|\^/|     Maple 2019 (X86 64 WINDOWS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
 \  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
> 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 7
# Begin Function number 8
> 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 8
# Begin Function number 9
> 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 9
# Begin Function number 10
> 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 10
# Begin Function number 11
> 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 11
# Begin Function number 12
> 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 12
# Begin Function number 13
> 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 13
# Begin Function number 14
> 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 14
# Begin Function number 15
> 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 15
# Begin Function number 16
> log_revs := proc(file,revs)
>     fprintf(file,revs);
> end;
           log_revs := proc(file, revs) fprintf(file, revs) end proc

# End Function number 16
# Begin Function number 17
> 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 17
# Begin Function number 18
> 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 18
# Begin Function number 19
> logstart := proc(file)
>     fprintf(file,"<tr>");
> end;
             logstart := proc(file) fprintf(file, "<tr>") end proc

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

# End Function number 20
# Begin Function number 21
> 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 21
# Begin Function number 22
> 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 22
# Begin Function number 23
> 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 23
# Begin Function number 24
> 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 24
# Begin Function number 25
> 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 25
# Begin Function number 26
> 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 26
# Begin Function number 27
> 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 27
# Begin Function number 28
> 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 28
# Begin Function number 29
> 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> convfloat := proc(mmm)
>     (mmm);
> end;
                      convfloat := proc(mmm) mmm end proc

# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
>     time();
> end;
                 elapsed_time_seconds := proc() time() end proc

# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
>     abs(x);
> end;
                      float_abs := proc(x) abs(x) end proc

# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
>     x^y;
> end;
                        expt := proc(x, y) x^y end proc

# End Function number 37
# Begin Function number 38
> neg := proc(x)
>     -x;
> end;
                           neg := proc(x) -x end proc

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

# End Function number 39
# Begin Function number 40
> 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 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(cosh(c(2.0)*c(x)+c(3.0))/c(2.0));
> end;
   exact_soln_y := proc(x) return cosh(c(2.0)*c(x) + c(3.0))/c(2.0) 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
>     ;
> 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
end proc

# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
>     local ret;
>     if (xf > x0) then # if number 3
>         ret := glob__1;
>     else
>         ret := glob__m1;
>     fi;# end if 3;
>     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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[1]) < min_size) then # if number 3
>         min_size := float_abs(array_y[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     if (min_size < glob__1) then # if number 3
>         min_size := glob__1;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[1]) < min_size then
        min_size := float_abs(array_y[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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 3
>         max_estimated_step_error := est_tmp;
>     fi;# end if 3;
>     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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[no_terms - 3]
         + array_y[no_terms - 2]*hn_div_ho
         + array_y[no_terms - 1]*hn_div_ho_2
         + array_y[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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
>         est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
>     fi;# end if 3;
>     if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
>         array_max_est_error[1] := c(est_tmp);
>     fi;# end if 3
>     ;
> 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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[no_terms - 3]))
         + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
    end if;
    if c(array_max_est_error[1]) <= c(est_tmp) then
        array_max_est_error[1] := 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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 3
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 3;
>     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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 3
>         if (iter >= 0)  then # if number 4
>             ind_var := array_x[1];
>             omniout_float(ALWAYS,"x[1]                             ",33,ind_var,20," ");
>             closed_form_val_y := evalf(exact_soln_y(ind_var));
>             omniout_float(ALWAYS,"y[1] (closed_form)               ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y[1] (numeric)                   ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 5
>                 relerr := abserr/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 6
>                     glob_good_digits := round(-log10(relerr));
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 6;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 5;
>             if (glob_good_digits < glob_min_good_digits) then # if number 5
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 5;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 5;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 5
>                 est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*21*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 6
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 6;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 5;
>             array_est_digits[1] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 5
>                 array_1st_rel_error[1] := relerr;
>             else
>                 array_last_rel_error[1] := relerr;
>             fi;# end if 5;
>             array_est_rel_error[1] := est_rel_err;
>             omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>             omniout_float(ALWAYS,"relative error                   ",4,relerr * c(100.0),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 4;
>         #BOTTOM DISPLAY ALOT
>     fi;# end if 3;
> 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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y(ind_var));
            omniout_float(ALWAYS, "y[1] (closed_form)               ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y[1] (numeric)                   ", 33,
                numeric_val, 20, " ");
            if c(glob_prec) < c(float_abs(closed_form_val_y)) then
                relerr := abserr/float_abs(closed_form_val_y);
                if c(glob_prec) < c(relerr) then
                    glob_good_digits := round(-log10(relerr))
                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)*21*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*c(100.0), 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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 3
>         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 3;
>     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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 - 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_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 3;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 4
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 5
>             found_sing := 0;
>         fi;# end if 5;
>         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 5
>         if (rad_c  < array_rad_test_poles[1,1]) then # if number 6
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_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 6;
>     fi;# end if 5;
>     #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[1,2] :=  glob_larger_float;
>     array_ord_test_poles[1,2] :=  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_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_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[1,2]) then # if number 8
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 9
>                 glob_min_pole_est := rad_c;
>             fi;# end if 9;
>             array_ord_test_poles[1,2] := 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[1,3] :=  glob_larger_float;
>     array_ord_test_poles[1,3] :=  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_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_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[1,3]) then # if number 10
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 11
>                 glob_min_pole_est := rad_c;
>             fi;# end if 11;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test1
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
>         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 10
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 10;
>         term := 1;
>         ratio := c(1.0);
>         while (term <= ATS_MAX_TERMS)  do # do number 1
>             array_y[term] := array_y[term]* ratio;
>             array_y_higher[1,term] := array_y_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 9;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 9
>         display_poles();
>     fi;# end if 9
> 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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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 - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
            array_y_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_y_higher[1, last_no - 1],
                array_y_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[1, 2] := glob_larger_float;
    array_ord_test_poles[1, 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_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_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_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_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[1, 3] := glob_larger_float;
    array_ord_test_poles[1, 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_y_higher[1, last_no - 5],
            array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
            array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_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_y_higher[1, last_no - 5],
                array_y_higher[1, last_no - 4],
                array_y_higher[1, last_no - 3],
                array_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_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;
    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_y[term] := array_y[term]*ratio;
            array_y_higher[1, term] := array_y_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_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 mult CONST - LINEAR $eq_no = 1 i = 1
>     array_tmp1[1] := array_const_2D0[1] * array_x[1];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 1
>     array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
>     array_tmp3[1] :=  sinh(array_tmp2[1]);
>     array_tmp3_g[1] :=  cosh(array_tmp2[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,2]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[2] := temporary;
>                 array_y_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
>     array_tmp1[2] := array_const_2D0[1] * array_x[2];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre sinh LINEAR $eq_no = 1
>     array_tmp3[2] := array_tmp3_g[1] * array_tmp2[2] / c(1);
>     array_tmp3_g[2] := array_tmp3[1] * array_tmp2[2] / c(1);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp4[2] := array_tmp3[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,3]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[3] := temporary;
>                 array_y_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre sinh LINEAR $eq_no = 1
>     array_tmp3[3] := array_tmp3_g[2] * array_tmp2[2] / c(2);
>     array_tmp3_g[3] := array_tmp3[2] * array_tmp2[2] / c(2);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp4[3] := array_tmp3[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[4] := temporary;
>                 array_y_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre sinh LINEAR $eq_no = 1
>     array_tmp3[4] := array_tmp3_g[3] * array_tmp2[2] / c(3);
>     array_tmp3_g[4] := array_tmp3[3] * array_tmp2[2] / c(3);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp4[4] := array_tmp3[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[5] := temporary;
>                 array_y_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre sinh LINEAR $eq_no = 1
>     array_tmp3[5] := array_tmp3_g[4] * array_tmp2[2] / c(4);
>     array_tmp3_g[5] := array_tmp3[4] * array_tmp2[2] / c(4);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp4[5] := array_tmp3[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[6] := temporary;
>                 array_y_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y_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 sinh LINEAR $eq_no = 1
>         array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_tmp2[2] / c(kkk - 1);
>         array_tmp3_g[kkk] := neg(array_tmp3[kkk - 1]) * array_tmp2[2] / c(kkk - 1);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp4[kkk] := array_tmp3[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y_set_initial[1,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y[kkk + order_d] := c(temporary);
>                 array_y_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_y_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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_2D0[1]*array_x[1];
    array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
    array_tmp3[1] := sinh(array_tmp2[1]);
    array_tmp3_g[1] := cosh(array_tmp2[1]);
    array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
    if not array_y_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y[2] := temporary; array_y_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := array_const_2D0[1]*array_x[2];
    array_tmp2[2] := array_tmp1[2];
    array_tmp3[2] := array_tmp3_g[1]*array_tmp2[2]/c(1);
    array_tmp3_g[2] := array_tmp3[1]*array_tmp2[2]/c(1);
    array_tmp4[2] := array_tmp3[2];
    if not array_y_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y[3] := temporary; array_y_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp3[3] := array_tmp3_g[2]*array_tmp2[2]/c(2);
    array_tmp3_g[3] := array_tmp3[2]*array_tmp2[2]/c(2);
    array_tmp4[3] := array_tmp3[3];
    if not array_y_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y[4] := temporary; array_y_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp3[4] := array_tmp3_g[3]*array_tmp2[2]/c(3);
    array_tmp3_g[4] := array_tmp3[3]*array_tmp2[2]/c(3);
    array_tmp4[4] := array_tmp3[4];
    if not array_y_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y[5] := temporary; array_y_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp3[5] := array_tmp3_g[4]*array_tmp2[2]/c(4);
    array_tmp3_g[5] := array_tmp3[4]*array_tmp2[2]/c(4);
    array_tmp4[5] := array_tmp3[5];
    if not array_y_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y[6] := temporary; array_y_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_tmp2[2]/c(kkk - 1);
        array_tmp3_g[kkk] :=
            neg(array_tmp3[kkk - 1])*array_tmp2[2]/c(kkk - 1);
        array_tmp4[kkk] := array_tmp3[kkk];
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y[kkk + order_d] := c(temporary);
                array_y_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_y_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_1,
>     array_const_0D0,
>     array_const_2D0,
>     array_const_3D0,
>     #END CONST
>     array_y_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_y,
>     array_x,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3_g,
>     array_tmp3,
>     array_tmp4,
>     array_m1,
>     array_y_higher,
>     array_y_higher_work,
>     array_y_higher_work2,
>     array_y_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_y_init:= Array(0..(40),[]);
>     array_norms:= Array(0..(40),[]);
>     array_fact_1:= Array(0..(40),[]);
>     array_1st_rel_error:= Array(0..(2),[]);
>     array_last_rel_error:= Array(0..(2),[]);
>     array_est_rel_error:= Array(0..(2),[]);
>     array_max_est_error:= Array(0..(2),[]);
>     array_type_pole:= Array(0..(2),[]);
>     array_type_real_pole:= Array(0..(2),[]);
>     array_type_complex_pole:= Array(0..(2),[]);
>     array_est_digits:= Array(0..(2),[]);
>     array_y:= Array(0..(40),[]);
>     array_x:= Array(0..(40),[]);
>     array_tmp0:= Array(0..(40),[]);
>     array_tmp1:= Array(0..(40),[]);
>     array_tmp2:= Array(0..(40),[]);
>     array_tmp3_g:= Array(0..(40),[]);
>     array_tmp3:= Array(0..(40),[]);
>     array_tmp4:= Array(0..(40),[]);
>     array_m1:= Array(0..(40),[]);
>     array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
>     array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
>     array_ord_test_poles := Array(0..(2) ,(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_y_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 <= 2) do # do number 1
>         array_1st_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_last_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_est_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_max_est_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_real_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_complex_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) 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_y[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_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_g[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_m1[term] := c(0.0);
>         term := term + 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_y_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_y_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_y_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 <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_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 <= 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 <=2) 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 <=2) 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 <=2) 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_y);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3_g);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_m1);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := c(1);
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := c(0.0);
>     zero_ats_ar(array_const_2D0);
>     array_const_2D0[1]   := c(2.0);
>     zero_ats_ar(array_const_3D0);
>     array_const_3D0[1]   := c(3.0);
>     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_y_set_initial[1,1] := true;
>     array_y_set_initial[1,2] := false;
>     array_y_set_initial[1,3] := false;
>     array_y_set_initial[1,4] := false;
>     array_y_set_initial[1,5] := false;
>     array_y_set_initial[1,6] := false;
>     array_y_set_initial[1,7] := false;
>     array_y_set_initial[1,8] := false;
>     array_y_set_initial[1,9] := false;
>     array_y_set_initial[1,10] := false;
>     array_y_set_initial[1,11] := false;
>     array_y_set_initial[1,12] := false;
>     array_y_set_initial[1,13] := false;
>     array_y_set_initial[1,14] := false;
>     array_y_set_initial[1,15] := false;
>     array_y_set_initial[1,16] := false;
>     array_y_set_initial[1,17] := false;
>     array_y_set_initial[1,18] := false;
>     array_y_set_initial[1,19] := false;
>     array_y_set_initial[1,20] := false;
>     array_y_set_initial[1,21] := false;
>     array_y_set_initial[1,22] := false;
>     array_y_set_initial[1,23] := false;
>     array_y_set_initial[1,24] := false;
>     array_y_set_initial[1,25] := false;
>     array_y_set_initial[1,26] := false;
>     array_y_set_initial[1,27] := false;
>     array_y_set_initial[1,28] := false;
>     array_y_set_initial[1,29] := false;
>     array_y_set_initial[1,30] := false;
>     array_y_set_initial[1,31] := false;
>     array_y_set_initial[1,32] := false;
>     array_y_set_initial[1,33] := false;
>     array_y_set_initial[1,34] := false;
>     array_y_set_initial[1,35] := false;
>     array_y_set_initial[1,36] := false;
>     array_y_set_initial[1,37] := false;
>     array_y_set_initial[1,38] := false;
>     array_y_set_initial[1,39] := false;
>     array_y_set_initial[1,40] := 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   := 1;
>     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,"##############R:\Temp/lin_sinhpostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; ");
>     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(2.0) ;");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"glob_min_h := 0.000000001;");
>     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:=12;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=2;");
>     omniout_str(ALWAYS,"glob_max_iter:=1000000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
>     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,"glob_h_reason:=1;");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y := proc(x)");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"return(cosh(c(2.0)*c(x)+c(3.0))/c(2.0));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(0.1);
>     x_end := c(2.0) ;
>     array_y_init[0 + 1] := exact_soln_y(x_start);
>     glob_look_poles := true;
>     glob_min_h := 0.000000001;
>     glob_type_given_pole := 3;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=12;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=2;
>     glob_max_iter:=1000000;
>     glob_upper_ratio_limit:=c(1.000001);
>     glob_lower_ratio_limit:=c(0.999999);
>     glob_look_poles:=true;
>     glob_h:=c(0.001);
>     glob_display_interval:=c(0.01);
>     glob_h_reason:=1;
>     #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 9
>         #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 10
>             glob_display_interval := c(display_max);
>         fi;# end if 10;
>         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 := 1;
>             #Start Series array_y
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y[term_no] := array_y_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 10
>                         array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 10;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             atomall();
>             if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
>                 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 10;
>             if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
>                 omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>                 glob_h_reason := 2;
>                 glob_h := glob_display_interval;
>                 found_h := true;
>             fi;# end if 10;
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if ( not found_h) then # if number 10
>                 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 11
>                     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 11;
>             fi;# end if 10;
>             opt_iter := opt_iter + 1;
>         od;# end do number 1;
>         if (( not found_h) and (opt_iter = 1)) then # if number 10
>             omniout_str(ALWAYS,"Beginning glob_h too large.");
>             found_h := false;
>         fi;# end if 10;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
>             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 10;
>     else
>         found_h := true;
>         glob_h := glob_h * glob_check_sign;
>     fi;# end if 9;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 9
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 9;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 9
>         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 := 1;
>         #Start Series array_y
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y[term_no] := array_y_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 10
>                     array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 10;
>                 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 10
>                 omniout_str(INFO," ");
>                 omniout_str(INFO,"TOP MAIN SOLVE Loop");
>             fi;# end if 10;
>             glob_iter   :=  glob_iter + 1;
>             glob_clock_sec   := elapsed_time_seconds();
>             track_estimated_error();
>             atomall();
>             track_estimated_error();
>             display_alot(current_iter);
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if (reached_interval()) then # if number 10
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 10;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[2,iii] := array_y_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_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_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_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_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_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_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_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_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_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_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_y[term_no] := array_y_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y_higher[ord,term_no] := array_y_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 10
>             omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
>         fi;# end if 10;
>         if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec  )) then # if number 10
>             omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
>         fi;# end if 10;
>         glob_clock_sec   := elapsed_time_seconds();
>         omniout_str(INFO,"diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(x_start,x_end);
>         if (glob_html_log)  then # if number 10
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2020-05-25T23:52:16-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"lin_sinh.ode.txt\">lin_sinh</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; ")
>             ;
>             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 11
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_min_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             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 11
>                 logitem_str(html_log_file,"Not Given")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 12
>                 logitem_str(html_log_file,"No Solution")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 13
>                 logitem_str(html_log_file,"Some Pole")
>                 ;
>                 logitem_str(html_log_file,"????")
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 14
>                 logitem_str(html_log_file,"No Pole")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 15
>                 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 16
>                 logitem_str(html_log_file,"Complex Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             fi;# end if 16;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_ratio_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_3_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_3_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_6_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_6_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             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 16
>                 logitem_time(html_log_file,(glob_total_exp_sec))
>                 ;
>                 0;
>             else
>                 logitem_str(html_log_file,"Done")
>                 ;
>                 0;
>             fi;# end if 16;
>             log_revs(html_log_file,"<td> 310 </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.lin_sinh.mxt.txt\">lin_sinh diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.lin_sinh.mxt.txt\">lin_sinh maple results</a>")
>             ;
>             logitem_str(html_log_file,"False singularity in three term test")
>             ;
>             logend(html_log_file)
>             ;
>             ;
>         fi;# end if 15;
>         if (glob_html_log)  then # if number 15
>             fclose(html_log_file);
>         fi;# end if 15
>         ;
>         ;;
>     fi;# end if 14
>     #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_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_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_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y_init := Array(0 .. 40, []);
    array_norms := Array(0 .. 40, []);
    array_fact_1 := Array(0 .. 40, []);
    array_1st_rel_error := Array(0 .. 2, []);
    array_last_rel_error := Array(0 .. 2, []);
    array_est_rel_error := Array(0 .. 2, []);
    array_max_est_error := Array(0 .. 2, []);
    array_type_pole := Array(0 .. 2, []);
    array_type_real_pole := Array(0 .. 2, []);
    array_type_complex_pole := Array(0 .. 2, []);
    array_est_digits := Array(0 .. 2, []);
    array_y := Array(0 .. 40, []);
    array_x := Array(0 .. 40, []);
    array_tmp0 := Array(0 .. 40, []);
    array_tmp1 := Array(0 .. 40, []);
    array_tmp2 := Array(0 .. 40, []);
    array_tmp3_g := Array(0 .. 40, []);
    array_tmp3 := Array(0 .. 40, []);
    array_tmp4 := Array(0 .. 40, []);
    array_m1 := Array(0 .. 40, []);
    array_y_higher := Array(0 .. 2, 0 .. 41, []);
    array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
    array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
    array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
    array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
    array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
    array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_fact_2 := Array(0 .. 40, 0 .. 41, []);
    term := 1;
    while term <= 40 do array_y_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 <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do
        array_last_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
    term := 1;
    while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_y[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_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_g[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_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_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_y_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_y_higher_work2[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_y_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 <= 3 do
            array_given_rad_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 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 <= 2 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 <= 2 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_y);
    zero_ats_ar(array_x);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3_g);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_m1);
    zero_ats_ar(array_const_1);
    array_const_1[1] := c(1);
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := c(0.);
    zero_ats_ar(array_const_2D0);
    array_const_2D0[1] := c(2.0);
    zero_ats_ar(array_const_3D0);
    array_const_3D0[1] := c(3.0);
    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_y_set_initial[1, 1] := true;
    array_y_set_initial[1, 2] := false;
    array_y_set_initial[1, 3] := false;
    array_y_set_initial[1, 4] := false;
    array_y_set_initial[1, 5] := false;
    array_y_set_initial[1, 6] := false;
    array_y_set_initial[1, 7] := false;
    array_y_set_initial[1, 8] := false;
    array_y_set_initial[1, 9] := false;
    array_y_set_initial[1, 10] := false;
    array_y_set_initial[1, 11] := false;
    array_y_set_initial[1, 12] := false;
    array_y_set_initial[1, 13] := false;
    array_y_set_initial[1, 14] := false;
    array_y_set_initial[1, 15] := false;
    array_y_set_initial[1, 16] := false;
    array_y_set_initial[1, 17] := false;
    array_y_set_initial[1, 18] := false;
    array_y_set_initial[1, 19] := false;
    array_y_set_initial[1, 20] := false;
    array_y_set_initial[1, 21] := false;
    array_y_set_initial[1, 22] := false;
    array_y_set_initial[1, 23] := false;
    array_y_set_initial[1, 24] := false;
    array_y_set_initial[1, 25] := false;
    array_y_set_initial[1, 26] := false;
    array_y_set_initial[1, 27] := false;
    array_y_set_initial[1, 28] := false;
    array_y_set_initial[1, 29] := false;
    array_y_set_initial[1, 30] := false;
    array_y_set_initial[1, 31] := false;
    array_y_set_initial[1, 32] := false;
    array_y_set_initial[1, 33] := false;
    array_y_set_initial[1, 34] := false;
    array_y_set_initial[1, 35] := false;
    array_y_set_initial[1, 36] := false;
    array_y_set_initial[1, 37] := false;
    array_y_set_initial[1, 38] := false;
    array_y_set_initial[1, 39] := false;
    array_y_set_initial[1, 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 := 1;
    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,
        "##############R:Temp/lin_sinhpostode.ode#################");
    omniout_str(ALWAYS,
        "diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; ")
        ;
    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(2.0) ;");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_min_h := 0.000000001;");
    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:=12;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=2;");
    omniout_str(ALWAYS, "glob_max_iter:=1000000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
    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, "glob_h_reason:=1;");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y := proc(x)");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "return(cosh(c(2.0)*c(x)+c(3.0))/c(2.0));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(0.1);
    x_end := c(2.0);
    array_y_init[1] := exact_soln_y(x_start);
    glob_look_poles := true;
    glob_min_h := 0.1*10^(-8);
    glob_type_given_pole := 3;
    glob_desired_digits_correct := 12;
    glob_max_minutes := 3.0;
    glob_subiter_method := 2;
    glob_max_iter := 1000000;
    glob_upper_ratio_limit := c(1.000001);
    glob_lower_ratio_limit := c(0.999999);
    glob_look_poles := true;
    glob_h := c(0.001);
    glob_display_interval := c(0.01);
    glob_h_reason := 1;
    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 := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y[term_no] := array_y_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_y_higher[r_order, term_no] :=
                            array_y_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;
            atomall();
            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 := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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();
            atomall();
            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 := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_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_y[term_no] := array_y_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y_higher[ord, term_no] :=
                        array_y_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  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *\
              x  +  3.0 )   ; ");
        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, "2020-05-25T23:52:16-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"lin_sinh.ode.txt\">lin_sinh</a>");
            logitem_str(html_log_file, "diff  (  y  ,  x  ,  1  )   =   s\
                inh  ( 2.0  *  x  +  3.0 )   ; ");
            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> 310 </td>");
            logitem_str(html_log_file, "<a href=\"diffeq.lin_sinh.mxt.txt\
                \">lin_sinh diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.lin_sinh.mxt.tx\
                t\">lin_sinh maple results</a>");
            logitem_str(html_log_file,
                "False singularity in three term test");
            logend(html_log_file)
        end if;
        if glob_html_log then fclose(html_log_file) end if
    end if
end proc

# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############R:Temp/lin_sinhpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; 
!
#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(2.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := 0.000000001;







glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=12;
glob_max_minutes:=(3.0);
glob_subiter_method:=2;
glob_max_iter:=1000000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
glob_h_reason:=1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)

return(cosh(c(2.0)*c(x)+c(3.0))/c(2.0));
end;

#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0.1                                          
y[1] (closed_form)                = 6.143323100271928714681585747527             
y[1] (numeric)                    = 6.143323100271928714681585747527             
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 12                                  
Estimated correct digits          = 14                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=4.4MB, alloc=40.3MB, time=0.08
 
TOP MAIN SOLVE Loop
x[1]                              = 0.11                                         
y[1] (closed_form)                = 6.2670188098996158101009032098535            
y[1] (numeric)                    = 6.2670188098996158100977640950475            
absolute error                    = 3.1391148060e-21                             
relative error                    = 5.0089442863029828395281670569080e-20      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y[1] (closed_form)                = 6.393221410612627695141275148605             
y[1] (numeric)                    = 6.3932214106126276951349332995107            
absolute error                    = 6.3418490943e-21                             
relative error                    = 9.9196456480807146564939835539026e-20      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.13                                         
y[1] (closed_form)                = 6.5219813851339733535750386982125            
y[1] (numeric)                    = 6.5219813851339733535654292142107            
absolute error                    = 9.6094840018e-21                             
relative error                    = 1.4733994831238856303620321368012e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y[1] (closed_form)                = 6.6533502391702838747758187275695            
y[1] (numeric)                    = 6.6533502391702838747628754009442            
absolute error                    = 1.29433266253e-20                            
relative error                    = 1.9453848302015913660040187819176e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y[1] (closed_form)                = 6.787380522014781858065993953743             
y[1] (numeric)                    = 6.7873805220147818580496492431966            
absolute error                    = 1.63447105464e-20                            
relative error                    = 2.4081028746489371743372880812708e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.16                                         
y[1] (closed_form)                = 6.924125847567699368341557186889             
y[1] (numeric)                    = 6.9241258475676993683217421905241            
absolute error                    = 1.98149963649e-20                            
relative error                    = 2.8617325567328609293516622277921e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y[1] (closed_form)                = 7.063640915782552890432596048689             
y[1] (numeric)                    = 7.0636409157825528904092404764488            
absolute error                    = 2.33555722402e-20                            
relative error                    = 3.3064495376620554553250584730372e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.18                                         
y[1] (closed_form)                = 7.2059815345468540781352837797455            
y[1] (numeric)                    = 7.2059815345468540781083159252951            
absolute error                    = 2.69678544504e-20                            
relative error                    = 3.7424262497913638066201928300248e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y[1] (closed_form)                = 7.35120464200600887396169285126              
y[1] (numeric)                    = 7.3512046420060088739310395633032            
absolute error                    = 3.06532879568e-20                            
relative error                    = 4.1698319458612269177250690171355e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=51.1MB, alloc=44.3MB, time=0.33
 
TOP MAIN SOLVE Loop
x[1]                              = 0.2                                          
y[1] (closed_form)                = 7.4993683293393348569112882913005            
y[1] (numeric)                    = 7.4993683293393348568768749443185            
absolute error                    = 3.44133469820e-20                            
relative error                    = 4.5888327484018486453422502520004e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y[1] (closed_form)                = 7.650531863997307528887489725279             
y[1] (numeric)                    = 7.6505318639973075288492401896798            
absolute error                    = 3.82495355992e-20                            
relative error                    = 4.9995916988724355774049175571180e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y[1] (closed_form)                = 7.8047557134093307481079503365275            
y[1] (numeric)                    = 7.8047557134093307480657869481925            
absolute error                    = 4.21633883350e-20                            
relative error                    = 5.4022688067685694223399939077326e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y[1] (closed_form)                = 7.962101569171514733789737382204             
y[1] (numeric)                    = 7.9621015691715147337435809114209            
absolute error                    = 4.61564707831e-20                            
relative error                    = 5.7970210982755331225737320042615e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y[1] (closed_form)                = 8.1226323717241370758192951460105            
y[1] (numeric)                    = 8.1226323717241370757690647657808            
absolute error                    = 5.02303802297e-20                            
relative error                    = 6.1840026645251127780792253712199e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.25                                         
y[1] (closed_form)                = 8.286412335528658062848258910688             
y[1] (numeric)                    = 8.2864123355286580627938721643952            
absolute error                    = 5.43867462928e-20                            
relative error                    = 6.5633647096720566858948306556611e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y[1] (closed_form)                = 8.4535069747543614706443719296285            
y[1] (numeric)                    = 8.4535069747543614705857446980541            
absolute error                    = 5.86272315744e-20                            
relative error                    = 6.9352555985917981674041826101843e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y[1] (closed_form)                = 8.6239831294848958095059561556035            
y[1] (numeric)                    = 8.623983129484895809443002623279             
absolute error                    = 6.29535323245e-20                            
relative error                    = 7.2998209040165606559477290867676e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y[1] (closed_form)                = 8.7979089924551989966641114543785            
y[1] (numeric)                    = 8.7979089924551989965967440752568            
absolute error                    = 6.73673791217e-20                            
relative error                    = 7.6572034536242732562534401959026e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y[1] (closed_form)                = 8.9753541363295015800386864132575            
y[1] (numeric)                    = 8.9753541363295015799668158756942            
absolute error                    = 7.18705375633e-20                            
relative error                    = 8.0075433761872348036471937851276e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=90.8MB, alloc=44.3MB, time=0.55
 
TOP MAIN SOLVE Loop
x[1]                              = 0.3                                          
y[1] (closed_form)                = 9.156389541531320078349082240405             
y[1] (numeric)                    = 9.1563895415313200782726174314315            
absolute error                    = 7.64648089735e-20                            
relative error                    = 8.3509781477374737694389504951615e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y[1] (closed_form)                = 9.341087624636572805987459534347             
y[1] (numeric)                    = 9.3410876246365728059063075032265            
absolute error                    = 8.11520311205e-20                            
relative error                    = 8.6876426366525306613877672360832e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y[1] (closed_form)                = 9.5295222673411758075642225724445            
y[1] (numeric)                    = 9.5295222673411758074782884934871            
absolute error                    = 8.59340789574e-20                            
relative error                    = 9.0176691492611829421158788894301e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y[1] (closed_form)                = 9.721768846014706326739361604255             
y[1] (numeric)                    = 9.7217688460147063266485487388894            
absolute error                    = 9.08128653656e-20                            
relative error                    = 9.3411874735971916611932626432888e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y[1] (closed_form)                = 9.9179042618519556687812859599535            
y[1] (numeric)                    = 9.9179042618519556686854956180276            
absolute error                    = 9.57903419259e-20                            
relative error                    = 9.6583249239807856751888227227116e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y[1] (closed_form)                = 10.118006971634432480024236655506            
y[1] (numeric)                    = 10.118006971634432479923368155811            
absolute error                    = 1.00868499695e-19                            
relative error                    = 9.9692063840025211295067240740644e-19      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y[1] (closed_form)                = 10.322157019114121455694907269837            
y[1] (numeric)                    = 10.322157019114121455588857899834            
absolute error                    = 1.06049370003e-19                            
relative error                    = 1.0273954349524269852989848826393e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.37                                         
y[1] (closed_form)                = 10.530436067032051398047099221434            
y[1] (numeric)                    = 10.530436067032051397935764196166            
absolute error                    = 1.11335025268e-19                            
relative error                    = 1.0572688971215528916933254965451e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y[1] (closed_form)                = 10.742927429784480478947598312151            
y[1] (numeric)                    = 10.742927429784480478830870732328            
absolute error                    = 1.16727579823e-19                            
relative error                    = 1.0865528096129169645825222949291e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y[1] (closed_form)                = 10.959716106749765616573251086625            
y[1] (numeric)                    = 10.959716106749765616451021895866            
absolute error                    = 1.22229190759e-19                            
relative error                    = 1.1152587308691568173737861913996e-18      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=130.6MB, alloc=44.3MB, time=0.78
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y[1] (closed_form)                = 11.180888816289247158334103012902            
y[1] (numeric)                    = 11.180888816289247158206260954104            
absolute error                    = 1.27842058798e-19                            
relative error                    = 1.1433979972303192410581095945915e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y[1] (closed_form)                = 11.406534030435749677246941490084            
y[1] (numeric)                    = 11.406534030435749677113373060925            
absolute error                    = 1.33568429159e-19                            
relative error                    = 1.1709817268120441569821525835053e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y[1] (closed_form)                = 11.636742010283574744597303940489            
y[1] (numeric)                    = 11.636742010283574744457893348023            
absolute error                    = 1.39410592466e-19                            
relative error                    = 1.1980208235501021948788162607224e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.43                                         
y[1] (closed_form)                = 11.871604842094142147871877690921            
y[1] (numeric)                    = 11.871604842094142147726506805256            
absolute error                    = 1.45370885665e-19                            
relative error                    = 1.2245259811002661820247859825520e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y[1] (closed_form)                = 12.11121647413172229186343300195             
y[1] (numeric)                    = 12.111216474131722291711981308999            
absolute error                    = 1.51451692951e-19                            
relative error                    = 1.2505076866100511136423177137138e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y[1] (closed_form)                = 12.355672754243994567058378521241            
y[1] (numeric)                    = 12.355672754243994566900723074512            
absolute error                    = 1.57655446729e-19                            
relative error                    = 1.2759762245633094996998567261832e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y[1] (closed_form)                = 12.605071468202464409735086797482            
y[1] (numeric)                    = 12.605071468202464409571102168901            
absolute error                    = 1.63984628581e-19                            
relative error                    = 1.3009416804551040733985694407131e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.47                                         
y[1] (closed_form)                = 12.859512378818075731809406109264            
y[1] (numeric)                    = 12.859512378818075731638964338999            
absolute error                    = 1.70441770265e-19                            
relative error                    = 1.3254139445112100670815653724539e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y[1] (closed_form)                = 13.119097265847665486947749814577            
y[1] (numeric)                    = 13.119097265847665486770720359853            
absolute error                    = 1.77029454724e-19                            
relative error                    = 1.3494027152680126036304468471295e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=170.2MB, alloc=44.3MB, time=1.02
 
TOP MAIN SOLVE Loop
x[1]                              = 0.49                                         
y[1] (closed_form)                = 13.383929966707223486867363869648            
y[1] (numeric)                    = 13.383929966707223486683613552529            
absolute error                    = 1.83750317119e-19                            
relative error                    = 1.3729175031256316793744238746222e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y[1] (closed_form)                = 13.654116418008243314600994806034            
y[1] (numeric)                    = 13.654116418008243314410387760147            
absolute error                    = 1.90607045887e-19                            
relative error                    = 1.3959676338749444958497762310816e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.51                                         
y[1] (closed_form)                = 13.929764697933779428916660502917            
y[1] (numeric)                    = 13.929764697933779428719058119108            
absolute error                    = 1.97602383809e-19                            
relative error                    = 1.4185622520839180080779183062035e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.52                                         
y[1] (closed_form)                = 14.210985069471161447755919963598            
y[1] (numeric)                    = 14.210985069471161447551180834483            
absolute error                    = 2.04739129115e-19                            
relative error                    = 1.4407103245420483129276776814868e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.53                                         
y[1] (closed_form)                = 14.49789002451865927284789372069             
y[1] (numeric)                    = 14.497890024518659272635873584095            
absolute error                    = 2.12020136595e-19                            
relative error                    = 1.4624206435311211857505810457786e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.54                                         
y[1] (closed_form)                = 14.790594328883742309645590047312            
y[1] (numeric)                    = 14.790594328883742309426141728558            
absolute error                    = 2.19448318754e-19                            
relative error                    = 1.4837018301925257102325866914647e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.55                                         
y[1] (closed_form)                = 15.089215068190932686257300851552            
y[1] (numeric)                    = 15.089215068190932686030274204592            
absolute error                    = 2.27026646960e-19                            
relative error                    = 1.5045623376300550368187468362756e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.56                                         
y[1] (closed_form)                = 15.393871694717616224773510852768            
y[1] (numeric)                    = 15.393871694717616224538752700121            
absolute error                    = 2.34758152647e-19                            
relative error                    = 1.5250104541767546679107419192804e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.57                                         
y[1] (closed_form)                = 15.704686075176546113863656846928            
y[1] (numeric)                    = 15.704686075176546113621010918409            
absolute error                    = 2.42645928519e-19                            
relative error                    = 1.5450543064501992387955395514440e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y[1] (closed_form)                = 16.021782539464152921220319460675            
y[1] (numeric)                    = 16.021782539464152920969626330881            
absolute error                    = 2.50693129794e-19                            
relative error                    = 1.5647018624582106531424285370184e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=210.0MB, alloc=44.3MB, time=1.25
 
TOP MAIN SOLVE Loop
x[1]                              = 0.59                                         
y[1] (closed_form)                = 16.345287930394160919841958331508            
y[1] (numeric)                    = 16.345287930394160919583055356049            
absolute error                    = 2.58902975459e-19                            
relative error                    = 1.5839609345612588729135716262184e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y[1] (closed_form)                = 16.675331654436404837808429753555            
y[1] (numeric)                    = 16.675331654436404837541151003997            
absolute error                    = 2.67278749558e-19                            
relative error                    = 1.6028391824332415299712650069903e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.61                                         
y[1] (closed_form)                = 17.012045733481143234775773958186            
y[1] (numeric)                    = 17.012045733481143234499950155669            
absolute error                    = 2.75823802517e-19                            
relative error                    = 1.6213441160351188933243502641137e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.62                                         
y[1] (closed_form)                = 17.355564857649574920740917574624            
y[1] (numeric)                    = 17.355564857649574920456376022155            
absolute error                    = 2.84541552469e-19                            
relative error                    = 1.6394830983768673600777505604087e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.63                                         
y[1] (closed_form)                = 17.706026439171683327793404671736            
y[1] (numeric)                    = 17.706026439171683327499969185107            
absolute error                    = 2.93435486629e-19                            
relative error                    = 1.6572633483694684272532554503261e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.64                                         
y[1] (closed_form)                = 18.063570667352960690983693715299            
y[1] (numeric)                    = 18.063570667352960690681184552607            
absolute error                    = 3.02509162692e-19                            
relative error                    = 1.6746919435963861626253184751114e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y[1] (closed_form)                = 18.428340564651999460879795436294            
y[1] (numeric)                    = 18.428340564651999460568029226047            
absolute error                    = 3.11766210247e-19                            
relative error                    = 1.6917758229680697730508550559500e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.66                                         
y[1] (closed_form)                = 18.800482043891382732088462520288            
y[1] (numeric)                    = 18.800482043891382731767252188049            
absolute error                    = 3.21210332239e-19                            
relative error                    = 1.7085217894366014782879220715537e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.67                                         
y[1] (closed_form)                = 19.180143966624758806734382871644            
y[1] (numeric)                    = 19.180143966624758806403537565202            
absolute error                    = 3.30845306442e-19                            
relative error                    = 1.7249365125606028896227561249652e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=249.7MB, alloc=44.3MB, time=1.47
 
TOP MAIN SOLVE Loop
x[1]                              = 0.68                                         
y[1] (closed_form)                = 19.56747820268344750096080541921             
y[1] (numeric)                    = 19.567478202683447500620130432238            
absolute error                    = 3.40674986972e-19                            
relative error                    = 1.7410265310799245814960006627500e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.69                                         
y[1] (closed_form)                = 19.962639690926397630939535606094            
y[1] (numeric)                    = 19.962639690926397630588832300259            
absolute error                    = 3.50703305835e-19                            
relative error                    = 1.7567982554652072798143221366126e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y[1] (closed_form)                = 20.365786501217796471394937778104            
y[1] (numeric)                    = 20.365786501217796471034003503614            
absolute error                    = 3.60934274490e-19                            
relative error                    = 1.7722579703387222731280203549273e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.71                                         
y[1] (closed_form)                = 20.777079897657123056804498505864            
y[1] (numeric)                    = 20.777079897657123056433126520401            
absolute error                    = 3.71371985463e-19                            
relative error                    = 1.7874118369486409868781266095098e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y[1] (closed_form)                = 21.1966844030869381896750493939              
y[1] (numeric)                    = 21.196684403086938189293028779926            
absolute error                    = 3.82020613974e-19                            
relative error                    = 1.8022658955018699329800077545415e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.73                                         
y[1] (closed_form)                = 21.624767864904215132013294776353            
y[1] (numeric)                    = 21.624767864904215131620410356731            
absolute error                    = 3.92884419622e-19                            
relative error                    = 1.8168260675742529847053877082670e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.74                                         
y[1] (closed_form)                = 22.061501522201536389763341605647            
y[1] (numeric)                    = 22.061501522201536389359373857578            
absolute error                    = 4.03967748069e-19                            
relative error                    = 1.8310981583119719936110476234463e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.75                                         
y[1] (closed_form)                = 22.507060074265013964152899969966            
y[1] (numeric)                    = 22.50706007426501396373762493717             
absolute error                    = 4.15275032796e-19                            
relative error                    = 1.8450878587685163856793004904138e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.76                                         
y[1] (closed_form)                = 22.961621750456333151366473566026            
y[1] (numeric)                    = 22.961621750456333150939662769159            
absolute error                    = 4.26810796867e-19                            
relative error                    = 1.8588007480722378678182797423479e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y[1] (closed_form)                = 23.42536838150687363983841696219             
y[1] (numeric)                    = 23.425368381506873639399837307445            
absolute error                    = 4.38579654745e-19                            
relative error                    = 1.8722422956269756402152744174895e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=289.5MB, alloc=44.3MB, time=1.70
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y[1] (closed_form)                = 23.89848547225242650420573277299             
y[1] (numeric)                    = 23.898485472252426503755146458864            
absolute error                    = 4.50586314126e-19                            
relative error                    = 1.8854178631911955562699184244319e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.79                                         
y[1] (closed_form)                = 24.381162275837601952527347158722            
y[1] (numeric)                    = 24.381162275837601952064511580887            
absolute error                    = 4.62835577835e-19                            
relative error                    = 1.8983327070247291079173772665265e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y[1] (closed_form)                = 24.873591869419610579274046645474            
y[1] (numeric)                    = 24.873591869419610578798714299731            
absolute error                    = 4.75332345743e-19                            
relative error                    = 1.9109919799214394494380094098537e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.81                                         
y[1] (closed_form)                = 25.375971231401700645987480826326            
y[1] (numeric)                    = 25.375971231401700645499399209608            
absolute error                    = 4.88081616718e-19                            
relative error                    = 1.9234007331865960643193696608682e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y[1] (closed_form)                = 25.888501320227145794313388773854            
y[1] (numeric)                    = 25.888501320227145793812300283207            
absolute error                    = 5.01088490647e-19                            
relative error                    = 1.9355639187019708407069005793196e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.83                                         
y[1] (closed_form)                = 26.41138715476530183709477321503             
y[1] (numeric)                    = 26.411387154765301836580415044582            
absolute error                    = 5.14358170448e-19                            
relative error                    = 1.9474863907524690358578985104409e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.84                                         
y[1] (closed_form)                = 26.944837896321888122069841242718            
y[1] (numeric)                    = 26.94483789632188812154194527855             
absolute error                    = 5.27895964168e-19                            
relative error                    = 1.9591729079953402556493624737064e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y[1] (closed_form)                = 27.489066932306298674205188632414            
y[1] (numeric)                    = 27.489066932306298673663481345309            
absolute error                    = 5.41707287105e-19                            
relative error                    = 1.9706281353200933453494933034448e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.86                                         
y[1] (closed_form)                = 28.04429196158941115670018389728             
y[1] (numeric)                    = 28.044291961589411156144386233305            
absolute error                    = 5.55797663975e-19                            
relative error                    = 1.9818566456812060280795153941698e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y[1] (closed_form)                = 28.610735081586037912366248145138            
y[1] (numeric)                    = 28.61073508158603791179607541402             
absolute error                    = 5.70172731118e-19                            
relative error                    = 1.9928629218791551528270165401299e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=329.3MB, alloc=44.3MB, time=1.94
 
TOP MAIN SOLVE Loop
x[1]                              = 0.88                                         
y[1] (closed_form)                = 29.18862287709685322691241110298             
y[1] (numeric)                    = 29.18862287709685322632757286423             
absolute error                    = 5.84838238750e-19                            
relative error                    = 2.0036513583136503895000077668143e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.89                                         
y[1] (closed_form)                = 29.778186510945334769617281941752            
y[1] (numeric)                    = 29.778186510945334769017481888483            
absolute error                    = 5.99800053269e-19                            
relative error                    = 2.0142262627327429510401862156600e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y[1] (closed_form)                = 30.379661816445975196472369581162            
y[1] (numeric)                    = 30.379661816445975195857305421561            
absolute error                    = 6.15064159601e-19                            
relative error                    = 2.0245918579252785665171873988971e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y[1] (closed_form)                = 30.99328939174075243336393675515             
y[1] (numeric)                    = 30.993289391740752432733300091557            
absolute error                    = 6.30636663593e-19                            
relative error                    = 2.0347522833799474942215396063991e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.92                                         
y[1] (closed_form)                = 31.619314696041594485243035403235            
y[1] (numeric)                    = 31.619314696041594484596511608781            
absolute error                    = 6.46523794454e-19                            
relative error                    = 2.0447115969118014332329345029872e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.93                                         
y[1] (closed_form)                = 32.257988147817337040457365417906            
y[1] (numeric)                    = 32.257988147817337039794633510658            
absolute error                    = 6.62731907248e-19                            
relative error                    = 2.0544737762663051822346256941030e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y[1] (closed_form)                = 32.909565224964449962463579799793            
y[1] (numeric)                    = 32.909565224964449961784312314358            
absolute error                    = 6.79267485435e-19                            
relative error                    = 2.0640427206851188899654365109089e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.95                                         
y[1] (closed_form)                = 33.574306567001602295144215955193            
y[1] (numeric)                    = 33.574306567001602294448078811723            
absolute error                    = 6.96137143470e-19                            
relative error                    = 2.0734222524619350469872943700260e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y[1] (closed_form)                = 34.252478079328944970343748031806            
y[1] (numeric)                    = 34.252478079328944969630400402369            
absolute error                    = 7.13347629437e-19                            
relative error                    = 2.0826161184159657163440542003128e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=369.1MB, alloc=44.3MB, time=2.16
 
TOP MAIN SOLVE Loop
x[1]                              = 0.97                                         
y[1] (closed_form)                = 34.944351039593816320849079263418            
y[1] (numeric)                    = 34.944351039593816320118173435655            
absolute error                    = 7.30905827763e-19                            
relative error                    = 2.0916279914165372679637727095722e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.98                                         
y[1] (closed_form)                = 35.650202206205418099247982954026            
y[1] (numeric)                    = 35.650202206205418098499164192067            
absolute error                    = 7.48818761959e-19                            
relative error                    = 2.1004614717968067616216504553355e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.99                                         
y[1] (closed_form)                = 36.370313929041869319954674031678            
y[1] (numeric)                    = 36.370313929041869319187580434239            
absolute error                    = 7.67093597439e-19                            
relative error                    = 2.1091200888053707449806537364104e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y[1] (closed_form)                = 37.104974262393922222053054022244            
y[1] (numeric)                    = 37.104974262393922221267316377864            
absolute error                    = 7.85737644380e-19                            
relative error                    = 2.1176073019847073415594655315082e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y[1] (closed_form)                = 37.854477080190519345279058605287            
y[1] (numeric)                    = 37.854477080190519344474300244636            
absolute error                    = 8.04758360651e-19                            
relative error                    = 2.1259265025540004071460815680763e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y[1] (closed_form)                = 38.619122193552283478333746393942            
y[1] (numeric)                    = 38.619122193552283477509583039151            
absolute error                    = 8.24163354791e-19                            
relative error                    = 2.1340810147378220165060960052342e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y[1] (closed_form)                = 39.399215470719963442907218699323            
y[1] (numeric)                    = 39.399215470719963442063258310267            
absolute error                    = 8.43960389056e-19                            
relative error                    = 2.1420740970926187063514852867491e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y[1] (closed_form)                = 40.195068959405808690794244399209            
y[1] (numeric)                    = 40.195068959405808689930087016685            
absolute error                    = 8.64157382524e-19                            
relative error                    = 2.1499089437979025477454595453610e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y[1] (closed_form)                = 41.007001011616814895313848966702            
y[1] (numeric)                    = 41.007001011616814894429086552439            
absolute error                    = 8.84762414263e-19                            
relative error                    = 2.1575886859230620550722141059519e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y[1] (closed_form)                = 41.835336410999771499601567671098            
y[1] (numeric)                    = 41.83533641099977149869578394454             
absolute error                    = 9.05783726558e-19                            
relative error                    = 2.1651163926575767754726368136188e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=408.9MB, alloc=44.3MB, time=2.39
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y[1] (closed_form)                = 42.68040650275905093875028644411             
y[1] (numeric)                    = 42.680406502759050937823056715894            
absolute error                    = 9.27229728216e-19                            
relative error                    = 2.1724950725482423751201947952826e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y[1] (closed_form)                = 43.542549326199108383748813037146            
y[1] (numeric)                    = 43.542549326199108382799704039221            
absolute error                    = 9.49108997925e-19                            
relative error                    = 2.1797276746814885825704951804746e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y[1] (closed_form)                = 44.422109749944710774372647096684            
y[1] (numeric)                    = 44.422109749944710773401216809002            
absolute error                    = 9.71430287682e-19                            
relative error                    = 2.1868170898461414796600527191752e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y[1] (closed_form)                = 45.319439609892985035600531894505            
y[1] (numeric)                    = 45.319439609892985034606329368203            
absolute error                    = 9.94202526302e-19                            
relative error                    = 2.1937661517000996695824973885518e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y[1] (closed_form)                = 46.234897849952468136228522202793            
y[1] (numeric)                    = 46.234897849952468135211087379812            
absolute error                    = 1.017434822981e-18                           
relative error                    = 2.2005776378762908320452166037483e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y[1] (closed_form)                = 47.168850665625456486250701843706            
y[1] (numeric)                    = 47.168850665625456485209565372756            
absolute error                    = 1.041136470950e-18                           
relative error                    = 2.2072542711089070056172073359903e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y[1] (closed_form)                = 48.121671650491089527222354432198            
y[1] (numeric)                    = 48.121671650491089526157037481014            
absolute error                    = 1.065316951184e-18                           
relative error                    = 2.2137987202968005504248518964454e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y[1] (closed_form)                = 49.093741945647762702175555408308            
y[1] (numeric)                    = 49.093741945647762701085569472109            
absolute error                    = 1.089985936199e-18                           
relative error                    = 2.2202136015741797910743343998678e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y[1] (closed_form)                = 50.08545039217464876286722559114             
y[1] (numeric)                    = 50.085450392174648761752072297223            
absolute error                    = 1.115153293917e-18                           
relative error                    = 2.2265014793422553729465687393879e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y[1] (closed_form)                = 51.097193686673314055729934036635            
y[1] (numeric)                    = 51.097193686673314054589104945017            
absolute error                    = 1.140829091618e-18                           
relative error                    = 2.2326648672988478329152770566060e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=448.7MB, alloc=44.3MB, time=2.62
 
TOP MAIN SOLVE Loop
x[1]                              = 1.17                                         
y[1] (closed_form)                = 52.1293765399516485069556997067              
y[1] (numeric)                    = 52.129376539951648505788676106745            
absolute error                    = 1.167023599955e-18                           
relative error                    = 2.2387062294148098167275679816432e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y[1] (closed_form)                = 53.18241183891358499452076928281             
y[1] (numeric)                    = 53.182411838913584993327021985716            
absolute error                    = 1.193747297094e-18                           
relative error                    = 2.2446279809757232236169786866141e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y[1] (closed_form)                = 54.25672081171936615345855326221             
y[1] (numeric)                    = 54.256720811719366152237542389353            
absolute error                    = 1.221010872857e-18                           
relative error                    = 2.2504324894497928752911035608520e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y[1] (closed_form)                = 55.352733196282424923269082283245            
y[1] (numeric)                    = 55.352733196282424922020257050199            
absolute error                    = 1.248825233046e-18                           
relative error                    = 2.2561220755217793508708291970329e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y[1] (closed_form)                = 56.47088741217027983633897664258             
y[1] (numeric)                    = 56.470887412170279835061775138804            
absolute error                    = 1.277201503776e-18                           
relative error                    = 2.2616990139608553432175116940848e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.22                                         
y[1] (closed_form)                = 57.61163073597820769752979454862             
y[1] (numeric)                    = 57.611630735978207696223643512689            
absolute error                    = 1.306151035931e-18                           
relative error                    = 2.2671655345373073689742928374165e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y[1] (closed_form)                = 58.775419480245845462353407942745            
y[1] (numeric)                    = 58.775419480245845461017722533037            
absolute error                    = 1.335685409708e-18                           
relative error                    = 2.2725238229170237872719276104137e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y[1] (closed_form)                = 59.96271917598829034007217537078             
y[1] (numeric)                    = 59.962719175988290338706358931525            
absolute error                    = 1.365816439255e-18                           
relative error                    = 2.2777760215416197552895980047754e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y[1] (closed_form)                = 61.17400475891471299554560355363             
y[1] (numeric)                    = 61.174004758914712994149047376246            
absolute error                    = 1.396556177384e-18                           
relative error                    = 2.2829242304599714095859082443810e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=488.5MB, alloc=44.3MB, time=2.86
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y[1] (closed_form)                = 62.409760759408973778052184780765            
y[1] (numeric)                    = 62.409760759408973776624267860362            
absolute error                    = 1.427916920403e-18                           
relative error                    = 2.2879705081832499331211916193907e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.27                                         
y[1] (closed_form)                = 63.670481496348236756686596485415            
y[1] (numeric)                    = 63.670481496348236755226685272396            
absolute error                    = 1.459911213019e-18                           
relative error                    = 2.2929168724799605851087437830241e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y[1] (closed_form)                = 64.956671274837111592229065908635            
y[1] (numeric)                    = 64.956671274837111590736514055253            
absolute error                    = 1.492551853382e-18                           
relative error                    = 2.2977653012219302540198915231007e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y[1] (closed_form)                = 66.268844587936419538726025543685            
y[1] (numeric)                    = 66.268844587936419537200173645504            
absolute error                    = 1.525851898181e-18                           
relative error                    = 2.3025177331351361441600548397875e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y[1] (closed_form)                = 67.60752632246727777093543479198             
y[1] (numeric)                    = 67.607526322467277769375610124104            
absolute error                    = 1.559824667876e-18                           
relative error                    = 2.3071760685875595244281037366173e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.31                                         
y[1] (closed_form)                = 68.973251968972826415458791312585            
y[1] (numeric)                    = 68.973251968972826413864307560552            
absolute error                    = 1.594483752033e-18                           
relative error                    = 2.3117421703565148066725289249455e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.32                                         
y[1] (closed_form)                = 70.366567835921585775899305414105            
y[1] (numeric)                    = 70.366567835921585774269462399354            
absolute error                    = 1.629843014751e-18                           
relative error                    = 2.3162178643577068329003298559917e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y[1] (closed_form)                = 71.788031268238127951019144629685            
y[1] (numeric)                    = 71.788031268238127949353228029491            
absolute error                    = 1.665916600194e-18                           
relative error                    = 2.3206049403545456635439719732053e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y[1] (closed_form)                = 73.23821087024847802832414978977             
y[1] (numeric)                    = 73.23821087024847802662143085148             
absolute error                    = 1.702718938290e-18                           
relative error                    = 2.3249051527304508026085930142619e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y[1] (closed_form)                = 74.71768673312942598619844074783             
y[1] (numeric)                    = 74.717686733129425984458175997372            
absolute error                    = 1.740264750458e-18                           
relative error                    = 2.3291202211248007497706398816147e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=528.4MB, alloc=44.3MB, time=3.08
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y[1] (closed_form)                = 76.227050666952732062047693351985            
y[1] (numeric)                    = 76.227050666952732060269124296462            
absolute error                    = 1.778569055523e-18                           
relative error                    = 2.3332518311561488555785762146202e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.37                                         
y[1] (closed_form)                = 77.766906437417046362562335812985            
y[1] (numeric)                    = 77.766906437417046360744688637267            
absolute error                    = 1.817647175718e-18                           
relative error                    = 2.3373016350865806892464048955824e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y[1] (closed_form)                = 79.33787000736223864041245052584             
y[1] (numeric)                    = 79.337870007362238638554935783027            
absolute error                    = 1.857514742813e-18                           
relative error                    = 2.3412712524808518594877656536625e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y[1] (closed_form)                = 80.940569783162747189519059182625            
y[1] (numeric)                    = 80.940569783162747187620871478253            
absolute error                    = 1.898187704372e-18                           
relative error                    = 2.3451622708577236879796844911149e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y[1] (closed_form)                = 82.575646866098507483748355202355            
y[1] (numeric)                    = 82.575646866098507481808672872239            
absolute error                    = 1.939682330116e-18                           
relative error                    = 2.3489762463033613925573289885737e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y[1] (closed_form)                = 84.243755308804012282141431504465            
y[1] (numeric)                    = 84.243755308804012280159416286022            
absolute error                    = 1.982015218443e-18                           
relative error                    = 2.3527147041080049152160525884314e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y[1] (closed_form)                = 85.945562376898086244087988189765            
y[1] (numeric)                    = 85.945562376898086242062784886678            
absolute error                    = 2.025203303087e-18                           
relative error                    = 2.3563791393973921759407641310055e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y[1] (closed_form)                = 87.68174881589903045273359677298             
y[1] (numeric)                    = 87.681748815899030450664332913136            
absolute error                    = 2.069263859844e-18                           
relative error                    = 2.3599710176729361598048930645430e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y[1] (closed_form)                = 89.453009123531906463345929438345            
y[1] (numeric)                    = 89.453009123531906461231714924809            
absolute error                    = 2.114214513536e-18                           
relative error                    = 2.3634917754598210896070581701900e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y[1] (closed_form)                = 91.26005182753688642107149765098             
y[1] (numeric)                    = 91.260051827536886418911424405965            
absolute error                    = 2.160073245015e-18                           
relative error                    = 2.3669428208271273891355911870958e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=568.3MB, alloc=44.3MB, time=3.31
 
TOP MAIN SOLVE Loop
x[1]                              = 1.46                                         
y[1] (closed_form)                = 93.103599769089796292290726226925            
y[1] (numeric)                    = 93.103599769089796290083867828535            
absolute error                    = 2.206858398390e-18                           
relative error                    = 2.3703255339893661674421752094526e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y[1] (closed_form)                = 94.98439039194822420585486754371             
y[1] (numeric)                    = 94.984390391948224203600278855374            
absolute error                    = 2.254588688336e-18                           
relative error                    = 2.3736412678257503172254221236932e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y[1] (closed_form)                = 96.903176037438856202874099326805            
y[1] (numeric)                    = 96.903176037438856200570816119184            
absolute error                    = 2.303283207621e-18                           
relative error                    = 2.3768913484642846648802319314196e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.49                                         
y[1] (closed_form)                = 98.86072424540403826257364048242             
y[1] (numeric)                    = 98.860724245404038260220679047727            
absolute error                    = 2.352961434693e-18                           
relative error                    = 2.3800770757578052355034056070583e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y[1] (closed_form)                = 100.8578180612279472417025564277             
y[1] (numeric)                    = 100.8578180612279472392989131862             
absolute error                    = 2.40364324150e-18                            
relative error                    = 2.3831997238338189414593802863781e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y[1] (closed_form)                = 102.89525634906518528960787945276            
y[1] (numeric)                    = 102.89525634906518528715253055132            
absolute error                    = 2.45534890144e-18                            
relative error                    = 2.3862605416039736748964294054667e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.52                                         
y[1] (closed_form)                = 104.97385411139709335317701811154            
y[1] (numeric)                    = 104.97385411139709335066891901405            
absolute error                    = 2.50809909749e-18                            
relative error                    = 2.3892607532809388595152580603983e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y[1] (closed_form)                = 107.09444281504361055785808975495            
y[1] (numeric)                    = 107.09444281504361055529617482454            
absolute error                    = 2.56191493041e-18                            
relative error                    = 2.3922015588003288194287779932087e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y[1] (closed_form)                = 109.25787072376108855539333416414            
y[1] (numeric)                    = 109.25787072376108855277651623688            
absolute error                    = 2.61681792726e-18                            
relative error                    = 2.3950841343743137196752484740983e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=608.1MB, alloc=44.3MB, time=3.55
 
TOP MAIN SOLVE Loop
x[1]                              = 1.55                                         
y[1] (closed_form)                = 111.46500323755910439870135520834            
y[1] (numeric)                    = 111.46500323755910439602852515836            
absolute error                    = 2.67283004998e-18                            
relative error                    = 2.3979096329307480947356433323585e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.56                                         
y[1] (closed_form)                = 113.71672323887200319334263850896            
y[1] (numeric)                    = 113.71672323887200319061266480482            
absolute error                    = 2.72997370414e-18                            
relative error                    = 2.4006791845430241088080558186560e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.57                                         
y[1] (closed_form)                = 116.01393144572364375831104205052            
y[1] (numeric)                    = 116.01393144572364375552277030254            
absolute error                    = 2.78827174798e-18                            
relative error                    = 2.4033938969514834805856036231022e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.58                                         
y[1] (closed_form)                = 118.3575467720266179033416371037             
y[1] (numeric)                    = 118.35754677202661790049388960221            
absolute error                    = 2.84774750149e-18                            
relative error                    = 2.4060548559486152836598917333723e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.59                                         
y[1] (closed_form)                = 120.74850669516006781449946661332            
y[1] (numeric)                    = 120.74850669516006781159104185756            
absolute error                    = 2.90842475576e-18                            
relative error                    = 2.4086631258327417989240127660407e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y[1] (closed_form)                = 123.18776763097313757610636932996            
y[1] (numeric)                    = 123.18776763097313757313604154745            
absolute error                    = 2.97032778251e-18                            
relative error                    = 2.4112197498440336941527298203840e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.61                                         
y[1] (closed_form)                = 125.6763053163640652097273284638             
y[1] (numeric)                    = 125.67630531636406520669384712003            
absolute error                    = 3.03348134377e-18                            
relative error                    = 2.4137257505572264338318633489332e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.62                                         
y[1] (closed_form)                = 128.2151151995879519681545144664             
y[1] (numeric)                    = 128.21511519958795196505660376458            
absolute error                    = 3.09791070182e-18                            
relative error                    = 2.4161821303187159877962505575392e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.63                                         
y[1] (closed_form)                = 130.80521283844933719627959468769            
y[1] (numeric)                    = 130.80521283844933719311595305844            
absolute error                    = 3.16364162925e-18                            
relative error                    = 2.4185898716110404316158914869225e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.64                                         
y[1] (closed_form)                = 133.44763430653886109810378060699            
y[1] (numeric)                    = 133.44763430653886109487308018768            
absolute error                    = 3.23070041931e-18                            
relative error                    = 2.4209499374779830370763525542195e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=648.0MB, alloc=44.3MB, time=3.77
 
TOP MAIN SOLVE Loop
x[1]                              = 1.65                                         
y[1] (closed_form)                = 136.14343660767651549155347391736            
y[1] (numeric)                    = 136.14343660767651548825436002097            
absolute error                    = 3.29911389639e-18                            
relative error                    = 2.4232632718806936738755373631635e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.66                                         
y[1] (closed_form)                = 138.89369809872726537738712711246            
y[1] (numeric)                    = 138.89369809872726537401821768564            
absolute error                    = 3.36890942682e-18                            
relative error                    = 2.4255308001269717580335309757136e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.67                                         
y[1] (closed_form)                = 141.6995189209581732084376699973             
y[1] (numeric)                    = 141.69951892095817320499755506757            
absolute error                    = 3.44011492973e-18                            
relative error                    = 2.4277534291763832031185735042694e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.68                                         
y[1] (closed_form)                = 144.56202144010957446040320894234            
y[1] (numeric)                    = 144.56202144010957445689045005405            
absolute error                    = 3.51275888829e-18                            
relative error                    = 2.4299320480554407880242896850747e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.69                                         
y[1] (closed_form)                = 147.48235069535633884210822487202            
y[1] (numeric)                    = 147.48235069535633883852135451099            
absolute error                    = 3.58687036103e-18                            
relative error                    = 2.4320675281608031591666933107225e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.7                                          
y[1] (closed_form)                = 150.46167485733880763594933984279            
y[1] (numeric)                    = 150.46167485733880763228686084926            
absolute error                    = 3.66247899353e-18                            
relative error                    = 2.4341607236544473617104413804912e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.71                                         
y[1] (closed_form)                = 153.50118569544662565062242336024            
y[1] (numeric)                    = 153.50118569544662564688280832998            
absolute error                    = 3.73961503026e-18                            
relative error                    = 2.4362124717913041330904082211250e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.72                                         
y[1] (closed_form)                = 156.60209905454238754944629525546            
y[1] (numeric)                    = 156.60209905454238754562798592881            
absolute error                    = 3.81830932665e-18                            
relative error                    = 2.4382235932355763880632384765574e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.73                                         
y[1] (closed_form)                = 159.76565534131579436921439045535            
y[1] (numeric)                    = 159.76565534131579436531579709386            
absolute error                    = 3.89859336149e-18                            
relative error                    = 2.4401948924261784666789570039968e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.74                                         
y[1] (closed_form)                = 162.99312002046286837699047680953            
y[1] (numeric)                    = 162.99312002046286837300997756008            
absolute error                    = 3.98049924945e-18                            
relative error                    = 2.4421271578519821781986935613052e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=687.9MB, alloc=44.3MB, time=4.00
 
TOP MAIN SOLVE Loop
x[1]                              = 1.75                                         
y[1] (closed_form)                = 166.28578412088870456660221928649            
y[1] (numeric)                    = 166.28578412088870456253815953253            
absolute error                    = 4.06405975396e-18                            
relative error                    = 2.4440211623895969828987922567209e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.76                                         
y[1] (closed_form)                = 169.64496475213624664489120016104            
y[1] (numeric)                    = 169.64496475213624664074189186067            
absolute error                    = 4.14930830037e-18                            
relative error                    = 2.4458776636444495594569376527968e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.77                                         
y[1] (closed_form)                = 173.07200563124766590392271856698            
y[1] (numeric)                    = 173.07200563124766589968643957777            
absolute error                    = 4.23627898921e-18                            
relative error                    = 2.4476974041867529457928316437692e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.78                                         
y[1] (closed_form)                = 176.56827762026909455561630321199            
y[1] (numeric)                    = 176.56827762026909455129129660205            
absolute error                    = 4.32500660994e-18                            
relative error                    = 2.4494811119137928076522346588039e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.79                                         
y[1] (closed_form)                = 180.13517927461372258895612533416            
y[1] (numeric)                    = 180.13517927461372258454059867941            
absolute error                    = 4.41552665475e-18                            
relative error                    = 2.4512295002735625671985500202369e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y[1] (closed_form)                = 183.77413740250261070012964163096            
y[1] (numeric)                    = 183.77413740250261069562176629805            
absolute error                    = 4.50787533291e-18                            
relative error                    = 2.4529432686367828269240381661983e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.81                                         
y[1] (closed_form)                = 187.48660763570700308007681854096            
y[1] (numeric)                    = 187.48660763570700307547472895586            
absolute error                    = 4.60208958510e-18                            
relative error                    = 2.4546231024895495806014996502199e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.82                                         
y[1] (closed_form)                = 191.27407501182044459456392742698            
y[1] (numeric)                    = 191.2740750118204445898657203287             
absolute error                    = 4.69820709828e-18                            
relative error                    = 2.4562696737598433055395204954339e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.83                                         
y[1] (closed_form)                = 195.13805456829361896738568502882            
y[1] (numeric)                    = 195.13805456829361896258941870808            
absolute error                    = 4.79626632074e-18                            
relative error                    = 2.4578836410718762759340040526470e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=727.8MB, alloc=44.3MB, time=4.23
 
TOP MAIN SOLVE Loop
x[1]                              = 1.84                                         
y[1] (closed_form)                = 199.08009194846952982253913609879            
y[1] (numeric)                    = 199.08009194846952981764282962131            
absolute error                    = 4.89630647748e-18                            
relative error                    = 2.4594656500095319492333044773259e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.85                                         
y[1] (closed_form)                = 203.1017640198614467383629686929             
y[1] (numeric)                    = 203.10176401986144673336460110702            
absolute error                    = 4.99836758588e-18                            
relative error                    = 2.4610163333643948812411188454223e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.86                                         
y[1] (closed_form)                = 207.20467950492093573587978209666            
y[1] (numeric)                    = 207.20467950492093573077729162489            
absolute error                    = 5.10249047177e-18                            
relative error                    = 2.4625363114199455956989234201499e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.87                                         
y[1] (closed_form)                = 211.3904796245482898238891881436             
y[1] (numeric)                    = 211.39047962454828981868047135791            
absolute error                    = 5.20871678569e-18                            
relative error                    = 2.4640261921640125315326818812409e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.88                                         
y[1] (closed_form)                = 215.66083875460277235328325977316            
y[1] (numeric)                    = 215.66083875460277234796617075362            
absolute error                    = 5.31708901954e-18                            
relative error                    = 2.4654865715282855291741207569696e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.89                                         
y[1] (closed_form)                = 220.01746509567528603151267816406            
y[1] (numeric)                    = 220.01746509567528602608502764036            
absolute error                    = 5.42765052370e-18                            
relative error                    = 2.4669180336841755335694358540988e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y[1] (closed_form)                = 224.46210135639138559523068997538            
y[1] (numeric)                    = 224.46210135639138558969024445116            
absolute error                    = 5.54044552422e-18                            
relative error                    = 2.4683211512054393753887144607937e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.91                                         
y[1] (closed_form)                = 228.99652545051796445701224487243            
y[1] (numeric)                    = 228.99652545051796445135672573178            
absolute error                    = 5.65551914065e-18                            
relative error                    = 2.4696964853608908108477809073400e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.92                                         
y[1] (closed_form)                = 233.62255120815246729568675391135            
y[1] (numeric)                    = 233.62255120815246728991383650744            
absolute error                    = 5.77291740391e-18                            
relative error                    = 2.4710445862593374925200155299440e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.93                                         
y[1] (closed_form)                = 238.3420291012791137579698709647             
y[1] (numeric)                    = 238.34202910127911375207718368979            
absolute error                    = 5.89268727491e-18                            
relative error                    = 2.4723659931610339833404182322818e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
memory used=767.5MB, alloc=44.3MB, time=4.47
 
TOP MAIN SOLVE Loop
x[1]                              = 1.94                                         
y[1] (closed_form)                = 243.15684698398236543508692128326            
y[1] (numeric)                    = 243.15684698398236542907204462008            
absolute error                    = 6.01487666318e-18                            
relative error                    = 2.4736612346253289001301297067993e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.95                                         
y[1] (closed_form)                = 248.06893084761373137082311403248            
y[1] (numeric)                    = 248.06893084761373136468357958636            
absolute error                    = 6.13953444612e-18                            
relative error                    = 2.4749308287588237888197031053088e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.96                                         
y[1] (closed_form)                = 253.0802455912139888922287518312             
y[1] (numeric)                    = 253.08024559121398888596204134272            
absolute error                    = 6.26671048848e-18                            
relative error                    = 2.4761752833930223732352807265906e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.97                                         
y[1] (closed_form)                = 258.19279580749899892374496204819            
y[1] (numeric)                    = 258.19279580749899891734850638581            
absolute error                    = 6.39645566238e-18                            
relative error                    = 2.4773950963174860854852098288242e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.98                                         
y[1] (closed_form)                = 263.40862658472352059082620281341            
y[1] (numeric)                    = 263.40862658472352058429738094577            
absolute error                    = 6.52882186764e-18                            
relative error                    = 2.4785907554702088129702475398893e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.99                                         
y[1] (closed_form)                = 268.72982432474378133056107538018            
y[1] (numeric)                    = 268.7298243247437813238972133277             
absolute error                    = 6.66386205248e-18                            
relative error                    = 2.4797627391097181357097175825097e-18      % 
Desired digits                    = 12                                  
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   = 0.25                                         
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; 
Iterations                       = 1900                                
Total Elapsed Time               = 4 Seconds
Elapsed Time(since restart)      = 4 Seconds
Time to Timeout                  = 2 Minutes 55 Seconds
Percent Done                     = 100.1                                      % 
> quit
memory used=794.5MB, alloc=44.3MB, time=4.61