|\^/|     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_y1 := proc(x)
> return(c(1.0) +	sin(c(x)));
> end;
          exact_soln_y1 := proc(x) return c(1.0) + sin(c(x)) end proc

> exact_soln_y2 := proc(x)
> return(c(1.0) +	sin(c(x)));
> end;
          exact_soln_y2 := proc(x) return c(1.0) + 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_y2ppp := proc(x)
> return(	neg(cos(c(x))));
> end;
           exact_soln_y2ppp := proc(x) return neg(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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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)*38*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)*38*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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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)*38*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)*38*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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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 - 4 - 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 - 4 - 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 - 4 - 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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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 - 14;
    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 - 14;
    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 - 14;
    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_4,
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_3,
#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,
> 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 add CONST FULL $eq_no = 1 i = 1
>     array_tmp1[1] := array_const_0D0[1] + array_y1[1];
>     #emit pre sub FULL - CONST $eq_no = 1 i = 1
>     array_tmp2[1] := array_tmp1[1] - array_const_1D0[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,5]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp2[1]) * (expt((glob_h) , c(4))) * c(factorial_3(0,4));
>             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);
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y2_higher[5,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #emit pre diff $eq_no = 2 i = 1 order_d = 3
>     array_tmp4[1] := array_y2_higher[4,1];
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[1] :=  neg(array_tmp4[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 add CONST FULL $eq_no = 1 i = 2
>     array_tmp1[2] := array_y1[2];
>     #emit pre sub FULL CONST $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,6]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp2[2]) * (expt((glob_h) , c(4))) * c(factorial_3(1,5));
>             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);
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y2_higher[5,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #emit pre diff $eq_no = 2 i = 2 order_d = 3
>     array_tmp4[2] := array_y2_higher[4,2];
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[2] :=  neg(array_tmp4[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 add CONST FULL $eq_no = 1 i = 3
>     array_tmp1[3] := array_y1[3];
>     #emit pre sub FULL CONST $eq_no = 1 i = 3
>     array_tmp2[3] := array_tmp1[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,7]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp2[3]) * (expt((glob_h) , c(4))) * c(factorial_3(2,6));
>             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);
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[5,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #emit pre diff $eq_no = 2 i = 3 order_d = 3
>     array_tmp4[3] := array_y2_higher[4,3];
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[3] :=  neg(array_tmp4[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 add CONST FULL $eq_no = 1 i = 4
>     array_tmp1[4] := array_y1[4];
>     #emit pre sub FULL CONST $eq_no = 1 i = 4
>     array_tmp2[4] := array_tmp1[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,8]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp2[4]) * (expt((glob_h) , c(4))) * c(factorial_3(3,7));
>             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);
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[5,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #emit pre diff $eq_no = 2 i = 4 order_d = 3
>     array_tmp4[4] := array_y2_higher[4,4];
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[4] :=  neg(array_tmp4[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 add CONST FULL $eq_no = 1 i = 5
>     array_tmp1[5] := array_y1[5];
>     #emit pre sub FULL CONST $eq_no = 1 i = 5
>     array_tmp2[5] := array_tmp1[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,9]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp2[5]) * (expt((glob_h) , c(4))) * c(factorial_3(4,8));
>             if (9 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[9] := temporary;
>                 array_y2_higher[1,9] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(8);
>             array_y2_higher[2,8] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(7);
>             array_y2_higher[3,7] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(6);
>             array_y2_higher[4,6] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_higher[5,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #emit pre diff $eq_no = 2 i = 5 order_d = 3
>     array_tmp4[5] := array_y2_higher[4,5];
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[5] :=  neg(array_tmp4[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 NOT FULL - FULL add $eq_no = 1
>         array_tmp1[kkk] := array_y1[kkk];
>         #emit FULL - NOT FULL sub $eq_no = 1
>         array_tmp2[kkk] := array_tmp1[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 4;
>         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_tmp2[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 diff $eq_no = 2
>         if (kkk <= ATS_MAX_TERMS) then # if number 1
>             array_tmp4[kkk] :=  array_y2_higher[4,kkk];
>         fi;# end if 1;
>         #emit neg FULL $eq_no = 2
>         array_tmp5[kkk] := neg(array_tmp4[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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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] := array_const_0D0[1] + array_y1[1];
    array_tmp2[1] := array_tmp1[1] - array_const_1D0[1];
    if not array_y2_set_initial[1, 5] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp2[1])*expt(glob_h, c(4))*c(factorial_3(0, 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);
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y2_higher[5, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp4[1] := array_y2_higher[4, 1];
    array_tmp5[1] := neg(array_tmp4[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] := array_y1[2];
    array_tmp2[2] := array_tmp1[2];
    if not array_y2_set_initial[1, 6] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp2[2])*expt(glob_h, c(4))*c(factorial_3(1, 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);
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y2_higher[5, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp4[2] := array_y2_higher[4, 2];
    array_tmp5[2] := neg(array_tmp4[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] := array_y1[3];
    array_tmp2[3] := array_tmp1[3];
    if not array_y2_set_initial[1, 7] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp2[3])*expt(glob_h, c(4))*c(factorial_3(2, 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);
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[5, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp4[3] := array_y2_higher[4, 3];
    array_tmp5[3] := neg(array_tmp4[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] := array_y1[4];
    array_tmp2[4] := array_tmp1[4];
    if not array_y2_set_initial[1, 8] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp2[4])*expt(glob_h, c(4))*c(factorial_3(3, 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);
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[5, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp4[4] := array_y2_higher[4, 4];
    array_tmp5[4] := neg(array_tmp4[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] := array_y1[5];
    array_tmp2[5] := array_tmp1[5];
    if not array_y2_set_initial[1, 9] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp2[5])*expt(glob_h, c(4))*c(factorial_3(4, 8));
            if 9 <= ATS_MAX_TERMS then
                array_y2[9] := temporary;
                array_y2_higher[1, 9] := temporary
            end if;
            temporary := c(temporary)*c(8)/c(glob_h);
            array_y2_higher[2, 8] := c(temporary);
            temporary := c(temporary)*c(7)/c(glob_h);
            array_y2_higher[3, 7] := c(temporary);
            temporary := c(temporary)*c(6)/c(glob_h);
            array_y2_higher[4, 6] := c(temporary);
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[5, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    array_tmp4[5] := array_y2_higher[4, 5];
    array_tmp5[5] := neg(array_tmp4[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] := array_y1[kkk];
        array_tmp2[kkk] := array_tmp1[kkk];
        order_d := 4;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y2_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp2[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;
        if kkk <= ATS_MAX_TERMS then
            array_tmp4[kkk] := array_y2_higher[4, kkk]
        end if;
        array_tmp5[kkk] := neg(array_tmp4[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_4,
>     array_const_0D0,
>     array_const_1D0,
>     array_const_1,
>     array_const_3,
>     #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,
>     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:= 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..(5) ,(0..40+ 1),[]);
>     array_y2_higher_work := Array(0..(5) ,(0..40+ 1),[]);
>     array_y2_higher_work2 := Array(0..(5) ,(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[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 <=5) 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 <=5) 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 <=5) 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);
>     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_4);
>     array_const_4[1]   := c(4);
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := c(0.0);
>     zero_ats_ar(array_const_1D0);
>     array_const_1D0[1]   := c(1.0);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := c(1);
>     zero_ats_ar(array_const_3);
>     array_const_3[1]   := c(3);
>     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] := true;
>     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/mtest8postode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y2  ,  x  ,  4  )   =  y1  -  1.0  ; ");
>     omniout_str(ALWAYS,"diff  (  y1  ,  x  ,  1  )   =  neg ( diff  (  y2  ,  x  ,  3  )  )    ; ");
>     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(1.4);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     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,"array_y2_init[3 + 1] := exact_soln_y2ppp(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(0.001);");
>     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_y1 := proc(x)");
>     omniout_str(ALWAYS,"return(c(1.0) +	sin(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
>     omniout_str(ALWAYS,"return(c(1.0) +	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_y2ppp := proc(x)");
>     omniout_str(ALWAYS,"return(	neg(cos(c(x))));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     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(1.4);
>     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);
>     array_y2_init[3 + 1] := exact_soln_y2ppp(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(0.001);
>     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 := 4;
>             #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 <= 5) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 5 + 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 := 4;
>         #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 <= 5) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 5 + 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  := 5;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y2
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 5;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5;
>             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 := 4;
>             calc_term := 2;
>             #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 := 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 := 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 := 3;
>             #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 := 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 := 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 := 4;
>             #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 := 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 := 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 := 5;
>             #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 := 5;
>             #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  ,  4  )   =  y1  -  1.0  ; ");
>         omniout_str(INFO,"diff  (  y1  ,  x  ,  1  )   =  neg ( diff  (  y2  ,  x  ,  3  )  )    ; ");
>         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,"2015-05-02T18:04:21-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"mtest8.ode.txt\">mtest8</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y2  ,  x  ,  4  )   =  y1  -  1.0  ; ")
>             ;
>             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.mtest8.mxt.txt\">mtest8 diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.mtest8.mxt.txt\">mtest8 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 ( diff  (  y2  ,  x  ,  3  )  )    ; ")
>             ;
>             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_4, array_const_0D0, array_const_1D0,
array_const_1, array_const_3, 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, 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 := 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 .. 5, 0 .. 41, []);
    array_y2_higher_work := Array(0 .. 5, 0 .. 41, []);
    array_y2_higher_work2 := Array(0 .. 5, 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[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 <= 5 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 <= 5 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 <= 5 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);
    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_4);
    array_const_4[1] := c(4);
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := c(0.);
    zero_ats_ar(array_const_1D0);
    array_const_1D0[1] := c(1.0);
    zero_ats_ar(array_const_1);
    array_const_1[1] := c(1);
    zero_ats_ar(array_const_3);
    array_const_3[1] := c(3);
    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] := true;
    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/mtest8postode.ode#################");
    omniout_str(ALWAYS, "diff  (  y2  ,  x  ,  4  )   =  y1  -  1.0  ; ");
    omniout_str(ALWAYS, "diff  (  y1  ,  x  ,  1  )   =  neg ( diff  (  y\
        2  ,  x  ,  3  )  )    ; ");
    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(1.4);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    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,
        "array_y2_init[3 + 1] := exact_soln_y2ppp(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(0.001);");
    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_y1 := proc(x)");
    omniout_str(ALWAYS, "return(c(1.0) +\tsin(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
    omniout_str(ALWAYS, "return(c(1.0) +\tsin(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
    omniout_str(ALWAYS, "return(\tcos(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_y2ppp := proc(x)");
    omniout_str(ALWAYS, "return(\tneg(cos(c(x))));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    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(1.4);
    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);
    array_y2_init[4] := exact_soln_y2ppp(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(0.001);
    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 := 4;
            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 <= 5 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 5 + 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 := 4;
        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 <= 5 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 5 + 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 := 5;
            ord := 5;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[5, iii] := array_y2_higher[5, 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 := 5;
            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 := 4;
            calc_term := 2;
            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 := 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 := 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 := 3;
            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 := 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 := 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 := 4;
            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 := 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 := 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 := 5;
            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 := 5;
            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  ,  4  )   =  y1  -  1.0  ; ")
            ;
        omniout_str(INFO, "diff  (  y1  ,  x  ,  1  )   =  neg ( diff  ( \
             y2  ,  x  ,  3  )  )    ; ");
        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, "2015-05-02T18:04:21-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"mtest8.ode.txt\">mtest8</a>");
            logitem_str(html_log_file,
                "diff  (  y2  ,  x  ,  4  )   =  y1  -  1.0  ; ");
            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.mtest8.mxt.txt\">mtest8 diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.mtest8.mxt.txt\\
                ">mtest8 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  )   =  n\
                eg ( diff  (  y2  ,  x  ,  3  )  )    ; ");
            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();
memory used=3.2MB, alloc=40.3MB, time=0.05
##############ECHO OF PROBLEM#################
##############temp/mtest8postode.ode#################
diff  (  y2  ,  x  ,  4  )   =  y1  -  1.0  ; 
diff  (  y1  ,  x  ,  1  )   =  neg ( diff  (  y2  ,  x  ,  3  )  )    ; 
!
#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(1.4);



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);
array_y2_init[3 + 1] := exact_soln_y2ppp(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(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(c(1.0) +	sin(c(x)));
end;
exact_soln_y2 := proc(x)
return(c(1.0) +	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_y2ppp := proc(x)
return(	neg(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)               = 1.0998334166468281523068141984106            
y2[1] (numeric)                   = 1.0998334166468281523068141984106            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.0998334166468281523068141984106            
y1[1] (numeric)                   = 1.0998334166468281523068141984106            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=45.0MB, alloc=40.3MB, time=0.52
memory used=86.0MB, alloc=40.3MB, time=0.97
 
TOP MAIN SOLVE Loop
memory used=127.0MB, alloc=40.3MB, time=1.41
x[1]                              = 0.11                                         
y2[1] (closed_form)               = 1.1097783008371748086649494900834            
y2[1] (numeric)                   = 1.1097783008371748086649494900834            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1097783008371748086649494900834            
y1[1] (numeric)                   = 1.1097783008371748086649494900834            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=168.2MB, alloc=40.3MB, time=1.83
memory used=209.3MB, alloc=40.3MB, time=2.26
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y2[1] (closed_form)               = 1.119712207288919359967350614271             
y2[1] (numeric)                   = 1.1197122072889193599673506142709            
absolute error                    = 1e-31                                        
relative error                    = 8.9308662841251848826513335689902e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.119712207288919359967350614271             
y1[1] (numeric)                   = 1.1197122072889193599673506142709            
absolute error                    = 1e-31                                        
relative error                    = 8.9308662841251848826513335689902e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=250.5MB, alloc=40.3MB, time=2.70
memory used=291.6MB, alloc=40.3MB, time=3.14
memory used=332.6MB, alloc=40.3MB, time=3.59
 
TOP MAIN SOLVE Loop
x[1]                              = 0.13                                         
y2[1] (closed_form)               = 1.1296341426196948595412058107083            
y2[1] (numeric)                   = 1.1296341426196948595412058107081            
absolute error                    = 2e-31                                        
relative error                    = 1.7704847300045926851243791841683e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1296341426196948595412058107083            
y1[1] (numeric)                   = 1.1296341426196948595412058107081            
absolute error                    = 2e-31                                        
relative error                    = 1.7704847300045926851243791841683e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=373.9MB, alloc=40.3MB, time=4.03
memory used=414.9MB, alloc=40.3MB, time=4.45
memory used=456.0MB, alloc=40.3MB, time=4.91
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y2[1] (closed_form)               = 1.1395431146442364817179883517054            
y2[1] (numeric)                   = 1.139543114644236481717988351705             
absolute error                    = 4e-31                                        
relative error                    = 3.5101787274181315499106401304621e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1395431146442364817179883517054            
y1[1] (numeric)                   = 1.139543114644236481717988351705             
absolute error                    = 4e-31                                        
relative error                    = 3.5101787274181315499106401304621e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=497.1MB, alloc=40.3MB, time=5.34
memory used=538.3MB, alloc=40.3MB, time=5.78
memory used=579.4MB, alloc=40.3MB, time=6.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y2[1] (closed_form)               = 1.1494381324735992214977254386876            
y2[1] (numeric)                   = 1.1494381324735992214977254386874            
absolute error                    = 2e-31                                        
relative error                    = 1.7399805552787651589749040948674e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1494381324735992214977254386876            
y1[1] (numeric)                   = 1.1494381324735992214977254386874            
absolute error                    = 2e-31                                        
relative error                    = 1.7399805552787651589749040948674e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=620.7MB, alloc=40.3MB, time=6.66
memory used=661.7MB, alloc=40.3MB, time=7.08
memory used=702.8MB, alloc=40.3MB, time=7.51
 
TOP MAIN SOLVE Loop
x[1]                              = 0.16                                         
y2[1] (closed_form)               = 1.159318206614245963311463159686             
y2[1] (numeric)                   = 1.1593182066142459633114631596857            
absolute error                    = 3e-31                                        
relative error                    = 2.5877278411432957513901436913893e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.159318206614245963311463159686             
y1[1] (numeric)                   = 1.1593182066142459633114631596857            
absolute error                    = 3e-31                                        
relative error                    = 2.5877278411432957513901436913893e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=743.9MB, alloc=40.3MB, time=7.95
memory used=785.1MB, alloc=40.3MB, time=8.39
 
TOP MAIN SOLVE Loop
memory used=826.1MB, alloc=40.3MB, time=8.83
x[1]                              = 0.17                                         
y2[1] (closed_form)               = 1.1691823490669960101576243766708            
y2[1] (numeric)                   = 1.1691823490669960101576243766706            
absolute error                    = 2e-31                                        
relative error                    = 1.7105971550083645811415309402222e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1691823490669960101576243766708            
y1[1] (numeric)                   = 1.1691823490669960101576243766706            
absolute error                    = 2e-31                                        
relative error                    = 1.7105971550083645811415309402222e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=867.4MB, alloc=40.3MB, time=9.26
memory used=908.4MB, alloc=40.3MB, time=9.70
 
TOP MAIN SOLVE Loop
memory used=949.5MB, alloc=40.3MB, time=10.14
x[1]                              = 0.18                                         
y2[1] (closed_form)               = 1.1790295734258241783418027396992            
y2[1] (numeric)                   = 1.1790295734258241783418027396989            
absolute error                    = 3e-31                                        
relative error                    = 2.5444654380323207512376551905900e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1790295734258241783418027396992            
y1[1] (numeric)                   = 1.1790295734258241783418027396989            
absolute error                    = 3e-31                                        
relative error                    = 2.5444654380323207512376551905900e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=990.5MB, alloc=40.3MB, time=10.67
memory used=1031.6MB, alloc=40.3MB, time=11.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y2[1] (closed_form)               = 1.1888588949765005779928511529813            
y2[1] (numeric)                   = 1.188858894976500577992851152981             
absolute error                    = 3e-31                                        
relative error                    = 2.5234281483500185301324555349713e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1888588949765005779928511529813            
y1[1] (numeric)                   = 1.188858894976500577992851152981             
absolute error                    = 3e-31                                        
relative error                    = 2.5234281483500185301324555349713e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1072.7MB, alloc=40.3MB, time=11.70
memory used=1113.8MB, alloc=40.3MB, time=12.19
memory used=1154.8MB, alloc=40.3MB, time=12.72
 
TOP MAIN SOLVE Loop
x[1]                              = 0.2                                          
y2[1] (closed_form)               = 1.1986693307950612154594126271184            
y2[1] (numeric)                   = 1.1986693307950612154594126271181            
absolute error                    = 3e-31                                        
relative error                    = 2.5027753050210606656367468154235e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.1986693307950612154594126271184            
y1[1] (numeric)                   = 1.1986693307950612154594126271181            
absolute error                    = 3e-31                                        
relative error                    = 2.5027753050210606656367468154235e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1196.1MB, alloc=40.3MB, time=13.16
memory used=1237.1MB, alloc=40.3MB, time=13.59
memory used=1278.2MB, alloc=40.3MB, time=14.03
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y2[1] (closed_form)               = 1.2084598998460995706087124262276            
y2[1] (numeric)                   = 1.2084598998460995706087124262274            
absolute error                    = 2e-31                                        
relative error                    = 1.6549990614125508560057056837875e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2084598998460995706087124262276            
y1[1] (numeric)                   = 1.2084598998460995706087124262274            
absolute error                    = 2e-31                                        
relative error                    = 1.6549990614125508560057056837875e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1319.3MB, alloc=40.3MB, time=14.47
memory used=1360.3MB, alloc=40.3MB, time=14.91
memory used=1401.3MB, alloc=40.3MB, time=15.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y2[1] (closed_form)               = 1.218229623080869319951791005457             
y2[1] (numeric)                   = 1.2182296230808693199517910054567            
absolute error                    = 3e-31                                        
relative error                    = 2.4625899281722293393850446163784e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.218229623080869319951791005457             
y1[1] (numeric)                   = 1.2182296230808693199517910054567            
absolute error                    = 3e-31                                        
relative error                    = 2.4625899281722293393850446163784e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1442.5MB, alloc=40.3MB, time=15.78
memory used=1483.7MB, alloc=40.3MB, time=16.23
memory used=1524.7MB, alloc=40.3MB, time=16.67
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y2[1] (closed_form)               = 1.2279775235351883954046172123601            
y2[1] (numeric)                   = 1.2279775235351883954046172123598            
absolute error                    = 3e-31                                        
relative error                    = 2.4430414584164278404004273601661e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2279775235351883954046172123601            
y1[1] (numeric)                   = 1.2279775235351883954046172123598            
absolute error                    = 3e-31                                        
relative error                    = 2.4430414584164278404004273601661e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1566.0MB, alloc=40.3MB, time=17.11
memory used=1607.0MB, alloc=40.3MB, time=17.55
 
TOP MAIN SOLVE Loop
memory used=1648.2MB, alloc=40.3MB, time=17.98
x[1]                              = 0.24                                         
y2[1] (closed_form)               = 1.2377026264271345883607920844898            
y2[1] (numeric)                   = 1.2377026264271345883607920844896            
absolute error                    = 2e-31                                        
relative error                    = 1.6158970315619209864958087473642e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2377026264271345883607920844898            
y1[1] (numeric)                   = 1.2377026264271345883607920844896            
absolute error                    = 2e-31                                        
relative error                    = 1.6158970315619209864958087473642e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1689.4MB, alloc=40.3MB, time=18.45
memory used=1730.6MB, alloc=40.3MB, time=18.89
 
TOP MAIN SOLVE Loop
x[1]                              = 0.25                                         
y2[1] (closed_form)               = 1.2474039592545229295968487048494            
y2[1] (numeric)                   = 1.2474039592545229295968487048492            
absolute error                    = 2e-31                                        
relative error                    = 1.6033298476904351319729627552716e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2474039592545229295968487048494            
y1[1] (numeric)                   = 1.2474039592545229295968487048492            
absolute error                    = 2e-31                                        
relative error                    = 1.6033298476904351319729627552716e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1771.8MB, alloc=40.3MB, time=19.33
memory used=1812.9MB, alloc=40.3MB, time=19.77
memory used=1853.9MB, alloc=40.3MB, time=20.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y2[1] (closed_form)               = 1.2570805518921550973533884643652            
y2[1] (numeric)                   = 1.2570805518921550973533884643649            
absolute error                    = 3e-31                                        
relative error                    = 2.3864819127814888902615199723276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2570805518921550973533884643652            
y1[1] (numeric)                   = 1.2570805518921550973533884643649            
absolute error                    = 3e-31                                        
relative error                    = 2.3864819127814888902615199723276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1895.1MB, alloc=40.3MB, time=20.64
memory used=1936.3MB, alloc=40.3MB, time=21.08
memory used=1977.5MB, alloc=40.3MB, time=21.52
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y2[1] (closed_form)               = 1.2667314366888311287322865210205            
y2[1] (numeric)                   = 1.2667314366888311287322865210202            
absolute error                    = 3e-31                                        
relative error                    = 2.3682999514418313301192155511596e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2667314366888311287322865210205            
y1[1] (numeric)                   = 1.2667314366888311287322865210202            
absolute error                    = 3e-31                                        
relative error                    = 2.3682999514418313301192155511596e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2018.7MB, alloc=40.3MB, time=21.95
memory used=2059.9MB, alloc=40.3MB, time=22.39
memory used=2101.0MB, alloc=40.3MB, time=22.83
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y2[1] (closed_form)               = 1.2763556485641137333196695584578            
y2[1] (numeric)                   = 1.2763556485641137333196695584576            
absolute error                    = 2e-31                                        
relative error                    = 1.5669613733836476662755628934786e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2763556485641137333196695584578            
y1[1] (numeric)                   = 1.2763556485641137333196695584576            
absolute error                    = 2e-31                                        
relative error                    = 1.5669613733836476662755628934786e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2142.2MB, alloc=40.3MB, time=23.28
memory used=2183.2MB, alloc=40.3MB, time=23.72
memory used=2224.3MB, alloc=40.3MB, time=24.16
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y2[1] (closed_form)               = 1.2859522251048355326839402055044            
y2[1] (numeric)                   = 1.2859522251048355326839402055042            
absolute error                    = 2e-31                                        
relative error                    = 1.5552677315340798752445732797177e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.2859522251048355326839402055044            
y1[1] (numeric)                   = 1.2859522251048355326839402055042            
absolute error                    = 2e-31                                        
relative error                    = 1.5552677315340798752445732797177e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2265.5MB, alloc=40.3MB, time=24.59
memory used=2306.6MB, alloc=40.3MB, time=25.03
 
TOP MAIN SOLVE Loop
memory used=2347.7MB, alloc=40.3MB, time=25.47
x[1]                              = 0.3                                          
y2[1] (closed_form)               = 1.295520206661339575105320745685             
y2[1] (numeric)                   = 1.2955202066613395751053207456848            
absolute error                    = 2e-31                                        
relative error                    = 1.5437814012597780076888756295055e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.295520206661339575105320745685             
y1[1] (numeric)                   = 1.2955202066613395751053207456848            
absolute error                    = 2e-31                                        
relative error                    = 1.5437814012597780076888756295055e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2388.9MB, alloc=40.3MB, time=25.91
memory used=2430.0MB, alloc=40.3MB, time=26.34
 
TOP MAIN SOLVE Loop
memory used=2471.2MB, alloc=40.3MB, time=26.78
x[1]                              = 0.31                                         
y2[1] (closed_form)               = 1.305058636443443501565643323959             
y2[1] (numeric)                   = 1.3050586364434435015656433239587            
absolute error                    = 3e-31                                        
relative error                    = 2.2987472870764064686855305439498e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.305058636443443501565643323959             
y1[1] (numeric)                   = 1.3050586364434435015656433239587            
absolute error                    = 3e-31                                        
relative error                    = 2.2987472870764064686855305439498e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2512.4MB, alloc=40.3MB, time=27.22
memory used=2553.5MB, alloc=40.3MB, time=27.66
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y2[1] (closed_form)               = 1.3145665606161177666617575434172            
y2[1] (numeric)                   = 1.3145665606161177666617575434168            
absolute error                    = 4e-31                                        
relative error                    = 3.0428280467785971822400630624494e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3145665606161177666617575434172            
y1[1] (numeric)                   = 1.3145665606161177666617575434168            
absolute error                    = 4e-31                                        
relative error                    = 3.0428280467785971822400630624494e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.9                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=2594.7MB, alloc=40.3MB, time=28.09
memory used=2635.8MB, alloc=40.3MB, time=28.53
memory used=2676.9MB, alloc=40.3MB, time=28.97
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y2[1] (closed_form)               = 1.3240430283948683467001956961702            
y2[1] (numeric)                   = 1.3240430283948683467001956961699            
absolute error                    = 3e-31                                        
relative error                    = 2.2657873918469908506683592895377e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3240430283948683467001956961702            
y1[1] (numeric)                   = 1.3240430283948683467001956961699            
absolute error                    = 3e-31                                        
relative error                    = 2.2657873918469908506683592895377e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2718.1MB, alloc=40.3MB, time=29.41
memory used=2759.2MB, alloc=40.3MB, time=29.84
memory used=2800.3MB, alloc=40.3MB, time=30.28
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y2[1] (closed_form)               = 1.3334870921408143967817714870308            
y2[1] (numeric)                   = 1.3334870921408143967817714870306            
absolute error                    = 2e-31                                        
relative error                    = 1.4998270412870278911587530301458e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3334870921408143967817714870308            
y1[1] (numeric)                   = 1.3334870921408143967817714870306            
absolute error                    = 2e-31                                        
relative error                    = 1.4998270412870278911587530301458e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2841.6MB, alloc=40.3MB, time=30.72
memory used=2882.6MB, alloc=40.3MB, time=31.16
memory used=2923.8MB, alloc=40.3MB, time=31.58
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y2[1] (closed_form)               = 1.3428978074554513491896349069176            
y2[1] (numeric)                   = 1.3428978074554513491896349069174            
absolute error                    = 2e-31                                        
relative error                    = 1.4893166024223679025311041078695e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3428978074554513491896349069176            
y1[1] (numeric)                   = 1.3428978074554513491896349069174            
absolute error                    = 2e-31                                        
relative error                    = 1.4893166024223679025311041078695e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2964.9MB, alloc=40.3MB, time=32.01
memory used=3006.0MB, alloc=40.3MB, time=32.45
 
TOP MAIN SOLVE Loop
memory used=3047.1MB, alloc=40.3MB, time=32.89
x[1]                              = 0.36                                         
y2[1] (closed_form)               = 1.3522742332750899768499134359207            
y2[1] (numeric)                   = 1.3522742332750899768499134359205            
absolute error                    = 2e-31                                        
relative error                    = 1.4789899495135501032851987062370e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3522742332750899768499134359207            
y1[1] (numeric)                   = 1.3522742332750899768499134359205            
absolute error                    = 2e-31                                        
relative error                    = 1.4789899495135501032851987062370e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3088.3MB, alloc=40.3MB, time=33.33
memory used=3129.4MB, alloc=40.3MB, time=33.77
 
TOP MAIN SOLVE Loop
memory used=3170.5MB, alloc=40.3MB, time=34.20
x[1]                              = 0.37                                         
y2[1] (closed_form)               = 1.3616154319649619780372924691272            
y2[1] (numeric)                   = 1.361615431964961978037292469127             
absolute error                    = 2e-31                                        
relative error                    = 1.4688435170816023561425718019009e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3616154319649619780372924691272            
y1[1] (numeric)                   = 1.361615431964961978037292469127             
absolute error                    = 2e-31                                        
relative error                    = 1.4688435170816023561425718019009e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.87                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3211.7MB, alloc=40.3MB, time=34.64
memory used=3252.9MB, alloc=40.3MB, time=35.08
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y2[1] (closed_form)               = 1.3709204694129826718454854663492            
y2[1] (numeric)                   = 1.3709204694129826718454854663492            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3709204694129826718454854663492            
y1[1] (numeric)                   = 1.3709204694129826718454854663492            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3294.1MB, alloc=40.3MB, time=35.52
memory used=3335.3MB, alloc=40.3MB, time=35.95
memory used=3376.4MB, alloc=40.3MB, time=36.39
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y2[1] (closed_form)               = 1.3801884151231614282311820978472            
y2[1] (numeric)                   = 1.3801884151231614282311820978472            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3801884151231614282311820978472            
y1[1] (numeric)                   = 1.3801884151231614282311820978472            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3417.6MB, alloc=40.3MB, time=36.83
memory used=3458.7MB, alloc=40.3MB, time=37.27
memory used=3500.0MB, alloc=40.3MB, time=37.70
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y2[1] (closed_form)               = 1.3894183423086504916663117567957            
y2[1] (numeric)                   = 1.3894183423086504916663117567958            
absolute error                    = 1e-31                                        
relative error                    = 7.1972563593654957565209332448654e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3894183423086504916663117567957            
y1[1] (numeric)                   = 1.3894183423086504916663117567958            
absolute error                    = 1e-31                                        
relative error                    = 7.1972563593654957565209332448654e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.85                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3541.2MB, alloc=40.3MB, time=38.14
memory used=3582.5MB, alloc=40.3MB, time=38.58
memory used=3623.5MB, alloc=40.3MB, time=39.01
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y2[1] (closed_form)               = 1.3986093279844228935937976400511            
y2[1] (numeric)                   = 1.3986093279844228935937976400513            
absolute error                    = 2e-31                                        
relative error                    = 1.4299918926482915148066202080604e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.3986093279844228935937976400511            
y1[1] (numeric)                   = 1.3986093279844228935937976400513            
absolute error                    = 2e-31                                        
relative error                    = 1.4299918926482915148066202080604e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.84                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3664.8MB, alloc=40.3MB, time=39.45
memory used=3705.9MB, alloc=40.3MB, time=39.89
memory used=3747.0MB, alloc=40.3MB, time=40.33
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y2[1] (closed_form)               = 1.4077604530595701859727871580863            
y2[1] (numeric)                   = 1.4077604530595701859727871580864            
absolute error                    = 1e-31                                        
relative error                    = 7.1034812622178727307631452987902e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4077604530595701859727871580863            
y1[1] (numeric)                   = 1.4077604530595701859727871580864            
absolute error                    = 1e-31                                        
relative error                    = 7.1034812622178727307631452987902e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3788.3MB, alloc=40.3MB, time=40.76
memory used=3829.4MB, alloc=40.3MB, time=41.20
 
TOP MAIN SOLVE Loop
memory used=3870.6MB, alloc=40.3MB, time=41.64
x[1]                              = 0.43                                         
y2[1] (closed_form)               = 1.4168708024292107662169186726246            
y2[1] (numeric)                   = 1.4168708024292107662169186726246            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4168708024292107662169186726246            
y1[1] (numeric)                   = 1.4168708024292107662169186726246            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3911.8MB, alloc=40.3MB, time=42.08
memory used=3952.9MB, alloc=40.3MB, time=42.52
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y2[1] (closed_form)               = 1.4259394650659996027697207507799            
y2[1] (numeric)                   = 1.42593946506599960276972075078              
absolute error                    = 1e-31                                        
relative error                    = 7.0129204254383618154964292748691e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4259394650659996027697207507799            
y1[1] (numeric)                   = 1.42593946506599960276972075078              
absolute error                    = 1e-31                                        
relative error                    = 7.0129204254383618154964292748691e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.82                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3994.1MB, alloc=40.3MB, time=42.95
memory used=4035.2MB, alloc=40.3MB, time=43.39
memory used=4076.3MB, alloc=40.3MB, time=43.84
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y2[1] (closed_form)               = 1.4349655341112302104208442462319            
y2[1] (numeric)                   = 1.4349655341112302104208442462321            
absolute error                    = 2e-31                                        
relative error                    = 1.3937616984220692739007625354088e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4349655341112302104208442462319            
y1[1] (numeric)                   = 1.4349655341112302104208442462321            
absolute error                    = 2e-31                                        
relative error                    = 1.3937616984220692739007625354088e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.81                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4117.6MB, alloc=40.3MB, time=44.28
memory used=4158.7MB, alloc=40.3MB, time=44.72
memory used=4199.9MB, alloc=40.3MB, time=45.16
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y2[1] (closed_form)               = 1.4439481069655197652415136439289            
y2[1] (numeric)                   = 1.4439481069655197652415136439291            
absolute error                    = 2e-31                                        
relative error                    = 1.3850913272797817201103545827305e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4439481069655197652415136439289            
y1[1] (numeric)                   = 1.4439481069655197652415136439291            
absolute error                    = 2e-31                                        
relative error                    = 1.3850913272797817201103545827305e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.8                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=4241.0MB, alloc=40.3MB, time=45.59
memory used=4282.2MB, alloc=40.3MB, time=46.03
memory used=4323.3MB, alloc=40.3MB, time=46.47
 
TOP MAIN SOLVE Loop
x[1]                              = 0.47                                         
y2[1] (closed_form)               = 1.4528862853790682907032748003964            
y2[1] (numeric)                   = 1.4528862853790682907032748003966            
absolute error                    = 2e-31                                        
relative error                    = 1.3765702244743716318964884762634e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4528862853790682907032748003964            
y1[1] (numeric)                   = 1.4528862853790682907032748003966            
absolute error                    = 2e-31                                        
relative error                    = 1.3765702244743716318964884762634e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4364.6MB, alloc=40.3MB, time=46.91
memory used=4405.7MB, alloc=40.3MB, time=47.34
memory used=4447.0MB, alloc=40.3MB, time=47.78
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y2[1] (closed_form)               = 1.4617791755414828891366429425886            
y2[1] (numeric)                   = 1.4617791755414828891366429425889            
absolute error                    = 3e-31                                        
relative error                    = 2.0522935681367318352779055472654e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4617791755414828891366429425886            
y1[1] (numeric)                   = 1.4617791755414828891366429425889            
absolute error                    = 3e-31                                        
relative error                    = 2.0522935681367318352779055472654e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4488.2MB, alloc=40.3MB, time=48.22
memory used=4529.5MB, alloc=40.3MB, time=48.66
 
TOP MAIN SOLVE Loop
memory used=4570.5MB, alloc=40.3MB, time=49.09
x[1]                              = 0.49                                         
y2[1] (closed_form)               = 1.470625888171158036181358337188             
y2[1] (numeric)                   = 1.4706258881711580361813583371881            
absolute error                    = 1e-31                                        
relative error                    = 6.7998258975542766679485161382967e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.470625888171158036181358337188             
y1[1] (numeric)                   = 1.4706258881711580361813583371881            
absolute error                    = 1e-31                                        
relative error                    = 6.7998258975542766679485161382967e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.78                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4611.9MB, alloc=40.3MB, time=49.53
memory used=4653.0MB, alloc=40.3MB, time=49.98
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y2[1] (closed_form)               = 1.4794255386042030002732879352156            
y2[1] (numeric)                   = 1.4794255386042030002732879352157            
absolute error                    = 1e-31                                        
relative error                    = 6.7593804075024437477288862816615e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4794255386042030002732879352156            
y1[1] (numeric)                   = 1.4794255386042030002732879352157            
absolute error                    = 1e-31                                        
relative error                    = 6.7593804075024437477288862816615e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.77                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4694.2MB, alloc=40.3MB, time=50.42
memory used=4735.3MB, alloc=40.3MB, time=50.86
memory used=4776.4MB, alloc=40.3MB, time=51.30
 
TOP MAIN SOLVE Loop
x[1]                              = 0.51                                         
y2[1] (closed_form)               = 1.4881772468829074945001302376746            
y2[1] (numeric)                   = 1.4881772468829074945001302376747            
absolute error                    = 1e-31                                        
relative error                    = 6.7196296818444895062143521595631e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4881772468829074945001302376746            
y1[1] (numeric)                   = 1.4881772468829074945001302376747            
absolute error                    = 1e-31                                        
relative error                    = 6.7196296818444895062143521595631e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.76                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4817.8MB, alloc=40.3MB, time=51.73
memory used=4858.9MB, alloc=40.3MB, time=52.17
memory used=4900.0MB, alloc=40.3MB, time=52.61
 
TOP MAIN SOLVE Loop
x[1]                              = 0.52                                         
y2[1] (closed_form)               = 1.4968801378437367143344589425478            
y2[1] (numeric)                   = 1.4968801378437367143344589425479            
absolute error                    = 1e-31                                        
relative error                    = 6.6805616209224672797258116287453e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.4968801378437367143344589425478            
y1[1] (numeric)                   = 1.4968801378437367143344589425479            
absolute error                    = 1e-31                                        
relative error                    = 6.6805616209224672797258116287453e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.75                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4941.3MB, alloc=40.3MB, time=53.05
memory used=4982.6MB, alloc=40.3MB, time=53.48
memory used=5023.7MB, alloc=40.3MB, time=53.92
 
TOP MAIN SOLVE Loop
x[1]                              = 0.53                                         
y2[1] (closed_form)               = 1.5055333412048469618136610224661            
y2[1] (numeric)                   = 1.5055333412048469618136610224662            
absolute error                    = 1e-31                                        
relative error                    = 6.6421644252642112677183443406037e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5055333412048469618136610224661            
y1[1] (numeric)                   = 1.5055333412048469618136610224662            
absolute error                    = 1e-31                                        
relative error                    = 6.6421644252642112677183443406037e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5064.9MB, alloc=40.3MB, time=54.36
memory used=5106.0MB, alloc=40.3MB, time=54.80
memory used=5147.2MB, alloc=40.3MB, time=55.23
 
TOP MAIN SOLVE Loop
x[1]                              = 0.54                                         
y2[1] (closed_form)               = 1.5141359916531131046772806829582            
y2[1] (numeric)                   = 1.5141359916531131046772806829584            
absolute error                    = 2e-31                                        
relative error                    = 1.3208853174518539592632826995509e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5141359916531131046772806829582            
y1[1] (numeric)                   = 1.5141359916531131046772806829584            
absolute error                    = 2e-31                                        
relative error                    = 1.3208853174518539592632826995509e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5188.5MB, alloc=40.3MB, time=55.67
memory used=5229.6MB, alloc=40.3MB, time=56.11
 
TOP MAIN SOLVE Loop
memory used=5270.8MB, alloc=40.3MB, time=56.56
x[1]                              = 0.55                                         
y2[1] (closed_form)               = 1.5226872289306591677883781077573            
y2[1] (numeric)                   = 1.5226872289306591677883781077576            
absolute error                    = 3e-31                                        
relative error                    = 1.9702010649336150579001937438213e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5226872289306591677883781077573            
y1[1] (numeric)                   = 1.5226872289306591677883781077576            
absolute error                    = 3e-31                                        
relative error                    = 1.9702010649336150579001937438213e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.73                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5312.1MB, alloc=40.3MB, time=57.00
memory used=5353.3MB, alloc=40.3MB, time=57.44
 
TOP MAIN SOLVE Loop
memory used=5394.5MB, alloc=40.3MB, time=57.88
x[1]                              = 0.56                                         
y2[1] (closed_form)               = 1.531186197920883403851869441112             
y2[1] (numeric)                   = 1.5311861979208834038518694411123            
absolute error                    = 3e-31                                        
relative error                    = 1.9592653095185556278376417192731e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.531186197920883403851869441112             
y1[1] (numeric)                   = 1.5311861979208834038518694411123            
absolute error                    = 3e-31                                        
relative error                    = 1.9592653095185556278376417192731e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.72                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5435.7MB, alloc=40.3MB, time=58.31
memory used=5476.9MB, alloc=40.3MB, time=58.75
 
TOP MAIN SOLVE Loop
x[1]                              = 0.57                                         
y2[1] (closed_form)               = 1.5396320487339692409944634930788            
y2[1] (numeric)                   = 1.5396320487339692409944634930792            
absolute error                    = 4e-31                                        
relative error                    = 2.5980233415439601059285561241638e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5396320487339692409944634930788            
y1[1] (numeric)                   = 1.5396320487339692409944634930792            
absolute error                    = 4e-31                                        
relative error                    = 2.5980233415439601059285561241638e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.71                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5518.1MB, alloc=40.3MB, time=59.19
memory used=5559.3MB, alloc=40.3MB, time=59.63
memory used=5600.6MB, alloc=40.3MB, time=60.08
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y2[1] (closed_form)               = 1.5480239367918735561826960595765            
y2[1] (numeric)                   = 1.5480239367918735561826960595769            
absolute error                    = 4e-31                                        
relative error                    = 2.5839393725975608816817965314317e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5480239367918735561826960595765            
y1[1] (numeric)                   = 1.5480239367918735561826960595769            
absolute error                    = 4e-31                                        
relative error                    = 2.5839393725975608816817965314317e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.7                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=5641.8MB, alloc=40.3MB, time=60.52
memory used=5683.0MB, alloc=40.3MB, time=60.95
memory used=5724.2MB, alloc=40.3MB, time=61.39
 
TOP MAIN SOLVE Loop
x[1]                              = 0.59                                         
y2[1] (closed_form)               = 1.5563610229127837757225433788758            
y2[1] (numeric)                   = 1.5563610229127837757225433788761            
absolute error                    = 3e-31                                        
relative error                    = 1.9275733302453152399987334892936e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5563610229127837757225433788758            
y1[1] (numeric)                   = 1.5563610229127837757225433788761            
absolute error                    = 3e-31                                        
relative error                    = 1.9275733302453152399987334892936e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.69                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5765.6MB, alloc=40.3MB, time=61.83
memory used=5806.8MB, alloc=40.3MB, time=62.27
memory used=5848.1MB, alloc=40.3MB, time=62.70
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y2[1] (closed_form)               = 1.5646424733950353572009454456587            
y2[1] (numeric)                   = 1.5646424733950353572009454456591            
absolute error                    = 4e-31                                        
relative error                    = 2.5564945781643077326410928561345e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5646424733950353572009454456587            
y1[1] (numeric)                   = 1.5646424733950353572009454456591            
absolute error                    = 4e-31                                        
relative error                    = 2.5564945781643077326410928561345e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.68                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5889.2MB, alloc=40.3MB, time=63.14
memory used=5930.5MB, alloc=40.3MB, time=63.58
 
TOP MAIN SOLVE Loop
memory used=5971.5MB, alloc=40.3MB, time=64.02
x[1]                              = 0.61                                         
y2[1] (closed_form)               = 1.5728674601004812611909760321627            
y2[1] (numeric)                   = 1.5728674601004812611909760321631            
absolute error                    = 4e-31                                        
relative error                    = 2.5431259158635423105558908746238e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5728674601004812611909760321627            
y1[1] (numeric)                   = 1.5728674601004812611909760321631            
absolute error                    = 4e-31                                        
relative error                    = 2.5431259158635423105558908746238e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.67                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6012.8MB, alloc=40.3MB, time=64.45
memory used=6053.9MB, alloc=40.3MB, time=64.89
 
TOP MAIN SOLVE Loop
memory used=6095.1MB, alloc=40.3MB, time=65.33
x[1]                              = 0.62                                         
y2[1] (closed_form)               = 1.5810351605373050758429632275822            
y2[1] (numeric)                   = 1.5810351605373050758429632275826            
absolute error                    = 4e-31                                        
relative error                    = 2.5299880102860107173400795091577e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5810351605373050758429632275822            
y1[1] (numeric)                   = 1.5810351605373050758429632275826            
absolute error                    = 4e-31                                        
relative error                    = 2.5299880102860107173400795091577e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.66                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6136.3MB, alloc=40.3MB, time=65.77
memory used=6177.6MB, alloc=40.3MB, time=66.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.63                                         
y2[1] (closed_form)               = 1.5891447579422695131181120907946            
y2[1] (numeric)                   = 1.5891447579422695131181120907951            
absolute error                    = 5e-31                                        
relative error                    = 3.1463464703330947989267061188544e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5891447579422695131181120907946            
y1[1] (numeric)                   = 1.5891447579422695131181120907951            
absolute error                    = 5e-31                                        
relative error                    = 3.1463464703330947989267061188544e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.65                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6218.7MB, alloc=40.3MB, time=66.64
memory used=6260.0MB, alloc=40.3MB, time=67.08
memory used=6301.0MB, alloc=40.3MB, time=67.51
 
TOP MAIN SOLVE Loop
x[1]                              = 0.64                                         
y2[1] (closed_form)               = 1.5971954413623920518835462392079            
y2[1] (numeric)                   = 1.5971954413623920518835462392085            
absolute error                    = 6e-31                                        
relative error                    = 3.7565847263388498195366901161187e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.5971954413623920518835462392079            
y1[1] (numeric)                   = 1.5971954413623920518835462392085            
absolute error                    = 6e-31                                        
relative error                    = 3.7565847263388498195366901161187e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.64                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6342.3MB, alloc=40.3MB, time=67.95
memory used=6383.5MB, alloc=40.3MB, time=68.41
memory used=6424.6MB, alloc=40.3MB, time=68.84
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y2[1] (closed_form)               = 1.6051864057360395603725216786059            
y2[1] (numeric)                   = 1.6051864057360395603725216786066            
absolute error                    = 7e-31                                        
relative error                    = 4.3608642429227597400408349078988e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6051864057360395603725216786059            
y1[1] (numeric)                   = 1.6051864057360395603725216786065            
absolute error                    = 6e-31                                        
relative error                    = 3.7378836367909369200350013496276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.63                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6465.9MB, alloc=40.3MB, time=69.28
memory used=6507.0MB, alloc=40.3MB, time=69.72
memory used=6548.1MB, alloc=40.3MB, time=70.16
 
TOP MAIN SOLVE Loop
x[1]                              = 0.66                                         
y2[1] (closed_form)               = 1.6131168519734337886151454793963            
y2[1] (numeric)                   = 1.613116851973433788615145479397             
absolute error                    = 7e-31                                        
relative error                    = 4.3394252508343903213419791140701e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6131168519734337886151454793963            
y1[1] (numeric)                   = 1.6131168519734337886151454793969            
absolute error                    = 6e-31                                        
relative error                    = 3.7195073578580488468645535263458e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.62                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6589.5MB, alloc=40.3MB, time=70.59
memory used=6630.7MB, alloc=40.3MB, time=71.03
 
TOP MAIN SOLVE Loop
memory used=6671.8MB, alloc=40.3MB, time=71.47
x[1]                              = 0.67                                         
y2[1] (closed_form)               = 1.6209859870365596803574439141266            
y2[1] (numeric)                   = 1.6209859870365596803574439141272            
absolute error                    = 6e-31                                        
relative error                    = 3.7014508749511331458246624977526e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6209859870365596803574439141266            
y1[1] (numeric)                   = 1.6209859870365596803574439141271            
absolute error                    = 5e-31                                        
relative error                    = 3.0845423957926109548538854147938e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.61                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6713.2MB, alloc=40.3MB, time=71.91
memory used=6754.3MB, alloc=40.3MB, time=72.34
 
TOP MAIN SOLVE Loop
memory used=6795.5MB, alloc=40.3MB, time=72.78
x[1]                              = 0.68                                         
y2[1] (closed_form)               = 1.6287930240184685137041781874202            
y2[1] (numeric)                   = 1.6287930240184685137041781874207            
absolute error                    = 5e-31                                        
relative error                    = 3.0697577447036672334270957658935e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6287930240184685137041781874202            
y1[1] (numeric)                   = 1.6287930240184685137041781874206            
absolute error                    = 4e-31                                        
relative error                    = 2.4558061957629337867416766127148e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.6                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=6836.8MB, alloc=40.3MB, time=73.22
memory used=6878.0MB, alloc=40.3MB, time=73.66
 
TOP MAIN SOLVE Loop
x[1]                              = 0.69                                         
y2[1] (closed_form)               = 1.6365371822219679402374292070087            
y2[1] (numeric)                   = 1.6365371822219679402374292070092            
absolute error                    = 5e-31                                        
relative error                    = 3.0552315305243315579132780160033e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6365371822219679402374292070087            
y1[1] (numeric)                   = 1.6365371822219679402374292070091            
absolute error                    = 4e-31                                        
relative error                    = 2.4441852244194652463306224128027e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.59                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6919.2MB, alloc=40.3MB, time=74.09
memory used=6960.4MB, alloc=40.3MB, time=74.53
memory used=7001.7MB, alloc=40.3MB, time=74.97
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y2[1] (closed_form)               = 1.6442176872376910536726143513987            
y2[1] (numeric)                   = 1.6442176872376910536726143513993            
absolute error                    = 6e-31                                        
relative error                    = 3.6491518407639105112956164712766e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6442176872376910536726143513987            
y1[1] (numeric)                   = 1.6442176872376910536726143513991            
absolute error                    = 4e-31                                        
relative error                    = 2.4327678938426070075304109808511e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7043.0MB, alloc=40.3MB, time=75.41
memory used=7084.1MB, alloc=40.3MB, time=75.84
memory used=7125.4MB, alloc=40.3MB, time=76.28
 
TOP MAIN SOLVE Loop
x[1]                              = 0.71                                         
y2[1] (closed_form)               = 1.6518337710215366812101279728528            
y2[1] (numeric)                   = 1.6518337710215366812101279728534            
absolute error                    = 6e-31                                        
relative error                    = 3.6323267542165849911319064238541e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6518337710215366812101279728528            
y1[1] (numeric)                   = 1.6518337710215366812101279728532            
absolute error                    = 4e-31                                        
relative error                    = 2.4215511694777233274212709492361e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7166.7MB, alloc=40.3MB, time=76.73
memory used=7207.8MB, alloc=40.3MB, time=77.17
memory used=7249.0MB, alloc=40.3MB, time=77.61
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y2[1] (closed_form)               = 1.6593846719714731536180038326482            
y2[1] (numeric)                   = 1.6593846719714731536180038326488            
absolute error                    = 6e-31                                        
relative error                    = 3.6157981336970836608452685196505e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6593846719714731536180038326482            
y1[1] (numeric)                   = 1.6593846719714731536180038326486            
absolute error                    = 4e-31                                        
relative error                    = 2.4105320891313891072301790131003e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.57                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7290.3MB, alloc=40.3MB, time=78.05
memory used=7331.5MB, alloc=40.3MB, time=78.48
 
TOP MAIN SOLVE Loop
memory used=7372.5MB, alloc=40.3MB, time=78.91
x[1]                              = 0.73                                         
y2[1] (closed_form)               = 1.6668696350036978737325941307615            
y2[1] (numeric)                   = 1.6668696350036978737325941307621            
absolute error                    = 6e-31                                        
relative error                    = 3.5995616417757164768053526716897e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6668696350036978737325941307615            
y1[1] (numeric)                   = 1.6668696350036978737325941307619            
absolute error                    = 4e-31                                        
relative error                    = 2.3997077611838109845369017811265e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.56                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7413.8MB, alloc=40.3MB, time=79.34
memory used=7455.0MB, alloc=40.3MB, time=79.78
 
TOP MAIN SOLVE Loop
memory used=7496.2MB, alloc=40.3MB, time=80.23
x[1]                              = 0.74                                         
y2[1] (closed_form)               = 1.6742879116281450674838811576082            
y2[1] (numeric)                   = 1.6742879116281450674838811576089            
absolute error                    = 7e-31                                        
relative error                    = 4.1808818849996460771224914217115e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6742879116281450674838811576082            
y1[1] (numeric)                   = 1.6742879116281450674838811576087            
absolute error                    = 5e-31                                        
relative error                    = 2.9863442035711757693732081583654e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.55                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7537.5MB, alloc=40.3MB, time=80.66
memory used=7578.7MB, alloc=40.3MB, time=81.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.75                                         
y2[1] (closed_form)               = 1.6816387600233341667332419527799            
y2[1] (numeric)                   = 1.6816387600233341667332419527805            
absolute error                    = 6e-31                                        
relative error                    = 3.5679482078045970477176178584378e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6816387600233341667332419527799            
y1[1] (numeric)                   = 1.6816387600233341667332419527803            
absolute error                    = 4e-31                                        
relative error                    = 2.3786321385363980318117452389586e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.54                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7619.9MB, alloc=40.3MB, time=81.55
memory used=7661.0MB, alloc=40.3MB, time=81.97
memory used=7702.1MB, alloc=40.3MB, time=82.41
 
TOP MAIN SOLVE Loop
x[1]                              = 0.76                                         
y2[1] (closed_form)               = 1.6889214451105513391477556387697            
y2[1] (numeric)                   = 1.6889214451105513391477556387703            
absolute error                    = 6e-31                                        
relative error                    = 3.5525630972180943514490345432969e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6889214451105513391477556387697            
y1[1] (numeric)                   = 1.6889214451105513391477556387701            
absolute error                    = 4e-31                                        
relative error                    = 2.3683753981453962342993563621979e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.53                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7743.4MB, alloc=40.3MB, time=82.86
memory used=7784.5MB, alloc=40.3MB, time=83.30
memory used=7825.7MB, alloc=40.3MB, time=83.72
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y2[1] (closed_form)               = 1.6961352386273567470198837344522            
y2[1] (numeric)                   = 1.6961352386273567470198837344528            
absolute error                    = 6e-31                                        
relative error                    = 3.5374537733533925365070462532402e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.6961352386273567470198837344522            
y1[1] (numeric)                   = 1.6961352386273567470198837344525            
absolute error                    = 3e-31                                        
relative error                    = 1.7687268866766962682535231266201e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.52                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7866.9MB, alloc=40.3MB, time=84.16
memory used=7908.2MB, alloc=40.3MB, time=84.61
memory used=7949.3MB, alloc=40.3MB, time=85.03
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y2[1] (closed_form)               = 1.7032794192004101843678973251179            
y2[1] (numeric)                   = 1.7032794192004101843678973251185            
absolute error                    = 6e-31                                        
relative error                    = 3.5226163906898189319837465571838e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7032794192004101843678973251179            
y1[1] (numeric)                   = 1.7032794192004101843678973251182            
absolute error                    = 3e-31                                        
relative error                    = 1.7613081953449094659918732785919e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.51                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7990.6MB, alloc=40.3MB, time=85.48
memory used=8031.7MB, alloc=40.3MB, time=85.92
memory used=8073.0MB, alloc=40.3MB, time=86.36
 
TOP MAIN SOLVE Loop
x[1]                              = 0.79                                         
y2[1] (closed_form)               = 1.7103532724176078098140288749692            
y2[1] (numeric)                   = 1.7103532724176078098140288749698            
absolute error                    = 6e-31                                        
relative error                    = 3.5080471951381820106893663116140e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7103532724176078098140288749692            
y1[1] (numeric)                   = 1.7103532724176078098140288749695            
absolute error                    = 3e-31                                        
relative error                    = 1.7540235975690910053446831558070e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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=8114.2MB, alloc=40.3MB, time=86.80
memory used=8155.4MB, alloc=40.3MB, time=87.23
 
TOP MAIN SOLVE Loop
memory used=8196.7MB, alloc=40.3MB, time=87.67
x[1]                              = 0.8                                          
y2[1] (closed_form)               = 1.7173560908995227616271746105814            
y2[1] (numeric)                   = 1.7173560908995227616271746105822            
absolute error                    = 8e-31                                        
relative error                    = 4.6583233625180972831297527110775e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7173560908995227616271746105814            
y1[1] (numeric)                   = 1.7173560908995227616271746105819            
absolute error                    = 5e-31                                        
relative error                    = 2.9114521015738108019560954444235e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.49                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8237.8MB, alloc=40.3MB, time=88.11
memory used=8279.0MB, alloc=40.3MB, time=88.55
 
TOP MAIN SOLVE Loop
x[1]                              = 0.81                                         
y2[1] (closed_form)               = 1.7242871743701425109281768525145            
y2[1] (numeric)                   = 1.7242871743701425109281768525154            
absolute error                    = 9e-31                                        
relative error                    = 5.2195481899861439942763895929832e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7242871743701425109281768525145            
y1[1] (numeric)                   = 1.724287174370142510928176852515             
absolute error                    = 5e-31                                        
relative error                    = 2.8997489944367466634868831072129e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.48                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8320.2MB, alloc=40.3MB, time=88.98
memory used=8361.4MB, alloc=40.3MB, time=89.42
memory used=8402.5MB, alloc=40.3MB, time=89.86
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y2[1] (closed_form)               = 1.7311458297268958793813133646877            
y2[1] (numeric)                   = 1.7311458297268958793813133646886            
absolute error                    = 9e-31                                        
relative error                    = 5.1988687754975746238225426161331e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7311458297268958793813133646877            
y1[1] (numeric)                   = 1.7311458297268958793813133646882            
absolute error                    = 5e-31                                        
relative error                    = 2.8882604308319859021236347867406e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.47                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8443.9MB, alloc=40.3MB, time=90.30
memory used=8485.0MB, alloc=40.3MB, time=90.73
memory used=8526.2MB, alloc=40.3MB, time=91.17
 
TOP MAIN SOLVE Loop
x[1]                              = 0.83                                         
y2[1] (closed_form)               = 1.7379313711099627187285802261381            
y2[1] (numeric)                   = 1.7379313711099627187285802261389            
absolute error                    = 8e-31                                        
relative error                    = 4.6031737115664405046844768767302e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7379313711099627187285802261381            
y1[1] (numeric)                   = 1.7379313711099627187285802261385            
absolute error                    = 4e-31                                        
relative error                    = 2.3015868557832202523422384383651e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.46                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8567.4MB, alloc=40.3MB, time=91.61
memory used=8608.6MB, alloc=40.3MB, time=92.05
memory used=8649.7MB, alloc=40.3MB, time=92.48
 
TOP MAIN SOLVE Loop
x[1]                              = 0.84                                         
y2[1] (closed_form)               = 1.7446431199708593212565726706296            
y2[1] (numeric)                   = 1.7446431199708593212565726706305            
absolute error                    = 9e-31                                        
relative error                    = 5.1586481481383576650537424502601e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7446431199708593212565726706296            
y1[1] (numeric)                   = 1.7446431199708593212565726706301            
absolute error                    = 5e-31                                        
relative error                    = 2.8659156378546431472520791390334e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.45                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8691.1MB, alloc=40.3MB, time=92.92
memory used=8732.2MB, alloc=40.3MB, time=93.36
memory used=8773.4MB, alloc=40.3MB, time=93.80
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y2[1] (closed_form)               = 1.7512804051402927027120715242355            
y2[1] (numeric)                   = 1.7512804051402927027120715242363            
absolute error                    = 8e-31                                        
relative error                    = 4.5680862850510400296794522876481e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7512804051402927027120715242355            
y1[1] (numeric)                   = 1.7512804051402927027120715242359            
absolute error                    = 4e-31                                        
relative error                    = 2.2840431425255200148397261438240e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.44                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8814.6MB, alloc=40.3MB, time=94.23
memory used=8855.8MB, alloc=40.3MB, time=94.67
 
TOP MAIN SOLVE Loop
memory used=8896.9MB, alloc=40.3MB, time=95.11
x[1]                              = 0.86                                         
y2[1] (closed_form)               = 1.7578425628952769722945887295286            
y2[1] (numeric)                   = 1.7578425628952769722945887295294            
absolute error                    = 8e-31                                        
relative error                    = 4.5510332773052770733185900131678e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7578425628952769722945887295286            
y1[1] (numeric)                   = 1.757842562895276972294588729529             
absolute error                    = 4e-31                                        
relative error                    = 2.2755166386526385366592950065839e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.43                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8938.2MB, alloc=40.3MB, time=95.55
memory used=8979.3MB, alloc=40.3MB, time=95.97
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y2[1] (closed_form)               = 1.7643289370255050781448028237228            
y2[1] (numeric)                   = 1.7643289370255050781448028237236            
absolute error                    = 8e-31                                        
relative error                    = 4.5343018708786003867776021485100e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7643289370255050781448028237228            
y1[1] (numeric)                   = 1.7643289370255050781448028237232            
absolute error                    = 4e-31                                        
relative error                    = 2.2671509354393001933888010742550e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.42                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9020.5MB, alloc=40.3MB, time=96.41
memory used=9061.7MB, alloc=40.3MB, time=96.84
memory used=9102.9MB, alloc=40.3MB, time=97.28
 
TOP MAIN SOLVE Loop
x[1]                              = 0.88                                         
y2[1] (closed_form)               = 1.770738878898969291209645130756             
y2[1] (numeric)                   = 1.7707388788989692912096451307567            
absolute error                    = 7e-31                                        
relative error                    = 3.9531520335468896382125887517276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.770738878898969291209645130756             
y1[1] (numeric)                   = 1.7707388788989692912096451307563            
absolute error                    = 3e-31                                        
relative error                    = 1.6942080143772384163768237507404e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.41                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9144.2MB, alloc=40.3MB, time=97.72
memory used=9185.4MB, alloc=40.3MB, time=98.16
memory used=9226.5MB, alloc=40.3MB, time=98.59
 
TOP MAIN SOLVE Loop
x[1]                              = 0.89                                         
y2[1] (closed_form)               = 1.7770717475268238654903337129732            
y2[1] (numeric)                   = 1.777071747526823865490333712974             
absolute error                    = 8e-31                                        
relative error                    = 4.5017878491027243390856112860058e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7770717475268238654903337129732            
y1[1] (numeric)                   = 1.7770717475268238654903337129736            
absolute error                    = 4e-31                                        
relative error                    = 2.2508939245513621695428056430029e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.4                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=9267.8MB, alloc=40.3MB, time=99.03
memory used=9309.0MB, alloc=40.3MB, time=99.47
memory used=9350.1MB, alloc=40.3MB, time=99.91
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y2[1] (closed_form)               = 1.7833269096274833884613823157136            
y2[1] (numeric)                   = 1.7833269096274833884613823157144            
absolute error                    = 8e-31                                        
relative error                    = 4.4859974673242095448996703276825e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7833269096274833884613823157136            
y1[1] (numeric)                   = 1.783326909627483388461382315714             
absolute error                    = 4e-31                                        
relative error                    = 2.2429987336621047724498351638412e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.39                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9391.4MB, alloc=40.3MB, time=100.34
memory used=9432.4MB, alloc=40.3MB, time=100.78
memory used=9473.7MB, alloc=40.3MB, time=101.22
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y2[1] (closed_form)               = 1.7895037396899504118789575178716            
y2[1] (numeric)                   = 1.7895037396899504118789575178725            
absolute error                    = 9e-31                                        
relative error                    = 5.0293272935877411778434150984747e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7895037396899504118789575178716            
y1[1] (numeric)                   = 1.7895037396899504118789575178721            
absolute error                    = 5e-31                                        
relative error                    = 2.7940707186598562099130083880415e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.38                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9514.9MB, alloc=40.3MB, time=101.66
memory used=9556.1MB, alloc=40.3MB, time=102.09
 
TOP MAIN SOLVE Loop
memory used=9597.3MB, alloc=40.3MB, time=102.53
x[1]                              = 0.92                                         
y2[1] (closed_form)               = 1.7956016200363660302682761024816            
y2[1] (numeric)                   = 1.7956016200363660302682761024825            
absolute error                    = 9e-31                                        
relative error                    = 5.0122476497975784017478027814179e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.7956016200363660302682761024816            
y1[1] (numeric)                   = 1.7956016200363660302682761024821            
absolute error                    = 5e-31                                        
relative error                    = 2.7845820276653213343043348785655e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.37                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9638.7MB, alloc=40.3MB, time=102.97
memory used=9679.8MB, alloc=40.3MB, time=103.41
 
TOP MAIN SOLVE Loop
x[1]                              = 0.93                                         
y2[1] (closed_form)               = 1.8016199408837771520843192159106            
y2[1] (numeric)                   = 1.8016199408837771520843192159117            
absolute error                    = 1.1e-30                                      
relative error                    = 6.1056162570025706157906685408112e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8016199408837771520843192159106            
y1[1] (numeric)                   = 1.8016199408837771520843192159112            
absolute error                    = 6e-31                                        
relative error                    = 3.3303361401832203358858192040788e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.36                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9721.1MB, alloc=40.3MB, time=103.84
memory used=9762.3MB, alloc=40.3MB, time=104.28
memory used=9803.4MB, alloc=40.3MB, time=104.72
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y2[1] (closed_form)               = 1.8075581004051142868702197986342            
y2[1] (numeric)                   = 1.8075581004051142868702197986353            
absolute error                    = 1.1e-30                                      
relative error                    = 6.0855581889924608420935918711385e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8075581004051142868702197986342            
y1[1] (numeric)                   = 1.8075581004051142868702197986348            
absolute error                    = 6e-31                                        
relative error                    = 3.3193953758140695502328682933483e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.35                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9844.8MB, alloc=40.3MB, time=105.16
memory used=9885.9MB, alloc=40.3MB, time=105.59
memory used=9927.1MB, alloc=40.3MB, time=106.03
 
TOP MAIN SOLVE Loop
x[1]                              = 0.95                                         
y2[1] (closed_form)               = 1.8134155047893737506854221021026            
y2[1] (numeric)                   = 1.8134155047893737506854221021037            
absolute error                    = 1.1e-30                                      
relative error                    = 6.0659015934010325456709830050373e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8134155047893737506854221021026            
y1[1] (numeric)                   = 1.8134155047893737506854221021032            
absolute error                    = 6e-31                                        
relative error                    = 3.3086735964005632067296270936567e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.34                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9968.3MB, alloc=40.3MB, time=106.47
memory used=10009.6MB, alloc=40.3MB, time=106.91
memory used=10050.8MB, alloc=40.3MB, time=107.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y2[1] (closed_form)               = 1.8191915683009982716332221464304            
y2[1] (numeric)                   = 1.8191915683009982716332221464316            
absolute error                    = 1.2e-30                                      
relative error                    = 6.5963366415595183056497609050378e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8191915683009982716332221464304            
y1[1] (numeric)                   = 1.819191568300998271633222146431             
absolute error                    = 6e-31                                        
relative error                    = 3.2981683207797591528248804525189e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.33                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10092.1MB, alloc=40.3MB, time=107.84
memory used=10133.2MB, alloc=40.3MB, time=108.28
memory used=10174.5MB, alloc=40.3MB, time=108.72
 
TOP MAIN SOLVE Loop
x[1]                              = 0.97                                         
y2[1] (closed_form)               = 1.8248857133384500574766200378563            
y2[1] (numeric)                   = 1.8248857133384500574766200378575            
absolute error                    = 1.2e-30                                      
relative error                    = 6.5757542580829200636082281336399e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8248857133384500574766200378563            
y1[1] (numeric)                   = 1.8248857133384500574766200378569            
absolute error                    = 6e-31                                        
relative error                    = 3.2878771290414600318041140668200e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.32                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10215.7MB, alloc=40.3MB, time=109.17
memory used=10256.9MB, alloc=40.3MB, time=109.59
 
TOP MAIN SOLVE Loop
memory used=10298.1MB, alloc=40.3MB, time=110.03
x[1]                              = 0.98                                         
y2[1] (closed_form)               = 1.8304973704919704680845332877192            
y2[1] (numeric)                   = 1.8304973704919704680845332877203            
absolute error                    = 1.1e-30                                      
relative error                    = 6.0092957123689306232259040553489e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8304973704919704680845332877192            
y1[1] (numeric)                   = 1.8304973704919704680845332877197            
absolute error                    = 5e-31                                        
relative error                    = 2.7314980510767866469208654797041e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.31                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10339.4MB, alloc=40.3MB, time=110.47
memory used=10380.6MB, alloc=40.3MB, time=110.91
 
TOP MAIN SOLVE Loop
memory used=10421.8MB, alloc=40.3MB, time=111.36
x[1]                              = 0.99                                         
y2[1] (closed_form)               = 1.8360259786005205167892594115471            
y2[1] (numeric)                   = 1.8360259786005205167892594115483            
absolute error                    = 1.2e-30                                      
relative error                    = 6.5358552329127691884278112370427e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8360259786005205167892594115471            
y1[1] (numeric)                   = 1.8360259786005205167892594115477            
absolute error                    = 6e-31                                        
relative error                    = 3.2679276164563845942139056185213e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.3                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=10463.0MB, alloc=40.3MB, time=111.80
memory used=10504.3MB, alloc=40.3MB, time=112.23
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y2[1] (closed_form)               = 1.8414709848078965066525023216303            
y2[1] (numeric)                   = 1.8414709848078965066525023216315            
absolute error                    = 1.2e-30                                      
relative error                    = 6.5165295022293539324380335270974e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8414709848078965066525023216303            
y1[1] (numeric)                   = 1.8414709848078965066525023216308            
absolute error                    = 5e-31                                        
relative error                    = 2.7152206259288974718491806362906e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.29                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10545.5MB, alloc=40.3MB, time=112.67
memory used=10586.7MB, alloc=40.3MB, time=113.11
memory used=10627.8MB, alloc=40.3MB, time=113.55
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y2[1] (closed_form)               = 1.846831844618015190123098784782             
y2[1] (numeric)                   = 1.8468318446180151901230987847831            
absolute error                    = 1.1e-30                                      
relative error                    = 5.9561459436904810767434459011377e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.846831844618015190123098784782             
y1[1] (numeric)                   = 1.8468318446180151901230987847824            
absolute error                    = 4e-31                                        
relative error                    = 2.1658712522510840279067076004137e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.28                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10669.1MB, alloc=40.3MB, time=113.98
memory used=10710.3MB, alloc=40.3MB, time=114.42
memory used=10751.3MB, alloc=40.3MB, time=114.86
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y2[1] (closed_form)               = 1.8521080219493629236165499854554            
y2[1] (numeric)                   = 1.8521080219493629236165499854566            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4791037335769840268276932677166e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8521080219493629236165499854554            
y1[1] (numeric)                   = 1.8521080219493629236165499854559            
absolute error                    = 5e-31                                        
relative error                    = 2.6996265556570766778448721948819e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10792.6MB, alloc=40.3MB, time=115.30
memory used=10833.8MB, alloc=40.3MB, time=115.72
memory used=10874.9MB, alloc=40.3MB, time=116.16
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y2[1] (closed_form)               = 1.8572989891886033721462743852944            
y2[1] (numeric)                   = 1.8572989891886033721462743852959            
absolute error                    = 1.5e-30                                      
relative error                    = 8.0762440981853100706155630168529e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8572989891886033721462743852944            
y1[1] (numeric)                   = 1.8572989891886033721462743852952            
absolute error                    = 8e-31                                        
relative error                    = 4.3073301856988320376616336089882e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10916.2MB, alloc=40.3MB, time=116.59
memory used=10957.4MB, alloc=40.3MB, time=117.03
 
TOP MAIN SOLVE Loop
memory used=10998.5MB, alloc=40.3MB, time=117.48
x[1]                              = 1.04                                         
y2[1] (closed_form)               = 1.8624042272433384032807916921162            
y2[1] (numeric)                   = 1.8624042272433384032807916921176            
absolute error                    = 1.4e-30                                      
relative error                    = 7.5171650682528144063824746906913e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8624042272433384032807916921162            
y1[1] (numeric)                   = 1.8624042272433384032807916921169            
absolute error                    = 7e-31                                        
relative error                    = 3.7585825341264072031912373453457e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.26                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11039.8MB, alloc=40.3MB, time=117.92
memory used=11080.9MB, alloc=40.3MB, time=118.36
 
TOP MAIN SOLVE Loop
memory used=11122.1MB, alloc=40.3MB, time=118.80
x[1]                              = 1.05                                         
y2[1] (closed_form)               = 1.8674232255940168943814094850003            
y2[1] (numeric)                   = 1.8674232255940168943814094850018            
absolute error                    = 1.5e-30                                      
relative error                    = 8.0324587348047916712101682283739e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8674232255940168943814094850003            
y1[1] (numeric)                   = 1.867423225594016894381409485001             
absolute error                    = 7e-31                                        
relative error                    = 3.7484807429089027798980785065745e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.25                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11163.3MB, alloc=40.3MB, time=119.23
memory used=11204.5MB, alloc=40.3MB, time=119.67
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y2[1] (closed_form)               = 1.8723554823449862622829459219974            
y2[1] (numeric)                   = 1.8723554823449862622829459219989            
absolute error                    = 1.5e-30                                      
relative error                    = 8.0112992118428352105393786046779e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8723554823449862622829459219974            
y1[1] (numeric)                   = 1.8723554823449862622829459219981            
absolute error                    = 7e-31                                        
relative error                    = 3.7386062988599897649183766821830e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.24                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11245.7MB, alloc=40.3MB, time=120.11
memory used=11286.9MB, alloc=40.3MB, time=120.55
memory used=11328.1MB, alloc=40.3MB, time=120.98
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y2[1] (closed_form)               = 1.8772005042746816103070632577768            
y2[1] (numeric)                   = 1.8772005042746816103070632577784            
absolute error                    = 1.6e-30                                      
relative error                    = 8.5233303334222831099541026365469e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8772005042746816103070632577768            
y1[1] (numeric)                   = 1.8772005042746816103070632577776            
absolute error                    = 8e-31                                        
relative error                    = 4.2616651667111415549770513182734e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.23                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11369.4MB, alloc=40.3MB, time=121.44
memory used=11410.5MB, alloc=40.3MB, time=121.88
memory used=11451.7MB, alloc=40.3MB, time=122.31
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y2[1] (closed_form)               = 1.8819578068849474737353349876248            
y2[1] (numeric)                   = 1.8819578068849474737353349876264            
absolute error                    = 1.6e-30                                      
relative error                    = 8.5017846529107396731745850412156e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8819578068849474737353349876248            
y1[1] (numeric)                   = 1.8819578068849474737353349876255            
absolute error                    = 7e-31                                        
relative error                    = 3.7195307856484486070138809555318e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.22                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11493.0MB, alloc=40.3MB, time=122.75
memory used=11534.1MB, alloc=40.3MB, time=123.17
memory used=11575.2MB, alloc=40.3MB, time=123.61
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y2[1] (closed_form)               = 1.886626914449487231608600628636             
y2[1] (numeric)                   = 1.8866269144494872316086006286377            
absolute error                    = 1.7e-30                                      
relative error                    = 9.0107905647898356518557107118975e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.886626914449487231608600628636             
y1[1] (numeric)                   = 1.8866269144494872316086006286368            
absolute error                    = 8e-31                                        
relative error                    = 4.2403720304893344244026873938341e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11616.5MB, alloc=40.3MB, time=124.06
memory used=11657.6MB, alloc=40.3MB, time=124.50
 
TOP MAIN SOLVE Loop
memory used=11698.7MB, alloc=40.3MB, time=124.94
x[1]                              = 1.1                                          
y2[1] (closed_form)               = 1.8912073600614353399518025778717            
y2[1] (numeric)                   = 1.8912073600614353399518025778734            
absolute error                    = 1.7e-30                                      
relative error                    = 8.9889667093130177826708112055367e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8912073600614353399518025778717            
y1[1] (numeric)                   = 1.8912073600614353399518025778725            
absolute error                    = 8e-31                                        
relative error                    = 4.2301019808531848389039111555467e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11740.0MB, alloc=40.3MB, time=125.37
memory used=11781.1MB, alloc=40.3MB, time=125.81
 
TOP MAIN SOLVE Loop
memory used=11822.4MB, alloc=40.3MB, time=126.25
x[1]                              = 1.11                                         
y2[1] (closed_form)               = 1.8956986856800476292406259593394            
y2[1] (numeric)                   = 1.895698685680047629240625959341             
absolute error                    = 1.6e-30                                      
relative error                    = 8.4401598845126008409534611289227e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.8956986856800476292406259593394            
y1[1] (numeric)                   = 1.8956986856800476292406259593401            
absolute error                    = 7e-31                                        
relative error                    = 3.6925699494742628679171392439037e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.2                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=11863.5MB, alloc=40.3MB, time=126.69
memory used=11904.7MB, alloc=40.3MB, time=127.12
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y2[1] (closed_form)               = 1.9001004421765049971191032473392            
y2[1] (numeric)                   = 1.9001004421765049971191032473409            
absolute error                    = 1.7e-30                                      
relative error                    = 8.9468954496568809515772926044896e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9001004421765049971191032473392            
y1[1] (numeric)                   = 1.9001004421765049971191032473399            
absolute error                    = 7e-31                                        
relative error                    = 3.6840157733881274506494734253781e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.19                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11946.1MB, alloc=40.3MB, time=127.56
memory used=11987.3MB, alloc=40.3MB, time=128.00
memory used=12028.3MB, alloc=40.3MB, time=128.44
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y2[1] (closed_form)               = 1.9044121893788259160370815224114            
y2[1] (numeric)                   = 1.904412189378825916037081522413             
absolute error                    = 1.6e-30                                      
relative error                    = 8.4015425280484160751648923102079e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9044121893788259160370815224114            
y1[1] (numeric)                   = 1.904412189378825916037081522412             
absolute error                    = 6e-31                                        
relative error                    = 3.1505784480181560281868346163280e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.18                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12069.4MB, alloc=40.3MB, time=128.87
memory used=12110.4MB, alloc=40.3MB, time=129.31
memory used=12151.3MB, alloc=40.3MB, time=129.75
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y2[1] (closed_form)               = 1.9086334961158832645942155781022            
y2[1] (numeric)                   = 1.9086334961158832645942155781038            
absolute error                    = 1.6e-30                                      
relative error                    = 8.3829609155243260606295714188113e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9086334961158832645942155781022            
y1[1] (numeric)                   = 1.9086334961158832645942155781027            
absolute error                    = 5e-31                                        
relative error                    = 2.6196752861013518939467410683785e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12192.2MB, alloc=40.3MB, time=130.17
memory used=12233.2MB, alloc=40.3MB, time=130.61
memory used=12274.0MB, alloc=40.3MB, time=131.05
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y2[1] (closed_form)               = 1.9127639402605210809440330497537            
y2[1] (numeric)                   = 1.9127639402605210809440330497552            
absolute error                    = 1.5e-30                                      
relative error                    = 7.8420549887389550837680369989356e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9127639402605210809440330497537            
y1[1] (numeric)                   = 1.912763940260521080944033049754             
absolute error                    = 3e-31                                        
relative error                    = 1.5684109977477910167536073997871e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12315.1MB, alloc=40.3MB, time=131.48
memory used=12355.9MB, alloc=40.3MB, time=131.92
memory used=12396.9MB, alloc=40.3MB, time=132.36
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y2[1] (closed_form)               = 1.9168031087717669266186616668743            
y2[1] (numeric)                   = 1.9168031087717669266186616668759            
absolute error                    = 1.6e-30                                      
relative error                    = 8.3472318710148306547578611616372e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9168031087717669266186616668743            
y1[1] (numeric)                   = 1.9168031087717669266186616668745            
absolute error                    = 2e-31                                        
relative error                    = 1.0434039838768538318447326452046e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.16                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12437.8MB, alloc=40.3MB, time=132.80
memory used=12478.7MB, alloc=40.3MB, time=133.22
 
TOP MAIN SOLVE Loop
memory used=12519.6MB, alloc=40.3MB, time=133.66
x[1]                              = 1.17                                         
y2[1] (closed_form)               = 1.920750597736135639573013008962             
y2[1] (numeric)                   = 1.9207505977361356395730130089636            
absolute error                    = 1.6e-30                                      
relative error                    = 8.3300768037548258455002428942027e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.920750597736135639573013008962             
y1[1] (numeric)                   = 1.9207505977361356395730130089621            
absolute error                    = 1e-31                                        
relative error                    = 5.2062980023467661534376518088767e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12560.6MB, alloc=40.3MB, time=134.09
memory used=12601.5MB, alloc=40.3MB, time=134.53
 
TOP MAIN SOLVE Loop
memory used=12642.4MB, alloc=40.3MB, time=134.95
x[1]                              = 1.18                                         
y2[1] (closed_form)               = 1.9246060124080203461075380258748            
y2[1] (numeric)                   = 1.9246060124080203461075380258765            
absolute error                    = 1.7e-30                                      
relative error                    = 8.8329766666009800468885060325817e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9246060124080203461075380258748            
y1[1] (numeric)                   = 1.924606012408020346107538025875             
absolute error                    = 2e-31                                        
relative error                    = 1.0391737254824682408104124744214e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12683.4MB, alloc=40.3MB, time=135.39
memory used=12724.3MB, alloc=40.3MB, time=135.83
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y2[1] (closed_form)               = 1.9283689672491666926020211116027            
y2[1] (numeric)                   = 1.9283689672491666926020211116044            
absolute error                    = 1.7e-30                                      
relative error                    = 8.8157402907445829835928863875063e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9283689672491666926020211116027            
y1[1] (numeric)                   = 1.9283689672491666926020211116028            
absolute error                    = 1e-31                                        
relative error                    = 5.1857295827909311668193449338272e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.14                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12765.2MB, alloc=40.3MB, time=136.27
memory used=12806.2MB, alloc=40.3MB, time=136.70
memory used=12847.0MB, alloc=40.3MB, time=137.14
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y2[1] (closed_form)               = 1.9320390859672263496701344354948            
y2[1] (numeric)                   = 1.9320390859672263496701344354965            
absolute error                    = 1.7e-30                                      
relative error                    = 8.7989938316850258313533357855703e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9320390859672263496701344354948            
y1[1] (numeric)                   = 1.9320390859672263496701344354949            
absolute error                    = 1e-31                                        
relative error                    = 5.1758787245206034302078445797472e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.13                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12888.1MB, alloc=40.3MB, time=137.58
memory used=12928.9MB, alloc=40.3MB, time=138.00
memory used=12969.8MB, alloc=40.3MB, time=138.45
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y2[1] (closed_form)               = 1.9356160015533859334164648885436            
y2[1] (numeric)                   = 1.9356160015533859334164648885454            
absolute error                    = 1.8e-30                                      
relative error                    = 9.2993651558751823590837647273125e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9356160015533859334164648885436            
y1[1] (numeric)                   = 1.9356160015533859334164648885438            
absolute error                    = 2e-31                                        
relative error                    = 1.0332627950972424843426405252569e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13010.8MB, alloc=40.3MB, time=138.88
memory used=13051.7MB, alloc=40.3MB, time=139.31
memory used=13092.6MB, alloc=40.3MB, time=139.75
 
TOP MAIN SOLVE Loop
x[1]                              = 1.22                                         
y2[1] (closed_form)               = 1.9390993563190675809352452718884            
y2[1] (numeric)                   = 1.9390993563190675809352452718902            
absolute error                    = 1.8e-30                                      
relative error                    = 9.2826599840499375289590803065862e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9390993563190675809352452718884            
y1[1] (numeric)                   = 1.9390993563190675809352452718884            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13133.6MB, alloc=40.3MB, time=140.19
memory used=13174.4MB, alloc=40.3MB, time=140.63
memory used=13215.4MB, alloc=40.3MB, time=141.06
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y2[1] (closed_form)               = 1.9424888019316975100238235653892            
y2[1] (numeric)                   = 1.9424888019316975100238235653911            
absolute error                    = 1.9e-30                                      
relative error                    = 9.7812661679725270480052204773684e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9424888019316975100238235653892            
y1[1] (numeric)                   = 1.9424888019316975100238235653893            
absolute error                    = 1e-31                                        
relative error                    = 5.1480348252486984463185370933518e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13256.3MB, alloc=40.3MB, time=141.50
memory used=13297.1MB, alloc=40.3MB, time=141.92
 
TOP MAIN SOLVE Loop
memory used=13337.9MB, alloc=40.3MB, time=142.36
x[1]                              = 1.24                                         
y2[1] (closed_form)               = 1.9457839994495389862847059630818            
y2[1] (numeric)                   = 1.9457839994495389862847059630838            
absolute error                    = 2.0e-30                                      
relative error                    = 1.0278633191380948165950190065184e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9457839994495389862847059630818            
y1[1] (numeric)                   = 1.945783999449538986284705963082             
absolute error                    = 2e-31                                        
relative error                    = 1.0278633191380948165950190065184e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13379.0MB, alloc=40.3MB, time=142.80
memory used=13420.0MB, alloc=40.3MB, time=143.25
 
TOP MAIN SOLVE Loop
memory used=13460.8MB, alloc=40.3MB, time=143.69
x[1]                              = 1.25                                         
y2[1] (closed_form)               = 1.948984619355586214348490847036             
y2[1] (numeric)                   = 1.9489846193555862143484908470381            
absolute error                    = 2.1e-30                                      
relative error                    = 1.0774841315547916577169562276573e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.948984619355586214348490847036             
y1[1] (numeric)                   = 1.9489846193555862143484908470362            
absolute error                    = 2e-31                                        
relative error                    = 1.0261753633855158644923392644355e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.1                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=13501.8MB, alloc=40.3MB, time=144.13
memory used=13542.7MB, alloc=40.3MB, time=144.55
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y2[1] (closed_form)               = 1.9520903415905157638568162214254            
y2[1] (numeric)                   = 1.9520903415905157638568162214275            
absolute error                    = 2.1e-30                                      
relative error                    = 1.0757698838307713983589213291601e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9520903415905157638568162214254            
y1[1] (numeric)                   = 1.9520903415905157638568162214256            
absolute error                    = 2e-31                                        
relative error                    = 1.0245427465054965698656393611049e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13583.7MB, alloc=40.3MB, time=144.98
memory used=13624.5MB, alloc=40.3MB, time=145.42
memory used=13665.3MB, alloc=40.3MB, time=145.84
 
TOP MAIN SOLVE Loop
x[1]                              = 1.27                                         
y2[1] (closed_form)               = 1.9551008555846922350901817421829            
y2[1] (numeric)                   = 1.9551008555846922350901817421851            
absolute error                    = 2.2e-30                                      
relative error                    = 1.1252616424957106651093628098137e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9551008555846922350901817421829            
y1[1] (numeric)                   = 1.9551008555846922350901817421832            
absolute error                    = 3e-31                                        
relative error                    = 1.5344476943123327251491311042914e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13706.4MB, alloc=40.3MB, time=146.28
memory used=13747.2MB, alloc=40.3MB, time=146.72
memory used=13788.2MB, alloc=40.3MB, time=147.16
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y2[1] (closed_form)               = 1.9580158602892249637007538591603            
y2[1] (numeric)                   = 1.9580158602892249637007538591626            
absolute error                    = 2.3e-30                                      
relative error                    = 1.1746585135731533012459987183515e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9580158602892249637007538591603            
y1[1] (numeric)                   = 1.9580158602892249637007538591606            
absolute error                    = 3e-31                                        
relative error                    = 1.5321632785736782190165200674150e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13829.2MB, alloc=40.3MB, time=147.58
memory used=13870.0MB, alloc=40.3MB, time=148.01
memory used=13910.9MB, alloc=40.3MB, time=148.45
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y2[1] (closed_form)               = 1.9608350642060726589055612912854            
y2[1] (numeric)                   = 1.9608350642060726589055612912878            
absolute error                    = 2.4e-30                                      
relative error                    = 1.2239683203399577690392480181938e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9608350642060726589055612912854            
y1[1] (numeric)                   = 1.9608350642060726589055612912857            
absolute error                    = 3e-31                                        
relative error                    = 1.5299604004249472112990600227422e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13952.0MB, alloc=40.3MB, time=148.89
memory used=13992.8MB, alloc=40.3MB, time=149.33
memory used=14033.8MB, alloc=40.3MB, time=149.75
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y2[1] (closed_form)               = 1.9635581854171929647013486300396            
y2[1] (numeric)                   = 1.963558185417192964701348630042             
absolute error                    = 2.4e-30                                      
relative error                    = 1.2222708844709265317948470052663e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9635581854171929647013486300396            
y1[1] (numeric)                   = 1.9635581854171929647013486300399            
absolute error                    = 3e-31                                        
relative error                    = 1.5278386055886581647435587565828e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14074.7MB, alloc=40.3MB, time=150.19
memory used=14115.7MB, alloc=40.3MB, time=150.63
 
TOP MAIN SOLVE Loop
memory used=14156.6MB, alloc=40.3MB, time=151.06
x[1]                              = 1.31                                         
y2[1] (closed_form)               = 1.9661849516127340291692578059375            
y2[1] (numeric)                   = 1.96618495161273402916925780594              
absolute error                    = 2.5e-30                                      
relative error                    = 1.2714978811883450226749757606044e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9661849516127340291692578059375            
y1[1] (numeric)                   = 1.9661849516127340291692578059379            
absolute error                    = 4e-31                                        
relative error                    = 2.0343966099013520362799612169670e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14197.6MB, alloc=40.3MB, time=151.50
memory used=14238.4MB, alloc=40.3MB, time=151.92
 
TOP MAIN SOLVE Loop
memory used=14279.4MB, alloc=40.3MB, time=152.38
x[1]                              = 1.32                                         
y2[1] (closed_form)               = 1.9687151001182652627358998459728            
y2[1] (numeric)                   = 1.9687151001182652627358998459753            
absolute error                    = 2.5e-30                                      
relative error                    = 1.2698637806200700275759373893996e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9687151001182652627358998459728            
y1[1] (numeric)                   = 1.9687151001182652627358998459732            
absolute error                    = 4e-31                                        
relative error                    = 2.0317820489921120441214998230394e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14320.3MB, alloc=40.3MB, time=152.81
memory used=14361.2MB, alloc=40.3MB, time=153.25
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y2[1] (closed_form)               = 1.9711483779210445623376830377638            
y2[1] (numeric)                   = 1.9711483779210445623376830377665            
absolute error                    = 2.7e-30                                      
relative error                    = 1.3697598974500690745034621659160e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9711483779210445623376830377638            
y1[1] (numeric)                   = 1.9711483779210445623376830377643            
absolute error                    = 5e-31                                        
relative error                    = 2.5365924026853131009323373442889e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14402.1MB, alloc=40.3MB, time=153.67
memory used=14443.0MB, alloc=40.3MB, time=154.11
memory used=14483.8MB, alloc=40.3MB, time=154.55
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y2[1] (closed_form)               = 1.9734845416953193747878703480896            
y2[1] (numeric)                   = 1.9734845416953193747878703480925            
absolute error                    = 2.9e-30                                      
relative error                    = 1.4694819942743299647053784620101e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9734845416953193747878703480896            
y1[1] (numeric)                   = 1.9734845416953193747878703480903            
absolute error                    = 7e-31                                        
relative error                    = 3.5470255034207964665302238738175e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14524.9MB, alloc=40.3MB, time=154.98
memory used=14565.8MB, alloc=40.3MB, time=155.42
memory used=14606.7MB, alloc=40.3MB, time=155.84
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y2[1] (closed_form)               = 1.9757233578266590692611135392652            
y2[1] (numeric)                   = 1.9757233578266590692611135392681            
absolute error                    = 2.9e-30                                      
relative error                    = 1.4678168320032751952784532850582e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9757233578266590692611135392652            
y1[1] (numeric)                   = 1.9757233578266590692611135392659            
absolute error                    = 7e-31                                        
relative error                    = 3.5430061462148021954997148260026e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14647.7MB, alloc=40.3MB, time=156.28
memory used=14688.6MB, alloc=40.3MB, time=156.72
memory used=14729.4MB, alloc=40.3MB, time=157.16
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y2[1] (closed_form)               = 1.9778646024353161856784924394266            
y2[1] (numeric)                   = 1.9778646024353161856784924394296            
absolute error                    = 3.0e-30                                      
relative error                    = 1.5167873454563791815565963522215e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9778646024353161856784924394266            
y1[1] (numeric)                   = 1.9778646024353161856784924394274            
absolute error                    = 8e-31                                        
relative error                    = 4.0447662545503444841509236059240e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14770.4MB, alloc=40.3MB, time=157.59
memory used=14811.2MB, alloc=40.3MB, time=158.01
memory used=14852.2MB, alloc=40.3MB, time=158.47
 
TOP MAIN SOLVE Loop
x[1]                              = 1.37                                         
y2[1] (closed_form)               = 1.9799080613986142228876885048919            
y2[1] (numeric)                   = 1.979908061398614222887688504895             
absolute error                    = 3.1e-30                                      
relative error                    = 1.5657292681611431878095862070644e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9799080613986142228876885048919            
y1[1] (numeric)                   = 1.9799080613986142228876885048926            
absolute error                    = 7e-31                                        
relative error                    = 3.5355177022993555853764849836938e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14893.2MB, alloc=40.3MB, time=158.91
memory used=14934.1MB, alloc=40.3MB, time=159.34
 
TOP MAIN SOLVE Loop
memory used=14975.0MB, alloc=40.3MB, time=159.78
x[1]                              = 1.38                                         
y2[1] (closed_form)               = 1.981853530372359727878131085206             
y2[1] (numeric)                   = 1.9818535303723597278781310852093            
absolute error                    = 3.3e-30                                      
relative error                    = 1.6651079151040898919730555924413e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.981853530372359727878131085206             
y1[1] (numeric)                   = 1.9818535303723597278781310852068            
absolute error                    = 8e-31                                        
relative error                    = 4.0366252487371876169043771937971e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15016.0MB, alloc=40.3MB, time=160.22
memory used=15056.9MB, alloc=40.3MB, time=160.64
 
TOP MAIN SOLVE Loop
memory used=15097.7MB, alloc=40.3MB, time=161.08
x[1]                              = 1.39                                         
y2[1] (closed_form)               = 1.9837008148112765448400382244429            
y2[1] (numeric)                   = 1.9837008148112765448400382244462            
absolute error                    = 3.3e-30                                      
relative error                    = 1.6635573143694818133269937362597e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 1.9837008148112765448400382244429            
y1[1] (numeric)                   = 1.9837008148112765448400382244437            
absolute error                    = 8e-31                                        
relative error                    = 4.0328662166532892444290757242660e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
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)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15138.7MB, alloc=40.3MB, time=161.52
memory used=15179.6MB, alloc=40.3MB, time=161.95
Finished!
diff  (  y2  ,  x  ,  4  )   =  y1  -  1.0  ; 
diff  (  y1  ,  x  ,  1  )   =  neg ( diff  (  y2  ,  x  ,  3  )  )    ; 
Iterations                       = 1300                                
Total Elapsed Time               = 2 Minutes 42 Seconds
Elapsed Time(since restart)      = 2 Minutes 42 Seconds
Time to Timeout                  = 17 Seconds
Percent Done                     = 100.1                                      % 
> quit
memory used=15207.6MB, alloc=40.3MB, time=162.25