2[1] (numeric)                   = 0.79560162003636603026827610248166           
absolute error                    = 4e-32                                        
relative error                    = 5.0276418489660247604101785447195e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.60582015664346284179740470667438           
y1[1] (numeric)                   = 0.60582015664346284179740470667434           
absolute error                    = 4e-32                                        
relative error                    = 6.6026195334304124270698785590394e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.482                                        
Order of pole (three term test)                    = 32.37                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.482                                        
Order of pole (three term test)                    = 32.63                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2009.3MB, alloc=40.3MB, time=21.55
x[1]                              = 0.93                                         
y2[1] (closed_form)               = 0.80161994088377715208431921591065           
y2[1] (numeric)                   = 0.80161994088377715208431921591069           
absolute error                    = 4e-32                                        
relative error                    = 4.9898958296746511500858070174123e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.59783398228729823849490708443298           
y1[1] (numeric)                   = 0.59783398228729823849490708443295           
absolute error                    = 3e-32                                        
relative error                    = 5.0181155452590251774666965637029e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4792                                       
Order of pole (three term test)                    = 32.36                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4792                                       
Order of pole (three term test)                    = 32.64                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y2[1] (closed_form)               = 0.80755810040511428687021979863415           
y2[1] (numeric)                   = 0.80755810040511428687021979863419           
absolute error                    = 4e-32                                        
relative error                    = 4.9532039837051802222261706080067e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.58978802503109822996098981522402           
y1[1] (numeric)                   = 0.58978802503109822996098981522398           
absolute error                    = 4e-32                                        
relative error                    = 6.7820976863494113271153801912102e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4763                                       
Order of pole (three term test)                    = 32.35                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4763                                       
Order of pole (three term test)                    = 32.65                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2050.2MB, alloc=40.3MB, time=21.98
x[1]                              = 0.95                                         
y2[1] (closed_form)               = 0.81341550478937375068542210210256           
y2[1] (numeric)                   = 0.8134155047893737506854221021026            
absolute error                    = 4e-32                                        
relative error                    = 4.9175359658724014073978637130131e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.58168308946388349416618097376046           
y1[1] (numeric)                   = 0.58168308946388349416618097376042           
absolute error                    = 4e-32                                        
relative error                    = 6.8765966768720352218474960314306e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4732                                       
Order of pole (three term test)                    = 32.34                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4732                                       
Order of pole (three term test)                    = 32.66                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y2[1] (closed_form)               = 0.81919156830099827163322214643043           
y2[1] (numeric)                   = 0.81919156830099827163322214643047           
absolute error                    = 4e-32                                        
relative error                    = 4.8828627573596640699462274663756e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.57351998607245666212505080035186           
y1[1] (numeric)                   = 0.57351998607245666212505080035182           
absolute error                    = 4e-32                                        
relative error                    = 6.9744735966265924045917017940464e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4698                                       
Order of pole (three term test)                    = 32.33                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4698                                       
Order of pole (three term test)                    = 32.67                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2091.2MB, alloc=40.3MB, time=22.42
 
TOP MAIN SOLVE Loop
x[1]                              = 0.97                                         
y2[1] (closed_form)               = 0.82488571333845005747662003785634           
y2[1] (numeric)                   = 0.82488571333845005747662003785639           
absolute error                    = 5e-32                                        
relative error                    = 6.0614457483621168476649654304519e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.56529953116035431303652775484986           
y1[1] (numeric)                   = 0.56529953116035431303652775484982           
absolute error                    = 4e-32                                        
relative error                    = 7.0758947770387408191732570034581e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4663                                       
Order of pole (three term test)                    = 32.32                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4663                                       
Order of pole (three term test)                    = 32.68                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2132.1MB, alloc=40.3MB, time=22.86
x[1]                              = 0.98                                         
y2[1] (closed_form)               = 0.83049737049197046808453328771915           
y2[1] (numeric)                   = 0.83049737049197046808453328771919           
absolute error                    = 4e-32                                        
relative error                    = 4.8163909268375863745909436309423e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.55702254676621730087665826735994           
y1[1] (numeric)                   = 0.5570225467662173008766582673599            
absolute error                    = 4e-32                                        
relative error                    = 7.1810378650234465546546371421035e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4626                                       
Order of pole (three term test)                    = 32.31                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4626                                       
Order of pole (three term test)                    = 32.69                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.99                                         
y2[1] (closed_form)               = 0.83602597860052051678925941154711           
y2[1] (numeric)                   = 0.83602597860052051678925941154715           
absolute error                    = 4e-32                                        
relative error                    = 4.7845403161943197137349486701668e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.54868986058158757534312640865361           
y1[1] (numeric)                   = 0.54868986058158757534312640865357           
absolute error                    = 4e-32                                        
relative error                    = 7.2900927962477247285085481914157e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4587                                       
Order of pole (three term test)                    = 32.3                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4587                                       
Order of pole (three term test)                    = 32.7                                         
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2173.1MB, alloc=40.3MB, time=23.30
x[1]                              = 1                                            
y2[1] (closed_form)               = 0.8414709848078965066525023216303            
y2[1] (numeric)                   = 0.84147098480789650665250232163034           
absolute error                    = 4e-32                                        
relative error                    = 4.7535804231124848650463978094982e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.54030230586813971740093660744298           
y1[1] (numeric)                   = 0.54030230586813971740093660744294           
absolute error                    = 4e-32                                        
relative error                    = 7.4032628707237024716470129655946e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4546                                       
Order of pole (three term test)                    = 32.29                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4546                                       
Order of pole (three term test)                    = 32.71                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y2[1] (closed_form)               = 0.84683184461801519012309878478201           
y2[1] (numeric)                   = 0.84683184461801519012309878478205           
absolute error                    = 4e-32                                        
relative error                    = 4.7234879337872569498653682560011e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.53186072137435546620673135577918           
y1[1] (numeric)                   = 0.53186072137435546620673135577914           
absolute error                    = 4e-32                                        
relative error                    = 7.5207659435045216640234971955352e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4504                                       
Order of pole (three term test)                    = 32.28                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4504                                       
Order of pole (three term test)                    = 32.72                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2214.1MB, alloc=40.3MB, time=23.73
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y2[1] (closed_form)               = 0.85210802194936292361654998545538           
y2[1] (numeric)                   = 0.85210802194936292361654998545542           
absolute error                    = 4e-32                                        
relative error                    = 4.6942405152450291279299190688993e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.52336595125164956988961380803381           
y1[1] (numeric)                   = 0.52336595125164956988961380803377           
absolute error                    = 4e-32                                        
relative error                    = 7.6428357451107545817513691119975e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.446                                        
Order of pole (three term test)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.446                                        
Order of pole (three term test)                    = 32.73                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y2[1] (closed_form)               = 0.85729898918860337214627438529442           
y2[1] (numeric)                   = 0.85729898918860337214627438529446           
absolute error                    = 4e-32                                        
relative error                    = 4.6658167692298669251161472849892e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.51481884496995534753350229983735           
y1[1] (numeric)                   = 0.51481884496995534753350229983731           
absolute error                    = 4e-32                                        
relative error                    = 7.7697233484788977329799985948386e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4414                                       
Order of pole (three term test)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4414                                       
Order of pole (three term test)                    = 32.73                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2255.0MB, alloc=40.3MB, time=24.17
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y2[1] (closed_form)               = 0.86240422724333840328079169211617           
y2[1] (numeric)                   = 0.86240422724333840328079169211621           
absolute error                    = 4e-32                                        
relative error                    = 4.6381961887941311601616055987808e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.50622025723277840373447342099217           
y1[1] (numeric)                   = 0.50622025723277840373447342099213           
absolute error                    = 4e-32                                        
relative error                    = 7.9016988017543027049133517140099e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4366                                       
Order of pole (three term test)                    = 32.26                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4366                                       
Order of pole (three term test)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2295.9MB, alloc=40.3MB, time=24.61
x[1]                              = 1.05                                         
y2[1] (closed_form)               = 0.86742322559401689438140948500027           
y2[1] (numeric)                   = 0.86742322559401689438140948500032           
absolute error                    = 5e-32                                        
relative error                    = 5.7641988967680320903848370056288e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.4975710478917269902908495728121            
y1[1] (numeric)                   = 0.49757104789172699029084957281205           
absolute error                    = 5e-32                                        
relative error                    = 1.0048816186523809907301842128511e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4316                                       
Order of pole (three term test)                    = 32.25                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4316                                       
Order of pole (three term test)                    = 32.75                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y2[1] (closed_form)               = 0.87235548234498626228294592199742           
y2[1] (numeric)                   = 0.87235548234498626228294592199747           
absolute error                    = 5e-32                                        
relative error                    = 5.7316083880844733951304004796531e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.48887208186052756191863753995641           
y1[1] (numeric)                   = 0.48887208186052756191863753995636           
absolute error                    = 5e-32                                        
relative error                    = 1.0227624332670466753014171352801e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4265                                       
Order of pole (three term test)                    = 32.24                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4265                                       
Order of pole (three term test)                    = 32.76                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2337.0MB, alloc=40.3MB, time=25.05
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y2[1] (closed_form)               = 0.87720050427468161030706325777682           
y2[1] (numeric)                   = 0.87720050427468161030706325777687           
absolute error                    = 5e-32                                        
relative error                    = 5.6999511236422274635245744627828e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.48012422902853412436509306817592           
y1[1] (numeric)                   = 0.48012422902853412436509306817587           
absolute error                    = 5e-32                                        
relative error                    = 1.0413971421764775058491869676880e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4212                                       
Order of pole (three term test)                    = 32.23                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4212                                       
Order of pole (three term test)                    = 32.77                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y2[1] (closed_form)               = 0.88195780688494747373533498762476           
y2[1] (numeric)                   = 0.8819578068849474737353349876248            
absolute error                    = 4e-32                                        
relative error                    = 4.5353643550453940554309143882855e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.47132836417374002391352478852603           
y1[1] (numeric)                   = 0.47132836417374002391352478852599           
absolute error                    = 4e-32                                        
relative error                    = 8.4866524148449695391110858294863e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4157                                       
Order of pole (three term test)                    = 32.22                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4157                                       
Order of pole (three term test)                    = 32.78                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2378.0MB, alloc=40.3MB, time=25.50
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y2[1] (closed_form)               = 0.88662691444948723160860062863605           
y2[1] (numeric)                   = 0.88662691444948723160860062863609           
absolute error                    = 4e-32                                        
relative error                    = 4.5114804601703610561744449553795e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.46248536687530087702789707387514           
y1[1] (numeric)                   = 0.4624853668753008770278970738751            
absolute error                    = 4e-32                                        
relative error                    = 8.6489222935317497832472570888137e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4101                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4101                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2418.9MB, alloc=40.3MB, time=25.94
x[1]                              = 1.1                                          
y2[1] (closed_form)               = 0.8912073600614353399518025778717            
y2[1] (numeric)                   = 0.89120736006143533995180257787174           
absolute error                    = 4e-32                                        
relative error                    = 4.4882932741088001976349666013015e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.45359612142557738777137005178472           
y1[1] (numeric)                   = 0.45359612142557738777137005178468           
absolute error                    = 4e-32                                        
relative error                    = 8.8184175548694361359441013322568e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4042                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4042                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y2[1] (closed_form)               = 0.89569868568004762924062595933937           
y2[1] (numeric)                   = 0.89569868568004762924062595933941           
absolute error                    = 4e-32                                        
relative error                    = 4.4657875063901113057757788876626e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.44466151674170684864373751193357           
y1[1] (numeric)                   = 0.44466151674170684864373751193353           
absolute error                    = 4e-32                                        
relative error                    = 8.9956064318547798541433820368516e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3983                                       
Order of pole (three term test)                    = 32.2                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3983                                       
Order of pole (three term test)                    = 32.8                                         
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2459.9MB, alloc=40.3MB, time=26.39
x[1]                              = 1.12                                         
y2[1] (closed_form)               = 0.90010044217650499711910324733915           
y2[1] (numeric)                   = 0.90010044217650499711910324733919           
absolute error                    = 4e-32                                        
relative error                    = 4.4439484890460934633598102869665e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.43568244627671216761398879396113           
y1[1] (numeric)                   = 0.43568244627671216761398879396108           
absolute error                    = 5e-32                                        
relative error                    = 1.1476248452810931966136643080683e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3922                                       
Order of pole (three term test)                    = 32.19                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3922                                       
Order of pole (three term test)                    = 32.81                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y2[1] (closed_form)               = 0.9044121893788259160370815224114            
y2[1] (numeric)                   = 0.90441218937882591603708152241144           
absolute error                    = 4e-32                                        
relative error                    = 4.4227621509030138433594605167464e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.42665980793015731037121583565354           
y1[1] (numeric)                   = 0.42665980793015731037121583565349           
absolute error                    = 5e-32                                        
relative error                    = 1.1718938383852838035126756695520e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3859                                       
Order of pole (three term test)                    = 32.18                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3859                                       
Order of pole (three term test)                    = 32.82                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2500.9MB, alloc=40.3MB, time=26.83
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y2[1] (closed_form)               = 0.9086334961158832645942155781022            
y2[1] (numeric)                   = 0.90863349611588326459421557810225           
absolute error                    = 5e-32                                        
relative error                    = 5.5027687416030733627236127748275e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.41759450395835809217518674082258           
y1[1] (numeric)                   = 0.41759450395835809217518674082253           
absolute error                    = 5e-32                                        
relative error                    = 1.1973337657955844704095920649772e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3794                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3794                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2541.8MB, alloc=40.3MB, time=27.27
x[1]                              = 1.15                                         
y2[1] (closed_form)               = 0.91276394026052108094403304975368           
y2[1] (numeric)                   = 0.91276394026052108094403304975372           
absolute error                    = 4e-32                                        
relative error                    = 4.3822940670271439652222300016056e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.40848744088415729815257671880992           
y1[1] (numeric)                   = 0.40848744088415729815257671880987           
absolute error                    = 5e-32                                        
relative error                    = 1.2240278401650901481232810221154e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3729                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3729                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y2[1] (closed_form)               = 0.91680310877176692661866166687433           
y2[1] (numeric)                   = 0.91680310877176692661866166687438           
absolute error                    = 5e-32                                        
relative error                    = 5.4537336884671520034321791063787e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.39933952940627315445163962339401           
y1[1] (numeric)                   = 0.39933952940627315445163962339396           
absolute error                    = 5e-32                                        
relative error                    = 1.2520673842216071583193422932265e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3661                                       
Order of pole (three term test)                    = 32.16                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3661                                       
Order of pole (three term test)                    = 32.84                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2582.8MB, alloc=40.3MB, time=27.70
x[1]                              = 1.17                                         
y2[1] (closed_form)               = 0.92075059773613563957301300896203           
y2[1] (numeric)                   = 0.92075059773613563957301300896207           
absolute error                    = 4e-32                                        
relative error                    = 4.3442817304000286082970840242612e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.3901516843082302153326619350505            
y1[1] (numeric)                   = 0.39015168430823021533266193505045           
absolute error                    = 5e-32                                        
relative error                    = 1.2815528424195823576679145161835e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3592                                       
Order of pole (three term test)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3592                                       
Order of pole (three term test)                    = 32.85                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y2[1] (closed_form)               = 0.92460601240802034610753802587476           
y2[1] (numeric)                   = 0.9246060124080203461075380258748            
absolute error                    = 4e-32                                        
relative error                    = 4.3261669795792284461947461557086e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.38092482436688177302959946671276           
y1[1] (numeric)                   = 0.38092482436688177302959946671271           
absolute error                    = 5e-32                                        
relative error                    = 1.3125949479166336459045018324427e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3522                                       
Order of pole (three term test)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3522                                       
Order of pole (three term test)                    = 32.85                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2623.8MB, alloc=40.3MB, time=28.14
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y2[1] (closed_form)               = 0.92836896724916669260202111160267           
y2[1] (numeric)                   = 0.92836896724916669260202111160271           
absolute error                    = 4e-32                                        
relative error                    = 4.3086317413779218660168510526906e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.37165987226053293806567955835047           
y1[1] (numeric)                   = 0.37165987226053293806567955835041           
absolute error                    = 6e-32                                        
relative error                    = 1.6143792881126564584180597771133e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.345                                        
Order of pole (three term test)                    = 32.14                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.345                                        
Order of pole (three term test)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y2[1] (closed_form)               = 0.93203908596722634967013443549483           
y2[1] (numeric)                   = 0.93203908596722634967013443549486           
absolute error                    = 3e-32                                        
relative error                    = 3.2187491331296916861153507673057e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.36235775447667357763837335562308           
y1[1] (numeric)                   = 0.36235775447667357763837335562302           
absolute error                    = 6e-32                                        
relative error                    = 1.6558221607994438741300597635427e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3377                                       
Order of pole (three term test)                    = 32.13                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3377                                       
Order of pole (three term test)                    = 32.87                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2664.7MB, alloc=40.3MB, time=28.58
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y2[1] (closed_form)               = 0.93561600155338593341646488854361           
y2[1] (numeric)                   = 0.93561600155338593341646488854364           
absolute error                    = 3e-32                                        
relative error                    = 3.2064436638740204488227490204825e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.35301940121933033870301071366479           
y1[1] (numeric)                   = 0.35301940121933033870301071366474           
absolute error                    = 5e-32                                        
relative error                    = 1.4163527507921607726194472010210e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3303                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3303                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2705.6MB, alloc=40.3MB, time=29.01
x[1]                              = 1.22                                         
y2[1] (closed_form)               = 0.93909935631906758093524527188837           
y2[1] (numeric)                   = 0.93909935631906758093524527188841           
absolute error                    = 4e-32                                        
relative error                    = 4.2594002147744668214178252652873e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.3436457463160470204755229744352            
y1[1] (numeric)                   = 0.34364574631604702047552297443515           
absolute error                    = 5e-32                                        
relative error                    = 1.4549867279316059969669624375757e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3227                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3227                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y2[1] (closed_form)               = 0.94248880193169751002382356538924           
y2[1] (numeric)                   = 0.94248880193169751002382356538928           
absolute error                    = 4e-32                                        
relative error                    = 4.2440822551967905351236704268380e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.33423772712450259823954724549766           
y1[1] (numeric)                   = 0.33423772712450259823954724549762           
absolute error                    = 4e-32                                        
relative error                    = 1.1967529920732172255226357687978e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.315                                        
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.315                                        
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2746.7MB, alloc=40.3MB, time=29.45
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y2[1] (closed_form)               = 0.94578399944953898628470596308179           
y2[1] (numeric)                   = 0.94578399944953898628470596308183           
absolute error                    = 4e-32                                        
relative error                    = 4.2292954864197980519401466092972e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.32479628443877623657769341569738           
y1[1] (numeric)                   = 0.32479628443877623657769341569733           
absolute error                    = 5e-32                                        
relative error                    = 1.5394264773193533328532731450800e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3072                                       
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3072                                       
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y2[1] (closed_form)               = 0.94898461935558621434849084703605           
y2[1] (numeric)                   = 0.94898461935558621434849084703609           
absolute error                    = 4e-32                                        
relative error                    = 4.2150314329817319509012309187414e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.31532236239526866544753855243804           
y1[1] (numeric)                   = 0.31532236239526866544753855243799           
absolute error                    = 5e-32                                        
relative error                    = 1.5856788468850516804239649773277e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2992                                       
Order of pole (three term test)                    = 32.1                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2992                                       
Order of pole (three term test)                    = 32.9                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=2787.5MB, alloc=40.3MB, time=29.87
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y2[1] (closed_form)               = 0.95209034159051576385681622142542           
y2[1] (numeric)                   = 0.95209034159051576385681622142546           
absolute error                    = 4e-32                                        
relative error                    = 4.2012819847723639069921691294771e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.30581690837828932688634248917648           
y1[1] (numeric)                   = 0.30581690837828932688634248917643           
absolute error                    = 5e-32                                        
relative error                    = 1.6349651909419936926311241884046e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2912                                       
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2912                                       
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2828.2MB, alloc=40.3MB, time=30.31
x[1]                              = 1.27                                         
y2[1] (closed_form)               = 0.95510085558469223509018174218289           
y2[1] (numeric)                   = 0.95510085558469223509018174218293           
absolute error                    = 4e-32                                        
relative error                    = 4.1880393851718265828985925974564e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.29628087292531873355113701608796           
y1[1] (numeric)                   = 0.2962808729253187335511370160879            
absolute error                    = 6e-32                                        
relative error                    = 2.0251054145882627970179539519263e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.283                                        
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.283                                        
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y2[1] (closed_form)               = 0.95801586028922496370075385916029           
y2[1] (numeric)                   = 0.95801586028922496370075385916033           
absolute error                    = 4e-32                                        
relative error                    = 4.1752962198270914871708018059787e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.28671520963195551277938689359259           
y1[1] (numeric)                   = 0.28671520963195551277938689359253           
absolute error                    = 6e-32                                        
relative error                    = 2.0926688917905514995231059523809e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2747                                       
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2747                                       
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2869.0MB, alloc=40.3MB, time=30.75
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y2[1] (closed_form)               = 0.96083506420607265890556129128537           
y2[1] (numeric)                   = 0.96083506420607265890556129128542           
absolute error                    = 5e-32                                        
relative error                    = 5.2038067575431840246021127215095e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.27712087505655764138660609006118           
y1[1] (numeric)                   = 0.27712087505655764138660609006113           
absolute error                    = 5e-32                                        
relative error                    = 1.8042668200219666751104385620871e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2663                                       
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2663                                       
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y2[1] (closed_form)               = 0.96355818541719296470134863003955           
y2[1] (numeric)                   = 0.9635581854171929647013486300396            
absolute error                    = 5e-32                                        
relative error                    = 5.1891002283740072132667345810900e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.26749882862458740699798410929287           
y1[1] (numeric)                   = 0.26749882862458740699798410929281           
absolute error                    = 6e-32                                        
relative error                    = 2.2430004762452647031662010378488e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2578                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2578                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2909.7MB, alloc=40.3MB, time=31.19
 
TOP MAIN SOLVE Loop
x[1]                              = 1.31                                         
y2[1] (closed_form)               = 0.9661849516127340291692578059375            
y2[1] (numeric)                   = 0.96618495161273402916925780593754           
absolute error                    = 4e-32                                        
relative error                    = 4.1399941008430017803635909710632e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.2578500325326696613381769786162            
y1[1] (numeric)                   = 0.25785003253266966133817697861613           
absolute error                    = 7e-32                                        
relative error                    = 2.7147562989401982375082344868540e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2491                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2491                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2950.4MB, alloc=40.3MB, time=31.63
x[1]                              = 1.32                                         
y2[1] (closed_form)               = 0.96871510011826526273589984597277           
y2[1] (numeric)                   = 0.96871510011826526273589984597281           
absolute error                    = 4e-32                                        
relative error                    = 4.1291810146364615586356910988074e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.24817545165237295957398272942735           
y1[1] (numeric)                   = 0.24817545165237295957398272942729           
absolute error                    = 6e-32                                        
relative error                    = 2.4176444366481443149116142792461e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2404                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2404                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y2[1] (closed_form)               = 0.9711483779210445623376830377638            
y2[1] (numeric)                   = 0.97114837792104456233768303776383           
absolute error                    = 3e-32                                        
relative error                    = 3.0891263046972862465940813612778e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.23847605343372320751578498601058           
y1[1] (numeric)                   = 0.23847605343372320751578498601052           
absolute error                    = 6e-32                                        
relative error                    = 2.5159758867225250007737051484604e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2316                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2316                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=2991.2MB, alloc=40.3MB, time=32.06
x[1]                              = 1.34                                         
y2[1] (closed_form)               = 0.97348454169531937478787034808955           
y2[1] (numeric)                   = 0.97348454169531937478787034808959           
absolute error                    = 4e-32                                        
relative error                    = 4.1089507112604132872534585579640e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.22875280780845946523263949230014           
y1[1] (numeric)                   = 0.22875280780845946523263949230009           
absolute error                    = 5e-32                                        
relative error                    = 2.1857655203894270738370516051356e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2227                                       
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2227                                       
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y2[1] (closed_form)               = 0.97572335782665906926111353926522           
y2[1] (numeric)                   = 0.97572335782665906926111353926525           
absolute error                    = 3e-32                                        
relative error                    = 3.0746419832382052117105986469068e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.21900668709304158142002217301063           
y1[1] (numeric)                   = 0.21900668709304158142002217301057           
absolute error                    = 6e-32                                        
relative error                    = 2.7396423733175751892052047086449e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2137                                       
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2137                                       
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3031.9MB, alloc=40.3MB, time=32.50
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y2[1] (closed_form)               = 0.97786460243531618567849243942663           
y2[1] (numeric)                   = 0.97786460243531618567849243942666           
absolute error                    = 3e-32                                        
relative error                    = 3.0679093941315296578650955118218e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.20923866589141935767597525239186           
y1[1] (numeric)                   = 0.2092386658914193576759752523918            
absolute error                    = 6e-32                                        
relative error                    = 2.8675388339139918263265268198604e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2046                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2046                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=3072.5MB, alloc=40.3MB, time=32.92
x[1]                              = 1.37                                         
y2[1] (closed_form)               = 0.97990806139861422288768850489193           
y2[1] (numeric)                   = 0.97990806139861422288768850489196           
absolute error                    = 3e-32                                        
relative error                    = 3.0615117052084725025716087432751e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.19944972099757296568819838964531           
y1[1] (numeric)                   = 0.19944972099757296568819838964525           
absolute error                    = 6e-32                                        
relative error                    = 3.0082769582179620667255642504104e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1954                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1954                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y2[1] (closed_form)               = 0.98185353037235972787813108520605           
y2[1] (numeric)                   = 0.98185353037235972787813108520608           
absolute error                    = 3e-32                                        
relative error                    = 3.0554455498696176470477246956131e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.1896408312978343632091500735982            
y1[1] (numeric)                   = 0.18964083129783436320915007359815           
absolute error                    = 5e-32                                        
relative error                    = 2.6365630048032268768302730981699e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1862                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1862                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=3113.3MB, alloc=40.3MB, time=33.36
x[1]                              = 1.39                                         
y2[1] (closed_form)               = 0.98370081481127654484003822444291           
y2[1] (numeric)                   = 0.98370081481127654484003822444294           
absolute error                    = 3e-32                                        
relative error                    = 3.0497077514117454340774764863295e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.17981297767299947659616321780405           
y1[1] (numeric)                   = 0.179812977672999476596163217804             
absolute error                    = 5e-32                                        
relative error                    = 2.7806669266624322323962265308107e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1769                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1769                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y2[1] (closed_form)               = 0.9854497299884601806594745788061            
y2[1] (numeric)                   = 0.98544972998846018065947457880612           
absolute error                    = 2e-32                                        
relative error                    = 2.0295302125897588018004976959041e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.16996714290024093861674803520365           
y1[1] (numeric)                   = 0.1699671429002409386167480352036            
absolute error                    = 5e-32                                        
relative error                    = 2.9417450424136724134971351549225e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1675                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1675                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3154.0MB, alloc=40.3MB, time=33.80
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y2[1] (closed_form)               = 0.98710010101385034142908886194224           
y2[1] (numeric)                   = 0.98710010101385034142908886194226           
absolute error                    = 2e-32                                        
relative error                    = 2.0261369621437586209832755845826e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.16010431155483119016356254936092           
y1[1] (numeric)                   = 0.16010431155483119016356254936086           
absolute error                    = 6e-32                                        
relative error                    = 3.7475567907770990973978279727178e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.158                                        
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.158                                        
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y2[1] (closed_form)               = 0.9886517628517197927362734733357            
y2[1] (numeric)                   = 0.98865176285171979273627347333572           
absolute error                    = 2e-32                                        
relative error                    = 2.0229569957282971866932254129557e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.15022546991168577348698210297591           
y1[1] (numeric)                   = 0.15022546991168577348698210297586           
absolute error                    = 5e-32                                        
relative error                    = 3.3283304109079434121197294153812e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1485                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1485                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3194.7MB, alloc=40.3MB, time=34.23
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y2[1] (closed_form)               = 0.99010456033717779485729149548183           
y2[1] (numeric)                   = 0.99010456033717779485729149548184           
absolute error                    = 1e-32                                        
relative error                    = 1.0099943380317855886696377570990e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.14033160584673666253389762457492           
y1[1] (numeric)                   = 0.14033160584673666253389762457487           
absolute error                    = 5e-32                                        
relative error                    = 3.5629892281434848002882724662369e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1389                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1389                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=3235.3MB, alloc=40.3MB, time=34.67
x[1]                              = 1.44                                         
y2[1] (closed_form)               = 0.99145834819168646252760446395798           
y2[1] (numeric)                   = 0.99145834819168646252760446395799           
absolute error                    = 1e-32                                        
relative error                    = 1.0086152401902637593773109568671e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.13042370873814549297752015612917           
y1[1] (numeric)                   = 0.13042370873814549297752015612912           
absolute error                    = 5e-32                                        
relative error                    = 3.8336588097173408686830180087611e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1293                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1293                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y2[1] (closed_form)               = 0.99271299103758849766535413432301           
y2[1] (numeric)                   = 0.99271299103758849766535413432301           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.12050276936736657053286662724802           
y1[1] (numeric)                   = 0.12050276936736657053286662724796           
absolute error                    = 6e-32                                        
relative error                    = 4.9791386799653616169897353061117e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1196                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1196                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3276.0MB, alloc=40.3MB, time=35.09
 
TOP MAIN SOLVE Loop
x[1]                              = 1.46                                         
y2[1] (closed_form)               = 0.99386836341164484228683230125003           
y2[1] (numeric)                   = 0.99386836341164484228683230125003           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.11056977982006955117464810912337           
y1[1] (numeric)                   = 0.11056977982006955117464810912332           
absolute error                    = 5e-32                                        
relative error                    = 4.5220312531475699145020520997350e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1099                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1099                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y2[1] (closed_form)               = 0.99492434977758089785992846273557           
y2[1] (numeric)                   = 0.99492434977758089785992846273556           
absolute error                    = 1e-32                                        
relative error                    = 1.0051015438747215131966719658863e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.10062573338693170090697460146241           
y1[1] (numeric)                   = 0.10062573338693170090697460146235           
absolute error                    = 6e-32                                        
relative error                    = 5.9626894612817024127037048144372e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1001                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1001                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3316.7MB, alloc=40.3MB, time=35.53
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y2[1] (closed_form)               = 0.99588084453764005648407513256269           
y2[1] (numeric)                   = 0.99588084453764005648407513256268           
absolute error                    = 1e-32                                        
relative error                    = 1.0041361930846981533387529555869e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.090671624464309655776226540647838          
y1[1] (numeric)                   = 0.090671624464309655776226540647782          
absolute error                    = 5.6e-32                                      
relative error                    = 6.1761328674598557348159486713071e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.0903                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.0903                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=3357.3MB, alloc=40.3MB, time=35.97
x[1]                              = 1.49                                         
y2[1] (closed_form)               = 0.9967377520431433885532007170437            
y2[1] (numeric)                   = 0.99673775204314338855320071704369           
absolute error                    = 1e-32                                        
relative error                    = 1.0032729250499136370322465272319e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.080708448454800614868318484563714          
y1[1] (numeric)                   = 0.080708448454800614868318484563658          
absolute error                    = 5.6e-32                                      
relative error                    = 6.9385548938364044366907287842106e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.08045                                      
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.08045                                      
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y2[1] (closed_form)               = 0.99749498660405443094172337114149           
y2[1] (numeric)                   = 0.99749498660405443094172337114148           
absolute error                    = 1e-32                                        
relative error                    = 1.0025113042467249099541836495087e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.070737201667702910088189851434269          
y1[1] (numeric)                   = 0.070737201667702910088189851434213          
absolute error                    = 5.6e-32                                      
relative error                    = 7.9166264256631457258770079231438e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.07056                                      
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.07056                                      
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3398.1MB, alloc=40.3MB, time=36.41
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y2[1] (closed_form)               = 0.99815247249754811924273786483671           
y2[1] (numeric)                   = 0.9981524724975481192427378648367            
absolute error                    = 1e-32                                        
relative error                    = 1.0018509471782693190283423781766e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.060758881219385906581595514916193          
y1[1] (numeric)                   = 0.060758881219385906581595514916138          
absolute error                    = 5.5e-32                                      
relative error                    = 9.0521745786279453292241481843831e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.06065                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.06065                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.52                                         
y2[1] (closed_form)               = 0.99871014397558300717231239411685           
y2[1] (numeric)                   = 0.99871014397558300717231239411683           
absolute error                    = 2e-32                                        
relative error                    = 2.0025830438034451924195109967198e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
y1[1] (closed_form)               = 0.050774484933579196726129270152727          
y1[1] (numeric)                   = 0.050774484933579196726129270152672          
absolute error                    = 5.5e-32                                      
relative error                    = 1.0832212295594612961736459614467e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.05071                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.05071                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
memory used=3438.7MB, alloc=40.3MB, time=36.84
SETTING H FOR POLE
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5295732321116218510026700794348            
y2[1] (closed_form)               = 0.9991504485492368314872334919759            
y2[1] (numeric)                   = 0.99915044854923683148723349197587           
absolute error                    = 3e-32                                        
relative error                    = 3.0025508214063158789389891578347e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.0045732321116218510026700794348199         
y1[1] (closed_form)               = 0.04121142030868195182202719513867           
y1[1] (numeric)                   = 0.041211420308681951822027195138595          
absolute error                    = 7.5e-32                                      
relative error                    = 1.8198838923345686225977498795070e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.0045732321116218510026700794348199         
SETTING H FOR POLE
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5336908730202989210390622783871            
y2[1] (closed_form)               = 0.99931167163057903777854626965503           
y2[1] (numeric)                   = 0.999311671630579037778546269655             
absolute error                    = 3e-32                                        
relative error                    = 3.0020664074751508165134020474147e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.0041176409086770700363921989522893         
y1[1] (closed_form)               = 0.037096939805026704146663979007538          
y1[1] (numeric)                   = 0.037096939805026704146663979007474          
absolute error                    = 6.4e-32                                      
relative error                    = 1.7252096894344875665527210397133e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.0041176409086770700363921989522893         
SETTING H FOR POLE
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.03707                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.03707                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
memory used=3481.1MB, alloc=40.3MB, time=37.28
SETTING H FOR POLE
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5407353617914117549724962276967            
y2[1] (closed_form)               = 0.99954820321568465118431041079522           
y2[1] (numeric)                   = 0.99954820321568465118431041079519           
absolute error                    = 3e-32                                        
relative error                    = 3.0013560029907367833215011270472e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.003337348278218813680713169219794          
y1[1] (closed_form)               = 0.03005643771800610341852530438231           
y1[1] (numeric)                   = 0.03005643771800610341852530438221           
absolute error                    = 1.00e-31                                     
relative error                    = 3.3270742507217466080616613707843e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.003337348278218813680713169219794          
SETTING H FOR POLE
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.03004                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.03004                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
SETTING H FOR POLE
memory used=3523.6MB, alloc=40.3MB, time=37.72
SETTING H FOR POLE
SETTING H FOR POLE
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5510693699425273269041131743915            
y2[1] (closed_form)               = 0.9998054298965872994841890101891            
y2[1] (numeric)                   = 0.99980542989658729948418901018908           
absolute error                    = 2e-32                                        
relative error                    = 2.0003892159366104371954757793603e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.0021911042091072126909989137502644         
y1[1] (closed_form)               = 0.019725677410427734221698583194151          
y1[1] (numeric)                   = 0.019725677410427734221698583194092          
absolute error                    = 5.9e-32                                      
relative error                    = 2.9910252901535530143010379398709e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.0021911042091072126909989137502644         
SETTING H FOR POLE
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.01972                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.01972                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
SETTING H FOR POLE
memory used=3566.2MB, alloc=40.3MB, time=38.16
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3608.7MB, alloc=40.3MB, time=38.59
SETTING H FOR POLE
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5603114716964416830381220255679            
y2[1] (closed_form)               = 0.99994503441032559051241859697847           
y2[1] (numeric)                   = 0.99994503441032559051241859697843           
absolute error                    = 4e-32                                        
relative error                    = 4.0002198744442261191720263494896e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.0011648667879042852165529374958281         
y1[1] (closed_form)               = 0.010484662995669947598371910527873          
y1[1] (numeric)                   = 0.010484662995669947598371910527808          
absolute error                    = 6.5e-32                                      
relative error                    = 6.1995316422515723086665498240414e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.0011648667879042852165529374958281         
SETTING H FOR POLE
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.01048                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.01048                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
SETTING H FOR POLE
memory used=3651.3MB, alloc=40.3MB, time=39.03
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3693.8MB, alloc=40.3MB, time=39.47
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3736.4MB, alloc=40.3MB, time=39.91
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3778.8MB, alloc=40.3MB, time=40.34
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3821.3MB, alloc=40.3MB, time=40.78
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3863.9MB, alloc=40.3MB, time=41.23
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3906.3MB, alloc=40.3MB, time=41.66
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
 
TOP MAIN SOLVE Loop
memory used=3948.8MB, alloc=40.3MB, time=42.09
x[1]                              = 1.5700435890621976307931942460509            
y2[1] (closed_form)               = 0.99999971669296626274002093689073           
y2[1] (numeric)                   = 0.99999971669296626274002093689067           
absolute error                    = 6e-32                                        
relative error                    = 6.0000016998426840009484986699256e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 8.3637482517366379525470504322472e-05        
y1[1] (closed_form)               = 0.00075273766161368901784272512500346        
y1[1] (numeric)                   = 0.00075273766161368901784272512475536        
absolute error                    = 2.4810e-31                                   
relative error                    = 3.2959690029077740269534117620798e-26      % 
Desired digits                    = 8                                   
Estimated correct digits          = 9                                   
Correct digits                    = 32                                  
h                                 = 8.3637482517366379525470504322472e-05        
SETTING H FOR POLE
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.0007527                                    
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.0007527                                    
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
SETTING H FOR POLE
SETTING H FOR POLE
memory used=3991.4MB, alloc=40.3MB, time=42.53
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4033.9MB, alloc=40.3MB, time=42.97
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4076.3MB, alloc=40.3MB, time=43.41
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4118.8MB, alloc=40.3MB, time=43.84
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4161.3MB, alloc=40.3MB, time=44.27
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4203.8MB, alloc=40.3MB, time=44.70
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4246.3MB, alloc=40.3MB, time=45.14
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4288.7MB, alloc=40.3MB, time=45.58
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4331.3MB, alloc=40.3MB, time=46.02
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4373.9MB, alloc=40.3MB, time=46.45
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4416.4MB, alloc=40.3MB, time=46.89
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4458.9MB, alloc=40.3MB, time=47.33
SETTING H FOR POLE
SETTING H FOR POLE
SETTING H FOR POLE
memory used=4501.4MB, alloc=40.3MB, time=47.75
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4542.8MB, alloc=40.3MB, time=48.19
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4583.7MB, alloc=40.3MB, time=48.64
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4624.7MB, alloc=40.3MB, time=49.08
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4665.7MB, alloc=40.3MB, time=49.52
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4706.6MB, alloc=40.3MB, time=49.95
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4747.5MB, alloc=40.3MB, time=50.39
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4788.4MB, alloc=40.3MB, time=50.84
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4829.4MB, alloc=40.3MB, time=51.28
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4870.3MB, alloc=40.3MB, time=51.73
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4911.4MB, alloc=40.3MB, time=52.17
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4952.2MB, alloc=40.3MB, time=52.61
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=4993.2MB, alloc=40.3MB, time=53.05
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5034.1MB, alloc=40.3MB, time=53.50
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5075.0MB, alloc=40.3MB, time=53.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5115.9MB, alloc=40.3MB, time=54.38
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5156.9MB, alloc=40.3MB, time=54.81
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5197.8MB, alloc=40.3MB, time=55.25
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5238.8MB, alloc=40.3MB, time=55.69
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5279.8MB, alloc=40.3MB, time=56.14
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5320.6MB, alloc=40.3MB, time=56.58
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5361.6MB, alloc=40.3MB, time=57.03
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5402.5MB, alloc=40.3MB, time=57.48
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5443.5MB, alloc=40.3MB, time=57.92
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5484.4MB, alloc=40.3MB, time=58.38
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5525.4MB, alloc=40.3MB, time=58.81
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5566.3MB, alloc=40.3MB, time=59.27
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5607.2MB, alloc=40.3MB, time=59.72
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5648.3MB, alloc=40.3MB, time=60.17
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5689.2MB, alloc=40.3MB, time=60.61
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5730.1MB, alloc=40.3MB, time=61.05
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5771.0MB, alloc=40.3MB, time=61.50
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5811.9MB, alloc=40.3MB, time=61.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5852.9MB, alloc=40.3MB, time=62.38
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5893.8MB, alloc=40.3MB, time=62.81
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5934.7MB, alloc=40.3MB, time=63.25
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=5975.7MB, alloc=40.3MB, time=63.69
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6016.7MB, alloc=40.3MB, time=64.12
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6057.6MB, alloc=40.3MB, time=64.56
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6098.6MB, alloc=40.3MB, time=65.00
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6139.5MB, alloc=40.3MB, time=65.44
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6180.4MB, alloc=40.3MB, time=65.87
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6221.3MB, alloc=40.3MB, time=66.31
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6262.3MB, alloc=40.3MB, time=66.75
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6303.1MB, alloc=40.3MB, time=67.19
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6344.0MB, alloc=40.3MB, time=67.63
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6385.0MB, alloc=40.3MB, time=68.08
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6425.9MB, alloc=40.3MB, time=68.51
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6466.9MB, alloc=40.3MB, time=68.95
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6507.8MB, alloc=40.3MB, time=69.39
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6548.7MB, alloc=40.3MB, time=69.83
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6589.6MB, alloc=40.3MB, time=70.27
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6630.6MB, alloc=40.3MB, time=70.72
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6671.5MB, alloc=40.3MB, time=71.16
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6712.5MB, alloc=40.3MB, time=71.59
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6753.4MB, alloc=40.3MB, time=72.03
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6794.3MB, alloc=40.3MB, time=72.47
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6835.2MB, alloc=40.3MB, time=72.91
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6876.1MB, alloc=40.3MB, time=73.36
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6917.1MB, alloc=40.3MB, time=73.80
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6957.9MB, alloc=40.3MB, time=74.23
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=6999.0MB, alloc=40.3MB, time=74.67
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7039.9MB, alloc=40.3MB, time=75.11
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7080.9MB, alloc=40.3MB, time=75.55
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7121.9MB, alloc=40.3MB, time=76.00
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7162.8MB, alloc=40.3MB, time=76.44
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7203.8MB, alloc=40.3MB, time=76.88
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7244.7MB, alloc=40.3MB, time=77.31
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7285.7MB, alloc=40.3MB, time=77.76
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7326.6MB, alloc=40.3MB, time=78.20
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7367.6MB, alloc=40.3MB, time=78.64
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7408.6MB, alloc=40.3MB, time=79.08
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7449.6MB, alloc=40.3MB, time=79.52
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7490.6MB, alloc=40.3MB, time=79.95
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7531.5MB, alloc=40.3MB, time=80.41
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7572.4MB, alloc=40.3MB, time=80.84
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7613.4MB, alloc=40.3MB, time=81.28
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7654.3MB, alloc=40.3MB, time=81.72
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7695.3MB, alloc=40.3MB, time=82.17
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7736.4MB, alloc=40.3MB, time=82.61
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7777.2MB, alloc=40.3MB, time=83.05
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7818.2MB, alloc=40.3MB, time=83.48
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7859.2MB, alloc=40.3MB, time=83.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7900.2MB, alloc=40.3MB, time=84.38
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7941.1MB, alloc=40.3MB, time=84.81
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=7982.0MB, alloc=40.3MB, time=85.25
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8023.0MB, alloc=40.3MB, time=85.69
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8063.9MB, alloc=40.3MB, time=86.14
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8104.9MB, alloc=40.3MB, time=86.58
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8145.8MB, alloc=40.3MB, time=87.01
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8186.6MB, alloc=40.3MB, time=87.45
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8227.7MB, alloc=40.3MB, time=87.89
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8268.7MB, alloc=40.3MB, time=88.34
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8309.6MB, alloc=40.3MB, time=88.78
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8350.6MB, alloc=40.3MB, time=89.22
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8391.5MB, alloc=40.3MB, time=89.67
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8432.5MB, alloc=40.3MB, time=90.11
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8473.5MB, alloc=40.3MB, time=90.55
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8514.4MB, alloc=40.3MB, time=90.98
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8555.4MB, alloc=40.3MB, time=91.44
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8596.3MB, alloc=40.3MB, time=91.88
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8637.2MB, alloc=40.3MB, time=92.31
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8678.1MB, alloc=40.3MB, time=92.75
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8719.1MB, alloc=40.3MB, time=93.19
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8759.9MB, alloc=40.3MB, time=93.63
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8800.9MB, alloc=40.3MB, time=94.08
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8841.9MB, alloc=40.3MB, time=94.52
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8882.9MB, alloc=40.3MB, time=94.95
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8923.8MB, alloc=40.3MB, time=95.39
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=8964.8MB, alloc=40.3MB, time=95.84
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9005.7MB, alloc=40.3MB, time=96.28
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9046.6MB, alloc=40.3MB, time=96.72
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9087.6MB, alloc=40.3MB, time=97.16
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9128.5MB, alloc=40.3MB, time=97.59
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9169.4MB, alloc=40.3MB, time=98.03
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9210.4MB, alloc=40.3MB, time=98.48
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9251.3MB, alloc=40.3MB, time=98.92
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9292.3MB, alloc=40.3MB, time=99.36
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9333.3MB, alloc=40.3MB, time=99.80
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9374.3MB, alloc=40.3MB, time=100.25
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9415.2MB, alloc=40.3MB, time=100.69
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9456.2MB, alloc=40.3MB, time=101.12
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9497.1MB, alloc=40.3MB, time=101.56
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9538.1MB, alloc=40.3MB, time=102.02
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9579.0MB, alloc=40.3MB, time=102.45
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9619.9MB, alloc=40.3MB, time=102.89
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9660.9MB, alloc=40.3MB, time=103.33
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9701.8MB, alloc=40.3MB, time=103.77
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9742.7MB, alloc=40.3MB, time=104.20
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9783.6MB, alloc=40.3MB, time=104.66
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9824.7MB, alloc=40.3MB, time=105.09
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9865.6MB, alloc=40.3MB, time=105.53
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9906.6MB, alloc=40.3MB, time=105.97
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9947.5MB, alloc=40.3MB, time=106.41
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=9988.4MB, alloc=40.3MB, time=106.86
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10029.3MB, alloc=40.3MB, time=107.30
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10070.3MB, alloc=40.3MB, time=107.73
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10111.2MB, alloc=40.3MB, time=108.17
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10152.1MB, alloc=40.3MB, time=108.61
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10193.0MB, alloc=40.3MB, time=109.06
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10233.9MB, alloc=40.3MB, time=109.50
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10274.9MB, alloc=40.3MB, time=109.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10315.8MB, alloc=40.3MB, time=110.37
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10356.7MB, alloc=40.3MB, time=110.83
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10397.7MB, alloc=40.3MB, time=111.27
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10438.6MB, alloc=40.3MB, time=111.70
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10479.6MB, alloc=40.3MB, time=112.14
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10520.6MB, alloc=40.3MB, time=112.59
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10561.6MB, alloc=40.3MB, time=113.03
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10602.5MB, alloc=40.3MB, time=113.47
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10643.5MB, alloc=40.3MB, time=113.91
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10684.4MB, alloc=40.3MB, time=114.34
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10725.3MB, alloc=40.3MB, time=114.80
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10766.2MB, alloc=40.3MB, time=115.23
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10807.1MB, alloc=40.3MB, time=115.67
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10848.1MB, alloc=40.3MB, time=116.11
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10889.1MB, alloc=40.3MB, time=116.55
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10930.1MB, alloc=40.3MB, time=117.00
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=10970.9MB, alloc=40.3MB, time=117.44
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11011.9MB, alloc=40.3MB, time=117.87
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11052.8MB, alloc=40.3MB, time=118.31
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11093.7MB, alloc=40.3MB, time=118.75
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11134.6MB, alloc=40.3MB, time=119.19
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11175.5MB, alloc=40.3MB, time=119.63
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11216.4MB, alloc=40.3MB, time=120.08
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11257.4MB, alloc=40.3MB, time=120.52
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11298.4MB, alloc=40.3MB, time=120.95
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11339.3MB, alloc=40.3MB, time=121.41
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11380.3MB, alloc=40.3MB, time=121.84
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11421.2MB, alloc=40.3MB, time=122.28
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11462.2MB, alloc=40.3MB, time=122.72
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11503.1MB, alloc=40.3MB, time=123.16
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11544.1MB, alloc=40.3MB, time=123.61
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11585.0MB, alloc=40.3MB, time=124.05
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11625.9MB, alloc=40.3MB, time=124.48
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11667.0MB, alloc=40.3MB, time=124.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11707.9MB, alloc=40.3MB, time=125.37
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11748.9MB, alloc=40.3MB, time=125.81
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11789.7MB, alloc=40.3MB, time=126.25
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11830.7MB, alloc=40.3MB, time=126.69
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11871.6MB, alloc=40.3MB, time=127.12
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11912.6MB, alloc=40.3MB, time=127.58
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11953.5MB, alloc=40.3MB, time=128.02
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=11994.4MB, alloc=40.3MB, time=128.45
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12035.4MB, alloc=40.3MB, time=128.89
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12076.3MB, alloc=40.3MB, time=129.33
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12117.3MB, alloc=40.3MB, time=129.77
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12158.2MB, alloc=40.3MB, time=130.22
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12199.2MB, alloc=40.3MB, time=130.66
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12240.1MB, alloc=40.3MB, time=131.09
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12281.1MB, alloc=40.3MB, time=131.53
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12322.1MB, alloc=40.3MB, time=131.98
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12363.1MB, alloc=40.3MB, time=132.42
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12404.1MB, alloc=40.3MB, time=132.86
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12445.0MB, alloc=40.3MB, time=133.30
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12486.0MB, alloc=40.3MB, time=133.73
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12527.0MB, alloc=40.3MB, time=134.19
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12568.0MB, alloc=40.3MB, time=134.62
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12608.9MB, alloc=40.3MB, time=135.06
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12649.8MB, alloc=40.3MB, time=135.50
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12690.8MB, alloc=40.3MB, time=135.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12731.8MB, alloc=40.3MB, time=136.38
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12772.8MB, alloc=40.3MB, time=136.81
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12813.7MB, alloc=40.3MB, time=137.25
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12854.6MB, alloc=40.3MB, time=137.70
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12895.6MB, alloc=40.3MB, time=138.14
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12936.5MB, alloc=40.3MB, time=138.58
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=12977.5MB, alloc=40.3MB, time=139.02
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13018.4MB, alloc=40.3MB, time=139.45
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13059.4MB, alloc=40.3MB, time=139.89
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13100.4MB, alloc=40.3MB, time=140.34
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13141.4MB, alloc=40.3MB, time=140.78
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13182.3MB, alloc=40.3MB, time=141.22
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13223.2MB, alloc=40.3MB, time=141.66
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13264.2MB, alloc=40.3MB, time=142.09
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13305.2MB, alloc=40.3MB, time=142.53
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13346.0MB, alloc=40.3MB, time=142.98
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13387.1MB, alloc=40.3MB, time=143.42
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13428.0MB, alloc=40.3MB, time=143.86
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13469.1MB, alloc=40.3MB, time=144.30
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13510.0MB, alloc=40.3MB, time=144.73
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13550.8MB, alloc=40.3MB, time=145.17
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13591.7MB, alloc=40.3MB, time=145.61
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13632.7MB, alloc=40.3MB, time=146.06
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13673.7MB, alloc=40.3MB, time=146.50
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13714.6MB, alloc=40.3MB, time=146.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13755.5MB, alloc=40.3MB, time=147.38
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13796.5MB, alloc=40.3MB, time=147.81
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13837.5MB, alloc=40.3MB, time=148.25
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13878.5MB, alloc=40.3MB, time=148.69
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13919.4MB, alloc=40.3MB, time=149.14
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=13960.4MB, alloc=40.3MB, time=149.58
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14001.4MB, alloc=40.3MB, time=150.02
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14042.4MB, alloc=40.3MB, time=150.47
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14083.3MB, alloc=40.3MB, time=150.91
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14124.3MB, alloc=40.3MB, time=151.34
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14165.3MB, alloc=40.3MB, time=151.78
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14206.2MB, alloc=40.3MB, time=152.22
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14247.1MB, alloc=40.3MB, time=152.66
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14287.9MB, alloc=40.3MB, time=153.09
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14329.0MB, alloc=40.3MB, time=153.55
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14369.9MB, alloc=40.3MB, time=153.98
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14410.9MB, alloc=40.3MB, time=154.42
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14451.8MB, alloc=40.3MB, time=154.86
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14492.8MB, alloc=40.3MB, time=155.30
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14533.7MB, alloc=40.3MB, time=155.75
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14574.7MB, alloc=40.3MB, time=156.19
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14615.7MB, alloc=40.3MB, time=156.63
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14656.6MB, alloc=40.3MB, time=157.06
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14697.5MB, alloc=40.3MB, time=157.50
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14738.4MB, alloc=40.3MB, time=157.94
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14779.4MB, alloc=40.3MB, time=158.38
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14820.3MB, alloc=40.3MB, time=158.83
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14861.3MB, alloc=40.3MB, time=159.27
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14902.2MB, alloc=40.3MB, time=159.70
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14943.2MB, alloc=40.3MB, time=160.14
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=14984.2MB, alloc=40.3MB, time=160.59
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=15025.1MB, alloc=40.3MB, time=161.03
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=15066.1MB, alloc=40.3MB, time=161.48
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
SETTING H FOR POLE
SETTING H FOR MIN H
memory used=15107.1MB, alloc=40.3MB, time=161.92
SETTING H FOR POLE
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memory used=15148.1MB, alloc=40.3MB, time=162.36
SETTING H FOR POLE
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memory used=15189.0MB, alloc=40.3MB, time=162.80
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memory used=15230.1MB, alloc=40.3MB, time=163.23
SETTING H FOR POLE
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memory used=15271.0MB, alloc=40.3MB, time=163.69
SETTING H FOR POLE
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memory used=15312.0MB, alloc=40.3MB, time=164.12
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memory used=15353.0MB, alloc=40.3MB, time=164.56
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memory used=15393.9MB, alloc=40.3MB, time=165.00
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memory used=15434.8MB, alloc=40.3MB, time=165.44
SETTING H FOR POLE
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memory used=15475.7MB, alloc=40.3MB, time=165.89
SETTING H FOR POLE
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memory used=15516.6MB, alloc=40.3MB, time=166.33
SETTING H FOR POLE
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memory used=15557.5MB, alloc=40.3MB, time=166.76
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memory used=15598.5MB, alloc=40.3MB, time=167.20
SETTING H FOR POLE
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memory used=15639.5MB, alloc=40.3MB, time=167.66
SETTING H FOR POLE
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memory used=15680.5MB, alloc=40.3MB, time=168.09
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memory used=15721.5MB, alloc=40.3MB, time=168.53
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memory used=15762.5MB, alloc=40.3MB, time=169.00
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memory used=15803.4MB, alloc=40.3MB, time=169.44
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memory used=15844.4MB, alloc=40.3MB, time=169.88
SETTING H FOR POLE
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memory used=15885.2MB, alloc=40.3MB, time=170.31
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memory used=15926.1MB, alloc=40.3MB, time=170.75
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memory used=15967.1MB, alloc=40.3MB, time=171.19
SETTING H FOR POLE
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memory used=16007.9MB, alloc=40.3MB, time=171.64
SETTING H FOR POLE
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memory used=16048.9MB, alloc=40.3MB, time=172.08
SETTING H FOR POLE
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memory used=16089.9MB, alloc=40.3MB, time=172.52
SETTING H FOR POLE
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memory used=16130.9MB, alloc=40.3MB, time=172.95
SETTING H FOR POLE
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memory used=16171.9MB, alloc=40.3MB, time=173.39
SETTING H FOR POLE
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memory used=16212.9MB, alloc=40.3MB, time=173.83
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memory used=16253.8MB, alloc=40.3MB, time=174.28
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memory used=16294.8MB, alloc=40.3MB, time=174.72
SETTING H FOR POLE
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memory used=16335.8MB, alloc=40.3MB, time=175.16
SETTING H FOR POLE
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memory used=16376.8MB, alloc=40.3MB, time=175.59
SETTING H FOR POLE
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memory used=16417.9MB, alloc=40.3MB, time=176.05
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memory used=16458.9MB, alloc=40.3MB, time=176.48
SETTING H FOR POLE
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memory used=16499.9MB, alloc=40.3MB, time=176.94
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memory used=16540.8MB, alloc=40.3MB, time=177.37
SETTING H FOR POLE
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memory used=16581.9MB, alloc=40.3MB, time=177.81
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memory used=16622.9MB, alloc=40.3MB, time=178.25
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memory used=16663.8MB, alloc=40.3MB, time=178.69
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memory used=16704.8MB, alloc=40.3MB, time=179.14
SETTING H FOR POLE
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memory used=16745.7MB, alloc=40.3MB, time=179.58
SETTING H FOR POLE
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memory used=16786.7MB, alloc=40.3MB, time=180.02
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Finished!
Maximum Time Reached before Solution Completed!
diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; 
diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; 
Iterations                       = 1434                                
Total Elapsed Time               = 3 Minutes 0 Seconds
Elapsed Time(since restart)      = 3 Minutes 0 Seconds
Expected Time Remaining          = 6 Minutes 59 Seconds
Optimized Time Remaining         = 6 Minutes 59 Seconds
Expected Total Time              = 9 Minutes 59 Seconds
Time to Timeout                  0.0 Seconds
Percent Done                     = 30.04                                      % 
> quit
memory used=16814.0MB, alloc=40.3MB, time=180.31