|\^/|     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(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) +
> c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));
> end;
exact_soln_y := proc(x)
    return
        c(10.0)*(c(0.1)*c(x) + c(0.2))*arctan(sqrt(c(0.1)*c(x) + c(0.2)))
         - c(10.0)*sqrt(c(0.1)*c(x) + c(0.2))
         + c(10.0)*arctan(sqrt(c(0.1)*c(x) + c(0.2)))
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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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)*24*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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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)*24*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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
#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,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> 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_0D1[1] * array_x[1];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 1
>     array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
>     #emit pre sqrt 1 $eq_no = 1
>     array_tmp3[1] :=  sqrt(array_tmp2[1]);
>     #emit pre arctan $eq_no = 1
>     array_tmp4[1] :=  arctan(array_tmp3[1]);
>     array_tmp4_a1[1] :=  sin(array_tmp4[1]);
>     array_tmp4_a2[1] :=  cos(array_tmp4[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[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_0D1[1] * array_x[2];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre sqrt 2 $eq_no = 1
>     array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
>     #emit pre arctan $eq_no = 1
>     array_tmp4[2] :=  (ats(2,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(1,array_tmp4_a1,array_tmp4,2) - att(1,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
>     array_tmp4_a1[2] :=  att(1,array_tmp4_a2,array_tmp4,1);
>     array_tmp4_a2[2] :=  neg(att(1,array_tmp4_a1,array_tmp4,1));
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
>     array_tmp3[3] := 0;
>     array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
>     #emit pre arctan $eq_no = 1
>     array_tmp4[3] :=  (ats(3,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(2,array_tmp4_a1,array_tmp4,2) - att(2,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
>     array_tmp4_a1[3] :=  att(2,array_tmp4_a2,array_tmp4,1);
>     array_tmp4_a2[3] :=  neg(att(2,array_tmp4_a1,array_tmp4,1));
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
>     array_tmp3[4] := 0;
>     array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
>     #emit pre arctan $eq_no = 1
>     array_tmp4[4] :=  (ats(4,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(3,array_tmp4_a1,array_tmp4,2) - att(3,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
>     array_tmp4_a1[4] :=  att(3,array_tmp4_a2,array_tmp4,1);
>     array_tmp4_a2[4] :=  neg(att(3,array_tmp4_a1,array_tmp4,1));
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
>     array_tmp3[5] := 0;
>     array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
>     #emit pre arctan $eq_no = 1
>     array_tmp4[5] :=  (ats(5,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(4,array_tmp4_a1,array_tmp4,2) - att(4,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
>     array_tmp4_a1[5] :=  att(4,array_tmp4_a2,array_tmp4,1);
>     array_tmp4_a2[5] :=  neg(att(4,array_tmp4_a1,array_tmp4,1));
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1
>         array_tmp3[kkk] := 0;
>         array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
>         #emit atan $eq_no = 1
>         array_tmp4[kkk] :=  (ats(kkk,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(kkk-1,array_tmp4_a1,array_tmp4,2) - att(kkk-1,array_tmp4_a2,array_tmp4,2))/(array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
>         array_tmp4_a1[kkk] :=  att(kkk-1,array_tmp4_a2,array_tmp4,1);
>         array_tmp4_a2[kkk] :=  neg(att(kkk-1,array_tmp4_a1,array_tmp4,1));
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp5[kkk] := array_tmp4[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_tmp5[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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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_0D1[1]*array_x[1];
    array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
    array_tmp3[1] := sqrt(array_tmp2[1]);
    array_tmp4[1] := arctan(array_tmp3[1]);
    array_tmp4_a1[1] := sin(array_tmp4[1]);
    array_tmp4_a2[1] := cos(array_tmp4[1]);
    array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
    if not array_y_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_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_0D1[1]*array_x[2];
    array_tmp2[2] := array_tmp1[2];
    array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
    array_tmp4[2] := (ats(2, array_tmp3, array_tmp4_a2, 2)
         - array_tmp3[1]*att(1, array_tmp4_a1, array_tmp4, 2)
         - att(1, array_tmp4_a2, array_tmp4, 2))/(
        array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
    array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp4, 1);
    array_tmp4_a2[2] := neg(att(1, array_tmp4_a1, array_tmp4, 1));
    array_tmp5[2] := array_tmp4[2];
    if not array_y_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_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] := 0;
    array_tmp3[3] :=
        neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
    array_tmp4[3] := (ats(3, array_tmp3, array_tmp4_a2, 2)
         - array_tmp3[1]*att(2, array_tmp4_a1, array_tmp4, 2)
         - att(2, array_tmp4_a2, array_tmp4, 2))/(
        array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
    array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp4, 1);
    array_tmp4_a2[3] := neg(att(2, array_tmp4_a1, array_tmp4, 1));
    array_tmp5[3] := array_tmp4[3];
    if not array_y_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_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] := 0;
    array_tmp3[4] :=
        neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
    array_tmp4[4] := (ats(4, array_tmp3, array_tmp4_a2, 2)
         - array_tmp3[1]*att(3, array_tmp4_a1, array_tmp4, 2)
         - att(3, array_tmp4_a2, array_tmp4, 2))/(
        array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
    array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp4, 1);
    array_tmp4_a2[4] := neg(att(3, array_tmp4_a1, array_tmp4, 1));
    array_tmp5[4] := array_tmp4[4];
    if not array_y_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_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] := 0;
    array_tmp3[5] :=
        neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
    array_tmp4[5] := (ats(5, array_tmp3, array_tmp4_a2, 2)
         - array_tmp3[1]*att(4, array_tmp4_a1, array_tmp4, 2)
         - att(4, array_tmp4_a2, array_tmp4, 2))/(
        array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
    array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp4, 1);
    array_tmp4_a2[5] := neg(att(4, array_tmp4_a1, array_tmp4, 1));
    array_tmp5[5] := array_tmp4[5];
    if not array_y_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_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] := 0;
        array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
            array_tmp3[1]*glob__2);
        array_tmp4[kkk] := (ats(kkk, array_tmp3, array_tmp4_a2, 2)
             - array_tmp3[1]*att(kkk - 1, array_tmp4_a1, array_tmp4, 2)
             - att(kkk - 1, array_tmp4_a2, array_tmp4, 2))/(
            array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
        array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp4, 1);
        array_tmp4_a2[kkk] :=
            neg(att(kkk - 1, array_tmp4_a1, array_tmp4, 1));
        array_tmp5[kkk] := array_tmp4[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_tmp5[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_0D1,
>     array_const_0D2,
>     #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,
>     array_tmp4_a1,
>     array_tmp4_a2,
>     array_tmp4,
>     array_tmp5,
>     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:= Array(0..(40),[]);
>     array_tmp4_a1:= Array(0..(40),[]);
>     array_tmp4_a2:= Array(0..(40),[]);
>     array_tmp4:= Array(0..(40),[]);
>     array_tmp5:= 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[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4_a1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4_a2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp5[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_m1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=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);
>     zero_ats_ar(array_tmp4_a1);
>     zero_ats_ar(array_tmp4_a2);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5);
>     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_0D1);
>     array_const_0D1[1]   := c(0.1);
>     zero_ats_ar(array_const_0D2);
>     array_const_0D2[1]   := c(0.2);
>     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/arctan_sqrtpostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =  arctan ( sqrt ( 0.1  *  x  +  0.2 )  )  ; ");
>     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(-1.0);");
>     omniout_str(ALWAYS,"x_end := c(0.5) ;");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_max_h :=c(0.01);");
>     omniout_str(ALWAYS,"");
>     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 := 1;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
>     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(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) +");
>     omniout_str(ALWAYS,"c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));");
>     omniout_str(ALWAYS,"end;");
>     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(-1.0);
>     x_end := c(0.5) ;
>     array_y_init[0 + 1] := exact_soln_y(x_start);
>     glob_look_poles := true;
>     glob_max_h :=c(0.01);
>     glob_type_given_pole := 1;
>     array_given_rad_poles[1,1] := c(-2.0);
>     array_given_rad_poles[1,2] := c(0.0);
>     array_given_ord_poles[1,1] := c(0.5);
>     array_given_ord_poles[1,2] := c(0.0);
>     #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  )   =  arctan ( sqrt ( 0.1  *  x  +  0.2 )  )  ; ");
>         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,"2020-05-25T23:33:40-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"arctan_sqrt.ode.txt\">arctan_sqrt</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =  arctan ( sqrt ( 0.1  *  x  +  0.2 )  )  ; ")
>             ;
>             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.arctan_sqrt.mxt.txt\">arctan_sqrt diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.arctan_sqrt.mxt.txt\">arctan_sqrt maple results</a>")
>             ;
>             logitem_str(html_log_file,"OK")
>             ;
>             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_0D1,
array_const_0D2, 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, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, 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 := Array(0 .. 40, []);
    array_tmp4_a1 := Array(0 .. 40, []);
    array_tmp4_a2 := Array(0 .. 40, []);
    array_tmp4 := Array(0 .. 40, []);
    array_tmp5 := 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[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp4_a1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_tmp4_a2[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 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);
    zero_ats_ar(array_tmp4_a1);
    zero_ats_ar(array_tmp4_a2);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5);
    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_0D1);
    array_const_0D1[1] := c(0.1);
    zero_ats_ar(array_const_0D2);
    array_const_0D2[1] := c(0.2);
    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/arctan_sqrtpostode.ode#################");
    omniout_str(ALWAYS, "diff  (  y  ,  x  ,  1  )   =  arctan ( sqrt ( 0\
        .1  *  x  +  0.2 )  )  ; ");
    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(-1.0);");
    omniout_str(ALWAYS, "x_end := c(0.5) ;");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_max_h :=c(0.01);");
    omniout_str(ALWAYS, "");
    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 := 1;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
    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(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arct\
        an(sqrt ( c(0.1) * c(x) +");
    omniout_str(ALWAYS, "c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2\
        )) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));");
    omniout_str(ALWAYS, "end;");
    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(-1.0);
    x_end := c(0.5);
    array_y_init[1] := exact_soln_y(x_start);
    glob_look_poles := true;
    glob_max_h := c(0.01);
    glob_type_given_pole := 1;
    array_given_rad_poles[1, 1] := c(-2.0);
    array_given_rad_poles[1, 2] := c(0.);
    array_given_ord_poles[1, 1] := c(0.5);
    array_given_ord_poles[1, 2] := c(0.);
    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  )   =  arctan ( sqrt (\
             0.1  *  x  +  0.2 )  )  ; ");
        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, "2020-05-25T23:33:40-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"arctan_sqrt.ode.txt\">arctan_sqrt</a>");
            logitem_str(html_log_file, "diff  (  y  ,  x  ,  1  )   =  ar\
                ctan ( sqrt ( 0.1  *  x  +  0.2 )  )  ; ");
            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.arctan_sqrt.mxt.\
                txt\">arctan_sqrt diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.arctan_sqrt.mxt\
                .txt\">arctan_sqrt maple results</a>");
            logitem_str(html_log_file, "OK");
            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/arctan_sqrtpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  arctan ( sqrt ( 0.1  *  x  +  0.2 )  )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-1.0);
x_end := c(0.5) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;

glob_max_h :=c(0.01);








glob_type_given_pole := 1;

array_given_rad_poles[1,1] := c(-2.0);

array_given_rad_poles[1,2] := c(0.0);

array_given_ord_poles[1,1] := c(0.5);

array_given_ord_poles[1,2] := c(0.0);
#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(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) +
c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
memory used=4.0MB, alloc=40.3MB, time=0.08
x[1]                              = -1                                           
y[1] (closed_form)                = 0.2067734006979846849057268715274            
y[1] (numeric)                    = 0.2067734006979846849057268715274            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 12                                  
Estimated correct digits          = 14                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1                                            
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=46.9MB, alloc=44.3MB, time=0.34
x[1]                              = -0.99                                        
y[1] (closed_form)                = 0.2098433472792641368555043144456            
y[1] (numeric)                    = 0.20984334730097405295755611903432           
absolute error                    = 2.170991610205180458872e-11                  
relative error                    = 1.0345772874638608994989768325821e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.01                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.98                                        
y[1] (closed_form)                = 0.2129275836241564841063350006698            
y[1] (numeric)                    = 0.21292758366742985782199607250847           
absolute error                    = 4.327337371566107183867e-11                  
relative error                    = 2.0323047384994481347784795477941e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.02                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=97.8MB, alloc=48.3MB, time=0.66
 
TOP MAIN SOLVE Loop
x[1]                              = -0.97                                        
y[1] (closed_form)                = 0.2160260266070554882293841593425            
y[1] (numeric)                    = 0.21602602667174792477693779113601           
absolute error                    = 6.469243654755363179351e-11                  
relative error                    = 2.9946593733924074034471683764752e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.03                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=140.6MB, alloc=48.3MB, time=0.91
 
TOP MAIN SOLVE Loop
x[1]                              = -0.96                                        
y[1] (closed_form)                = 0.2191385942764167633263892707943            
y[1] (numeric)                    = 0.21913859436238588321673699167058           
absolute error                    = 8.596911989034772087628e-11                  
relative error                    = 3.9230478854814638898503579722372e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.04                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=183.3MB, alloc=48.3MB, time=1.22
 
TOP MAIN SOLVE Loop
x[1]                              = -0.95                                        
y[1] (closed_form)                = 0.222265205826929311510599588409             
y[1] (numeric)                    = 0.22226520593403470373467580717407           
absolute error                    = 1.0710539222407621876507e-10                 
relative error                    = 4.8188105657651024783774002242518e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.05                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=225.9MB, alloc=48.3MB, time=1.47
 
TOP MAIN SOLVE Loop
x[1]                              = -0.94                                        
y[1] (closed_form)                = 0.2254057815726103520737336123899            
y[1] (numeric)                    = 0.22540578170071352882347451552989           
absolute error                    = 1.2810317674974090313999e-10                 
relative error                    = 5.6832249756856749701476800477639e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.06                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=268.6MB, alloc=48.3MB, time=1.78
x[1]                              = -0.93                                        
y[1] (closed_form)                = 0.2285602429207842958146292209825            
y[1] (numeric)                    = 0.22856024306974864867303139166858           
absolute error                    = 1.4896435285840217068608e-10                 
relative error                    = 6.5175093863560111914816051948622e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.07                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.92                                        
y[1] (closed_form)                = 0.2317285123469087287520930723332            
y[1] (numeric)                    = 0.23172851251659948629118898305735           
absolute error                    = 1.6969075753909591072415e-10                 
relative error                    = 7.3228260010171163070165434387221e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.08                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=311.4MB, alloc=48.3MB, time=2.05
 
TOP MAIN SOLVE Loop
x[1]                              = -0.91                                        
y[1] (closed_form)                = 0.2349105133702121609397222989308            
y[1] (numeric)                    = 0.23491051356049634766839440017671           
absolute error                    = 1.9028418672867210124591e-10                 
relative error                    = 8.1002839761705231873364671525229e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.09                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=354.2MB, alloc=48.3MB, time=2.34
 
TOP MAIN SOLVE Loop
x[1]                              = -0.9                                         
y[1] (closed_form)                = 0.2381061705301100746984857747175            
y[1] (numeric)                    = 0.2381061707408564713049518626446            
absolute error                    = 2.1074639660646608792710e-10                 
relative error                    = 8.8509422556025625837480035723362e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.1                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=396.9MB, alloc=48.3MB, time=2.66
 
TOP MAIN SOLVE Loop
x[1]                              = -0.89                                        
y[1] (closed_form)                = 0.2413154093633674799913232404755            
y[1] (numeric)                    = 0.24131540959444658482786560527638           
absolute error                    = 2.3107910483654236480088e-10                 
relative error                    = 9.5758122303987843933277436912788e-08      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.11                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=439.5MB, alloc=48.3MB, time=2.97
 
TOP MAIN SOLVE Loop
x[1]                              = -0.88                                        
y[1] (closed_form)                = 0.2445381563819777599994919165791            
y[1] (numeric)                    = 0.24453815663326175175958296593477           
absolute error                    = 2.5128399176009104935567e-10                 
relative error                    = 1.0275860237024770965190928798961e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.12                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.87                                        
y[1] (closed_form)                = 0.2477743390517290737984719785184            
y[1] (numeric)                    = 0.24777433932309177533888024250615           
absolute error                    = 2.7136270154040826398775e-10                 
relative error                    = 1.0952009904615446522410262640730e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.13                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=482.3MB, alloc=48.3MB, time=3.28
 
TOP MAIN SOLVE Loop
x[1]                              = -0.86                                        
y[1] (closed_form)                = 0.2510238857714309814521663923804            
y[1] (numeric)                    = 0.25102388606274782471491889446058           
absolute error                    = 2.9131684326275250208018e-10                 
relative error                    = 1.1605144361760464012876105795354e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.14                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=525.1MB, alloc=48.3MB, time=3.59
 
TOP MAIN SOLVE Loop
x[1]                              = -0.85                                        
y[1] (closed_form)                = 0.2542867258527752754741027378562            
y[1] (numeric)                    = 0.25428672616392326746534177672875           
absolute error                    = 3.1114799199123903887255e-10                 
relative error                    = 1.2236108312290937531169342069615e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.15                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=567.8MB, alloc=48.3MB, time=3.89
 
TOP MAIN SOLVE Loop
x[1]                              = -0.84                                        
y[1] (closed_form)                = 0.2575627895008062466531133369146            
y[1] (numeric)                    = 0.25756278983166393643792621027479           
absolute error                    = 3.3085768978481287336019e-10                 
relative error                    = 1.2845709988856025815470212822615e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.16                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=610.6MB, alloc=48.3MB, time=4.20
 
TOP MAIN SOLVE Loop
x[1]                              = -0.83                                        
y[1] (closed_form)                = 0.2608520077949767865359891983483            
y[1] (numeric)                    = 0.26085200814542423321021613950186           
absolute error                    = 3.5044744667422694115356e-10                 
relative error                    = 1.3434722992420665941128259072215e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.17                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=653.5MB, alloc=48.3MB, time=4.50
 
TOP MAIN SOLVE Loop
x[1]                              = -0.82                                        
y[1] (closed_form)                = 0.2641543126707678378771234862469            
y[1] (numeric)                    = 0.26415431304068657947896933912821           
absolute error                    = 3.6991874160184585288131e-10                 
relative error                    = 1.4003888025212705353330870781099e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.18                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.81                                        
y[1] (closed_form)                = 0.2674696369018497522585482465425            
y[1] (numeric)                    = 0.26746963729112277558454391370944           
absolute error                    = 3.8927302332599566716694e-10                 
relative error                    = 1.4553914524093914210595539764115e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.19                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=696.2MB, alloc=48.3MB, time=4.81
 
TOP MAIN SOLVE Loop
x[1]                              = -0.8                                         
y[1] (closed_form)                = 0.2707979140827651047093237769262            
y[1] (numeric)                    = 0.27079791449127681600081049865112           
absolute error                    = 4.0851171129148672172492e-10                 
relative error                    = 1.5085482200820482329519173043660e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.2                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=739.0MB, alloc=48.3MB, time=5.13
 
TOP MAIN SOLVE Loop
x[1]                              = -0.79                                        
y[1] (closed_form)                = 0.2741390786121134520937499455057            
y[1] (numeric)                    = 0.27413907903974964856159882440019           
absolute error                    = 4.2763619646784887889449e-10                 
relative error                    = 1.5599242495190644126869914151910e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.21                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=781.8MB, alloc=48.3MB, time=5.44
 
TOP MAIN SOLVE Loop
x[1]                              = -0.78                                        
y[1] (closed_form)                = 0.2774930656762194086241129758525            
y[1] (numeric)                    = 0.2774930661228672507808492615255            
absolute error                    = 4.4664784215673628567300e-10                 
relative error                    = 1.6095819946646439654585756605416e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.22                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=824.6MB, alloc=48.3MB, time=5.75
 
TOP MAIN SOLVE Loop
x[1]                              = -0.77                                        
y[1] (closed_form)                = 0.280859811233266251184085642735             
y[1] (numeric)                    = 0.28085981169881423595396717011908           
absolute error                    = 4.6554798476988152738408e-10                 
relative error                    = 1.6575813489500060230470367316789e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.23                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=867.4MB, alloc=48.3MB, time=6.03
x[1]                              = -0.76                                        
y[1] (closed_form)                = 0.2842392519978780621075074361681            
y[1] (numeric)                    = 0.28423925248221599668641395796836           
absolute error                    = 4.8433793457890652180026e-10                 
relative error                    = 1.7039797676589799815449002960392e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.24                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.75                                        
y[1] (closed_form)                = 0.2876313254261341703301939651331            
y[1] (numeric)                    = 0.2876313259291531467684233017149            
absolute error                    = 5.0301897643822933658180e-10                 
relative error                    = 1.7488323835833670055127909876014e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.25                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=910.3MB, alloc=48.3MB, time=6.33
 
TOP MAIN SOLVE Loop
x[1]                              = -0.74                                        
y[1] (closed_form)                = 0.291035969701000365922901642126             
y[1] (numeric)                    = 0.29103597022259273640514366343905           
absolute error                    = 5.2159237048224202131305e-10                 
relative error                    = 1.7921921163837817308549909147981e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.26                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=953.0MB, alloc=48.3MB, time=6.61
 
TOP MAIN SOLVE Loop
x[1]                              = -0.73                                        
y[1] (closed_form)                = 0.2944531237181620402557813326571            
y[1] (numeric)                    = 0.29445312425822139305365558513831           
absolute error                    = 5.4005935279787425248121e-10                 
relative error                    = 1.8341097760429806467534353449236e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.27                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=995.7MB, alloc=48.3MB, time=6.84
 
TOP MAIN SOLVE Loop
x[1]                              = -0.72                                        
y[1] (closed_form)                = 0.2978827270722450466163704224485            
y[1] (numeric)                    = 0.29788272763066618268997126457029           
absolute error                    = 5.5842113607360084212179e-10                 
relative error                    = 1.8746341607721612196338083327558e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.28                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1038.5MB, alloc=48.3MB, time=7.09
 
TOP MAIN SOLVE Loop
x[1]                              = -0.71                                        
y[1] (closed_form)                = 0.3013247200434106860373975463146            
y[1] (numeric)                    = 0.301324720620089596263295270284             
absolute error                    = 5.7667891022589772396940e-10                 
relative error                    = 1.9138121497061967753722542943839e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.29                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=1081.2MB, alloc=48.3MB, time=7.33
x[1]                              = -0.7                                         
y[1] (closed_form)                = 0.3047790435843118022863083163984            
y[1] (numeric)                    = 0.30477904417914564529040900384045           
absolute error                    = 5.9483384300410068744205e-10                 
relative error                    = 1.9516887907010912579232352006472e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.3                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.69                                        
y[1] (closed_form)                = 0.3082456393073975202000756613172            
y[1] (numeric)                    = 0.30824563992028460077464933944273           
absolute error                    = 6.1288708057457367812553e-10                 
relative error                    = 1.9883073835259447710601797258786e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.31                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1124.0MB, alloc=48.3MB, time=7.58
 
TOP MAIN SOLVE Loop
x[1]                              = -0.68                                        
y[1] (closed_form)                = 0.3117244494725546844758829327758            
y[1] (numeric)                    = 0.31172445010339443256093166942093           
absolute error                    = 6.3083974808504873664513e-10                 
relative error                    = 2.0237095587222781638545636137396e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.32                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1166.9MB, alloc=48.3MB, time=7.81
 
TOP MAIN SOLVE Loop
x[1]                              = -0.67                                        
y[1] (closed_form)                = 0.3152154169750745532030517941364            
y[1] (numeric)                    = 0.31521541762376750341300922652742           
absolute error                    = 6.4869295020995743239102e-10                 
relative error                    = 2.0579353523855477872405740529443e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.33                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1209.5MB, alloc=48.3MB, time=8.06
 
TOP MAIN SOLVE Loop
x[1]                              = -0.66                                        
y[1] (closed_form)                = 0.3187184853339337732972111820288            
y[1] (numeric)                    = 0.31871848600038154497474498530616           
absolute error                    = 6.6644777167753380327736e-10                 
relative error                    = 2.0910232771069758012332656081613e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.34                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1252.3MB, alloc=48.3MB, time=8.30
 
TOP MAIN SOLVE Loop
x[1]                              = -0.65                                        
y[1] (closed_form)                = 0.3222335986803791149349894215527            
y[1] (numeric)                    = 0.3222335993644843927144206093628            
absolute error                    = 6.8410527777943118781010e-10                 
relative error                    = 2.1230103892983228215126089402163e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.35                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.64                                        
y[1] (closed_form)                = 0.3257607017468058703615198997314            
y[1] (numeric)                    = 0.32576070244847238522507969161372           
absolute error                    = 7.0166651486355979188232e-10                 
relative error                    = 2.1539323531078430059609329358183e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.36                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1295.0MB, alloc=48.3MB, time=8.56
 
TOP MAIN SOLVE Loop
x[1]                              = -0.63                                        
y[1] (closed_form)                = 0.3292997398559202302490799520606            
y[1] (numeric)                    = 0.32929974057505274105989819241668           
absolute error                    = 7.1913251081081824035608e-10                 
relative error                    = 2.1838235011222997855219352496321e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.37                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1337.8MB, alloc=48.3MB, time=8.80
 
TOP MAIN SOLVE Loop
x[1]                              = -0.62                                        
y[1] (closed_form)                = 0.3328506589101763392443057410535            
y[1] (numeric)                    = 0.33285065964668061474066634301673           
absolute error                    = 7.3650427549636060196323e-10                 
relative error                    = 2.2127168920375036223737832065147e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.38                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1380.5MB, alloc=48.3MB, time=9.05
 
TOP MAIN SOLVE Loop
x[1]                              = -0.61                                        
y[1] (closed_form)                = 0.3364134053814791025056057473275            
y[1] (numeric)                    = 0.33641340613526190374161608036155           
absolute error                    = 7.5378280123601033303405e-10                 
relative error                    = 2.2406443654682884335746515510736e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.39                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1423.3MB, alloc=48.3MB, time=9.28
 
TOP MAIN SOLVE Loop
x[1]                              = -0.6                                         
y[1] (closed_form)                = 0.339987926301144167889213235273             
y[1] (numeric)                    = 0.33998792707211323110761739159812           
absolute error                    = 7.7096906321840415632512e-10                 
relative error                    = 2.2676365940581037608152082469066e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.4                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1466.1MB, alloc=48.3MB, time=9.53
 
TOP MAIN SOLVE Loop
x[1]                              = -0.59                                        
y[1] (closed_form)                = 0.3435741692501068449193465873502            
y[1] (numeric)                    = 0.34357417003817086484276856550884           
absolute error                    = 7.8806401992342197815864e-10                 
relative error                    = 2.2937231330384040665056111754561e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.41                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.58                                        
y[1] (closed_form)                = 0.3471720823493720426467976190994            
y[1] (numeric)                    = 0.34717208315444065617423107823743           
absolute error                    = 8.0506861352743345913803e-10                 
relative error                    = 2.3189324673787084246306194966776e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.42                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1509.0MB, alloc=48.3MB, time=9.76
 
TOP MAIN SOLVE Loop
x[1]                              = -0.57                                        
y[1] (closed_form)                = 0.3507816142506976147803404569847            
y[1] (numeric)                    = 0.35078161507268138507620816286728           
absolute error                    = 8.2198377029586770588258e-10                 
relative error                    = 2.3432920566595316952510430016462e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.43                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1551.7MB, alloc=48.3MB, time=10.02
 
TOP MAIN SOLVE Loop
x[1]                              = -0.56                                        
y[1] (closed_form)                = 0.3544027141275037928373046823655            
y[1] (numeric)                    = 0.35440271496631419380089434652752           
absolute error                    = 8.3881040096358966416202e-10                 
relative error                    = 2.3668283777923045730359054062942e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.44                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1594.4MB, alloc=48.3MB, time=10.25
 
TOP MAIN SOLVE Loop
x[1]                              = -0.55                                        
y[1] (closed_form)                = 0.3580353316660016672286211399639            
y[1] (numeric)                    = 0.3580353325215510683321662333407            
absolute error                    = 8.5554940110354509337680e-10                 
relative error                    = 2.3895669657028610683794700084244e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.45                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1637.2MB, alloc=48.3MB, time=10.50
 
TOP MAIN SOLVE Loop
x[1]                              = -0.54                                        
y[1] (closed_form)                = 0.3616794170565339428522248714526            
y[1] (numeric)                    = 0.36167941792873559433634029066331           
absolute error                    = 8.7220165148411541921071e-10                 
relative error                    = 2.4115324520880379028538390735179e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.46                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=1680.1MB, alloc=48.3MB, time=10.73
x[1]                              = -0.53                                        
y[1] (closed_form)                = 0.3653349209851214505597181343872            
y[1] (numeric)                    = 0.36533492187388946897532236506574           
absolute error                    = 8.8876801841560423067854e-10                 
relative error                    = 2.4327486023483640673768406143008e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.47                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.52                                        
y[1] (closed_form)                = 0.3690017946252091393902940525425            
y[1] (numeric)                    = 0.3690017955304584934765527016233            
absolute error                    = 9.0524935408625864908080e-10                 
relative error                    = 2.4532383507936864151446781637258e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.48                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1722.8MB, alloc=48.3MB, time=10.98
 
TOP MAIN SOLVE Loop
x[1]                              = -0.51                                        
y[1] (closed_form)                = 0.3726799896296055073039299529798            
y[1] (numeric)                    = 0.37267999055125200419214114576787           
absolute error                    = 9.2164649688821119278807e-10                 
relative error                    = 2.4730238342128473312630163580806e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.49                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1765.5MB, alloc=48.3MB, time=11.22
 
TOP MAIN SOLVE Loop
x[1]                              = -0.5                                         
y[1] (closed_form)                = 0.3763694581226096508310269379457            
y[1] (numeric)                    = 0.37636945906056992256473797813378           
absolute error                    = 9.3796027173371104018808e-10                 
relative error                    = 2.4921264238931743752909994663677e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.5                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1808.4MB, alloc=48.3MB, time=11.47
 
TOP MAIN SOLVE Loop
x[1]                              = -0.49                                        
y[1] (closed_form)                = 0.3800701526923203270957283983101            
y[1] (numeric)                    = 0.38007015364651181745772610204219           
absolute error                    = 9.5419149036199770373209e-10                 
relative error                    = 2.5105667561705327123516002656314e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.51                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1851.1MB, alloc=48.3MB, time=11.70
 
TOP MAIN SOLVE Loop
x[1]                              = -0.48                                        
y[1] (closed_form)                = 0.3837820263831216255442279350842            
y[1] (numeric)                    = 0.38378202735346257718138295924024           
absolute error                    = 9.7034095163715502415604e-10                 
relative error                    = 2.5283647615860045689801679741440e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.52                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.47                                        
y[1] (closed_form)                = 0.3875050326883400418698014574148            
y[1] (numeric)                    = 0.38750503367474948370707048926941           
absolute error                    = 9.8640944183726903185461e-10                 
relative error                    = 2.5455396927208731916180190689498e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.53                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1893.9MB, alloc=48.3MB, time=11.95
 
TOP MAIN SOLVE Loop
x[1]                              = -0.46                                        
y[1] (closed_form)                = 0.3912391255430679335002518881803            
y[1] (numeric)                    = 0.39123912654546566843545144920626           
absolute error                    = 1.00239773493519956102596e-09                
relative error                    = 2.5621101507774808975028115232438e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.54                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1936.6MB, alloc=48.3MB, time=12.19
 
TOP MAIN SOLVE Loop
x[1]                              = -0.45                                        
y[1] (closed_form)                = 0.3949842593171485150045308084656            
y[1] (numeric)                    = 0.39498426033545510787579331147669           
absolute error                    = 1.01830659287126250301109e-09                
relative error                    = 2.5780941109696824251802124555283e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.55                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1979.4MB, alloc=48.3MB, time=12.44
 
TOP MAIN SOLVE Loop
x[1]                              = -0.44                                        
y[1] (closed_form)                = 0.3987403888083177232649493748547            
y[1] (numeric)                    = 0.39874038984245448908305658695759           
absolute error                    = 1.03413676581810721210289e-09                
relative error                    = 2.5935089467830080081377967100766e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.56                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2022.2MB, alloc=48.3MB, time=12.67
 
TOP MAIN SOLVE Loop
x[1]                              = -0.43                                        
y[1] (closed_form)                = 0.4025074692354984466102672521353            
y[1] (numeric)                    = 0.40250747028538743904832904810333           
absolute error                    = 1.04988899243806179596803e-09                
relative error                    = 2.6083714531612688423577693187294e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.57                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2064.9MB, alloc=48.3MB, time=12.91
 
TOP MAIN SOLVE Loop
x[1]                              = -0.42                                        
y[1] (closed_form)                = 0.4062854562322427696541749767082            
y[1] (numeric)                    = 0.40628545729780676978738277852626           
absolute error                    = 1.06556400013320780181806e-09                
relative error                    = 2.6226978686731655607955170243985e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.58                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.41                                        
y[1] (closed_form)                = 0.4100743058403180366560248804034            
y[1] (numeric)                    = 0.41007430692148054194445999895006           
absolute error                    = 1.08116250528843511854666e-09                
relative error                    = 2.6365038967094837615533789404231e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.59                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2107.6MB, alloc=48.3MB, time=13.16
 
TOP MAIN SOLVE Loop
x[1]                              = -0.4                                         
y[1] (closed_form)                = 0.413873974503432681121619835001             
y[1] (numeric)                    = 0.41387397560011789462933756100291           
absolute error                    = 1.09668521350771772600191e-09                
relative error                    = 2.6498047257586664013439173178238e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.6                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2150.3MB, alloc=48.3MB, time=13.39
 
TOP MAIN SOLVE Loop
x[1]                              = -0.39                                        
y[1] (closed_form)                = 0.4176844190610979083807031750911            
y[1] (numeric)                    = 0.41768442017323072822454438390817           
absolute error                    = 1.11213281984384120881707e-09                
relative error                    = 2.6626150488059287615228085669822e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.61                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2193.2MB, alloc=48.3MB, time=13.64
 
TOP MAIN SOLVE Loop
x[1]                              = -0.38                                        
y[1] (closed_form)                = 0.42150559674262145128849558375              
y[1] (numeric)                    = 0.42150559787012746031029927254973           
absolute error                    = 1.12750600902180368879973e-09                
relative error                    = 2.6749490818986164052667776523292e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.62                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2235.9MB, alloc=48.3MB, time=13.88
 
TOP MAIN SOLVE Loop
x[1]                              = -0.37                                        
y[1] (closed_form)                = 0.425337465161229747260803106973             
y[1] (numeric)                    = 0.42533746630403520291690610019944           
absolute error                    = 1.14280545565610299322644e-09                
relative error                    = 2.6868205819181895718230378906163e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.63                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=2278.7MB, alloc=48.3MB, time=14.13
x[1]                              = -0.36                                        
y[1] (closed_form)                = 0.4291799823083150078119403418769            
y[1] (numeric)                    = 0.42917998346634683227405478623036           
absolute error                    = 1.15803182446211444435346e-09                
relative error                    = 2.6982428635970390501228611052652e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.64                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.35                                        
y[1] (closed_form)                = 0.4330331065478037698552825990097            
y[1] (numeric)                    = 0.43303310772098954031703820614594           
absolute error                    = 1.17318577046175560713624e-09                
relative error                    = 2.7092288158162896867093423455745e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.65                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2321.4MB, alloc=48.3MB, time=14.36
 
TOP MAIN SOLVE Loop
x[1]                              = -0.34                                        
y[1] (closed_form)                = 0.4368967966106436314689666136988            
y[1] (numeric)                    = 0.43689679779891157065259326157119           
absolute error                    = 1.18826793918362664787239e-09                
relative error                    = 2.7197909172188199003079396767287e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.66                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2364.2MB, alloc=48.3MB, time=14.59
 
TOP MAIN SOLVE Loop
x[1]                              = -0.33                                        
y[1] (closed_form)                = 0.440771011589404983834053488825             
y[1] (numeric)                    = 0.44077101279268395069186110648923           
absolute error                    = 1.20327896685780761766423e-09                
relative error                    = 2.7299412511699110780461757865177e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.67                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2406.9MB, alloc=48.3MB, time=14.84
 
TOP MAIN SOLVE Loop
x[1]                              = -0.32                                        
y[1] (closed_form)                = 0.4446557109329946558186135659894            
y[1] (numeric)                    = 0.44465571215121413642410052972893           
absolute error                    = 1.21821948060548696373953e-09                
relative error                    = 2.7396915200962322442641557115864e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.68                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2449.7MB, alloc=48.3MB, time=15.08
 
TOP MAIN SOLVE Loop
x[1]                              = -0.31                                        
y[1] (closed_form)                = 0.4485508544414784883978704206448            
y[1] (numeric)                    = 0.44855085567456858702145929288063           
absolute error                    = 1.23309009862358887223583e-09                
relative error                    = 2.7490530592322561559997213033262e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.69                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=2492.3MB, alloc=48.3MB, time=15.33
x[1]                              = -0.3                                         
y[1] (closed_form)                = 0.4524564022610099529474128806185            
y[1] (numeric)                    = 0.4524564035089013833119735230657            
absolute error                    = 1.24789143036456064244720e-09                
relative error                    = 2.7580368498016866916897573489532e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.7                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.29                                        
y[1] (closed_form)                = 0.4563723148788620205942278294427            
y[1] (numeric)                    = 0.45637231614148609730570299946504           
absolute error                    = 1.26262407671147517002234e-09                
relative error                    = 2.7666535316600481967524295647051e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.71                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2535.2MB, alloc=48.3MB, time=15.56
 
TOP MAIN SOLVE Loop
x[1]                              = -0.28                                        
y[1] (closed_form)                = 0.4602985531185595794211151529698            
y[1] (numeric)                    = 0.46029855439584820956971291423909           
absolute error                    = 1.27728863014859776126929e-09                
relative error                    = 2.7749134154232398679878111348776e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.72                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2577.9MB, alloc=48.3MB, time=15.81
 
TOP MAIN SOLVE Loop
x[1]                              = -0.27                                        
y[1] (closed_form)                = 0.4642350781351097825480956062084            
y[1] (numeric)                    = 0.46423507942699545747565650562691           
absolute error                    = 1.29188567492756089941851e-09                
relative error                    = 2.7828264941055872062533474760852e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.73                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2620.7MB, alloc=48.3MB, time=16.05
 
TOP MAIN SOLVE Loop
x[1]                              = -0.26                                        
y[1] (closed_form)                = 0.4681818514103277931063126207937            
y[1] (numeric)                    = 0.46818185271674358033559784478771           
absolute error                    = 1.30641578722928522399401e-09                
relative error                    = 2.7904024542897232961020299339734e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.74                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2663.5MB, alloc=48.3MB, time=16.28
 
TOP MAIN SOLVE Loop
x[1]                              = -0.25                                        
y[1] (closed_form)                = 0.4721388347482554720150978770824            
y[1] (numeric)                    = 0.472138836069135007336877731657             
absolute error                    = 1.32087953532177985457460e-09                
relative error                    = 2.7976506868495007537394478217328e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.75                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.24                                        
y[1] (closed_form)                = 0.4761059902706706314039822644049            
y[1] (numeric)                    = 0.4761059916059481111179325435042            
absolute error                    = 1.33527747971395027909930e-09                
relative error                    = 2.8045802972460664887256279259201e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.76                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2706.4MB, alloc=48.3MB, time=16.56
 
TOP MAIN SOLVE Loop
x[1]                              = -0.23                                        
y[1] (closed_form)                = 0.480083280412684550614745534565             
y[1] (numeric)                    = 0.48008328176229472392028285850015           
absolute error                    = 1.34961017330553732393515e-09                
relative error                    = 2.8112001154162220930012093008717e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.77                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2749.1MB, alloc=48.3MB, time=16.80
 
TOP MAIN SOLVE Loop
x[1]                              = -0.22                                        
y[1] (closed_form)                = 0.4840706679184255230943028924077            
y[1] (numeric)                    = 0.48407066928230368462760911065506           
absolute error                    = 1.36387816153330621824736e-09                
relative error                    = 2.8175187052712391009857228314544e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.78                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2791.9MB, alloc=48.3MB, time=17.05
 
TOP MAIN SOLVE Loop
x[1]                              = -0.21                                        
y[1] (closed_form)                = 0.4880681158368062712617785600281            
y[1] (numeric)                    = 0.48806811721488825377537900938031           
absolute error                    = 1.37808198251360044935221e-09                
relative error                    = 2.8235443738233971914983210965860e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.79                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2834.6MB, alloc=48.3MB, time=17.28
 
TOP MAIN SOLVE Loop
x[1]                              = -0.2                                         
y[1] (closed_form)                = 0.4920755875173731327115335479803            
y[1] (numeric)                    = 0.49207558890959529989290451774014           
absolute error                    = 1.39222216718137096975984e-09                
relative error                    = 2.8292851799566614810975109458502e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.8                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2877.4MB, alloc=48.3MB, time=17.52
 
TOP MAIN SOLVE Loop
x[1]                              = -0.19                                        
y[1] (closed_form)                = 0.4960930466062349850020679162583            
y[1] (numeric)                    = 0.49609304801253422442785526833688           
absolute error                    = 1.40629923942578735207858e-09                
relative error                    = 2.8347489428571094488209624545383e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.81                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.18                                        
y[1] (closed_form)                = 0.5001204570420699378775993472525            
y[1] (numeric)                    = 0.50012045846238365410013303408268           
absolute error                    = 1.42031371622253368683018e-09                
relative error                    = 2.8399432501179559841956435040178e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.82                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2920.2MB, alloc=48.3MB, time=17.77
 
TOP MAIN SOLVE Loop
x[1]                              = -0.17                                        
y[1] (closed_form)                = 0.5041577830522078811690993965937            
y[1] (numeric)                    = 0.50415778448647398893198776950857           
absolute error                    = 1.43426610776288837291487e-09                
relative error                    = 2.8448754655333039908052375323646e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.83                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2963.1MB, alloc=48.3MB, time=18.00
 
TOP MAIN SOLVE Loop
x[1]                              = -0.16                                        
y[1] (closed_form)                = 0.5082049891487870339146327940732            
y[1] (numeric)                    = 0.50820499059694395149431624783876           
absolute error                    = 1.44815691757968345376556e-09                
relative error                    = 2.8495527365940654984487058779114e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.84                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3005.8MB, alloc=48.3MB, time=18.25
 
TOP MAIN SOLVE Loop
x[1]                              = -0.15                                        
y[1] (closed_form)                = 0.5122620401249826955108233986591            
y[1] (numeric)                    = 0.51226204158696933818105919595927           
absolute error                    = 1.46198664267023579730017e-09                
relative error                    = 2.8539820016988520831808503757530e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.85                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3048.5MB, alloc=48.3MB, time=18.50
 
TOP MAIN SOLVE Loop
x[1]                              = -0.14                                        
y[1] (closed_form)                = 0.5163289010513064530400494434402            
y[1] (numeric)                    = 0.51632890252706222665638864157855           
absolute error                    = 1.47575577361633919813835e-09                
relative error                    = 2.8581699970920214543676491720061e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.86                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=3091.2MB, alloc=48.3MB, time=18.75
x[1]                              = -0.13                                        
y[1] (closed_form)                = 0.520405537271974150389695372105             
y[1] (numeric)                    = 0.52040553876143894509109876213826           
absolute error                    = 1.48946479470140339003326e-09                
relative error                    = 2.8621232635404873624956334175278e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.87                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.12                                        
y[1] (closed_form)                = 0.5244919144013409744650510933611            
y[1] (numeric)                    = 0.5244919159044551584898740825987            
absolute error                    = 1.50311418402482298923760e-09                
relative error                    = 2.8658481527603506561206857084986e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.88                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3134.0MB, alloc=48.3MB, time=19.02
 
TOP MAIN SOLVE Loop
x[1]                              = -0.11                                        
y[1] (closed_form)                = 0.5285879983204020617674729872698            
y[1] (numeric)                    = 0.52858799983710647538112952729983           
absolute error                    = 1.51670441361365654003003e-09                
relative error                    = 2.8693508336038886320100040729613e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.89                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3176.8MB, alloc=48.3MB, time=19.27
 
TOP MAIN SOLVE Loop
x[1]                              = -0.1                                         
y[1] (closed_form)                = 0.532693755173357074932223040807             
y[1] (numeric)                    = 0.53269375670359302446391613739775           
absolute error                    = 1.53023594953169309659075e-09                
relative error                    = 2.8726372980169461481021633832679e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.9                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3219.6MB, alloc=48.3MB, time=19.52
 
TOP MAIN SOLVE Loop
x[1]                              = -0.09                                        
y[1] (closed_form)                = 0.5368091513642372435609592089912            
y[1] (numeric)                    = 0.53680915290794649554694035482607           
absolute error                    = 1.54370925198598114583487e-09                
relative error                    = 2.8757133667763037740183073371430e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.91                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3262.3MB, alloc=48.3MB, time=19.77
 
TOP MAIN SOLVE Loop
x[1]                              = -0.08                                        
y[1] (closed_form)                = 0.5409341535535934069042465690815            
y[1] (numeric)                    = 0.54093415511071818233513871800553           
absolute error                    = 1.55712477543089214892403e-09                
relative error                    = 2.8785846950161541021197374670255e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.92                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.07                                        
y[1] (closed_form)                = 0.5450687286552436377090321408691            
y[1] (numeric)                    = 0.54506873022572660637882069131561           
absolute error                    = 1.57048296866978855044651e-09                
relative error                    = 2.8812567775523958849264133548227e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
memory used=3305.0MB, alloc=48.3MB, time=20.02
Radius of convergence (given) for eq  1            = 1.93                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.06                                        
y[1] (closed_form)                = 0.5492128438330790669015007566237            
y[1] (numeric)                    = 0.54921284541686334185586452601981           
absolute error                    = 1.58378427495436376939611e-09                
relative error                    = 2.8837349540130556355465114576498e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.94                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3347.7MB, alloc=48.3MB, time=20.25
 
TOP MAIN SOLVE Loop
x[1]                              = -0.05                                        
y[1] (closed_form)                = 0.5533664664979265677813446968633            
y[1] (numeric)                    = 0.55336646809495569986306413783791           
absolute error                    = 1.59702913208171944097461e-09                
relative error                    = 2.8860244137827665366455178437185e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.95                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3390.5MB, alloc=48.3MB, time=20.50
 
TOP MAIN SOLVE Loop
x[1]                              = -0.04                                        
y[1] (closed_form)                = 0.5575295643044669961111118915169            
y[1] (numeric)                    = 0.55752956591468496860035491053446           
absolute error                    = 1.61021797248924301901756e-09                
relative error                    = 2.8881302007688738321537303884869e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.96                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3433.2MB, alloc=48.3MB, time=20.73
 
TOP MAIN SOLVE Loop
x[1]                              = -0.03                                        
y[1] (closed_form)                = 0.5617021051482077189435731381261            
y[1] (numeric)                    = 0.56170210677155894229091990989914           
absolute error                    = 1.62335122334734677177304e-09                
relative error                    = 2.8900572179963932730453015877919e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.97                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3476.1MB, alloc=48.3MB, time=20.98
 
TOP MAIN SOLVE Loop
x[1]                              = -0.02                                        
y[1] (closed_form)                = 0.5658840571625082002884541849081            
y[1] (numeric)                    = 0.56588405879893750693858139023492           
absolute error                    = 1.63642930665012720532682e-09                
relative error                    = 2.8918102320387236655131104416826e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.98                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = -0.01                                        
y[1] (closed_form)                = 0.5700753887156574458228619141914            
y[1] (numeric)                    = 0.57007539036511008512686393999951           
absolute error                    = 1.64945263930400202580811e-09                
relative error                    = 2.8933938772907051967427451407072e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 1.99                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3518.8MB, alloc=48.3MB, time=21.22
 
TOP MAIN SOLVE Loop
x[1]                              = 0                                            
y[1] (closed_form)                = 0.574276068408002141840802853496             
y[1] (numeric)                    = 0.57427607007042377505518275391167           
absolute error                    = 1.66242163321437990041567e-09                
relative error                    = 2.8948126600903211151591066941297e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2                                            
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3561.7MB, alloc=48.3MB, time=21.47
 
TOP MAIN SOLVE Loop
x[1]                              = 0.01                                         
y[1] (closed_form)                = 0.5784860650691243555580059987217            
y[1] (numeric)                    = 0.57848606674446105092842249395513           
absolute error                    = 1.67533669537041649523343e-09                
relative error                    = 2.8960709626950606948274197372008e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.01                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3604.4MB, alloc=48.3MB, time=21.72
 
TOP MAIN SOLVE Loop
x[1]                              = 0.02                                         
y[1] (closed_form)                = 0.5827053477550676947787185334702            
y[1] (numeric)                    = 0.58270534944326592270662708532549           
absolute error                    = 1.68819822792790855185529e-09                
relative error                    = 2.8971730471186954421277018790814e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.02                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3647.2MB, alloc=48.3MB, time=21.95
 
TOP MAIN SOLVE Loop
x[1]                              = 0.03                                         
y[1] (closed_form)                = 0.5869338857456108548294622871315            
y[1] (numeric)                    = 0.58693388744661748311983839935713           
absolute error                    = 1.70100662829037611222563e-09                
relative error                    = 2.8981230588339674764687669802757e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.03                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=3690.0MB, alloc=48.3MB, time=22.20
x[1]                              = 0.04                                         
y[1] (closed_form)                = 0.5911716485415875096075407873844            
y[1] (numeric)                    = 0.59117165025534979879592219658928           
absolute error                    = 1.71376228918838140920488e-09                
relative error                    = 2.8989250303464482476003018518908e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.04                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.05                                         
y[1] (closed_form)                = 0.5954186058622515316144663998797            
y[1] (numeric)                    = 0.59541860758871713037159780653171           
absolute error                    = 1.72646559875713140665201e-09                
relative error                    = 2.8995828846445965915427079101510e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.05                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3733.0MB, alloc=48.3MB, time=22.44
 
TOP MAIN SOLVE Loop
x[1]                              = 0.06                                         
y[1] (closed_form)                = 0.5996747276426865529800746320268            
y[1] (numeric)                    = 0.59967472938180349359248412691959           
absolute error                    = 1.73911694061240949489279e-09                
relative error                    = 2.9001004385308269640608182619396e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.06                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3775.7MB, alloc=48.3MB, time=22.67
 
TOP MAIN SOLVE Loop
x[1]                              = 0.07                                         
y[1] (closed_form)                = 0.6039399840312589057641610608667            
y[1] (numeric)                    = 0.60393998578297559968904148387001           
absolute error                    = 1.75171669392488042300331e-09                
relative error                    = 2.9004814058381909485686786315797e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.07                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3818.4MB, alloc=48.3MB, time=22.92
 
TOP MAIN SOLVE Loop
x[1]                              = 0.08                                         
y[1] (closed_form)                = 0.6082143453871130052799445802238            
y[1] (numeric)                    = 0.60821434715137823877275575644392           
absolute error                    = 1.76426523349281117622012e-09                
relative error                    = 2.9007294005370772708005101875837e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.08                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3861.2MB, alloc=48.3MB, time=23.16
 
TOP MAIN SOLVE Loop
x[1]                              = 0.09                                         
y[1] (closed_form)                = 0.6124977822777082648471944619937            
y[1] (numeric)                    = 0.61249778405447119466044364487257           
absolute error                    = 1.77676292981324918287887e-09                
relative error                    = 2.9008479397361470526095483466433e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.09                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=3904.1MB, alloc=48.3MB, time=23.39
x[1]                              = 0.1                                          
y[1] (closed_form)                = 0.6167902654763966542809178815185            
y[1] (numeric)                    = 0.6167902672656068034326158401295            
absolute error                    = 1.78921014915169795861100e-09                
relative error                    = 2.9008404465815414179028749383257e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.1                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.11                                         
y[1] (closed_form)                = 0.6210917659600400375813974854367            
y[1] (numeric)                    = 0.62109176776164729119172654961389           
absolute error                    = 1.80160725361032906417719e-09                
relative error                    = 2.9007102530582273680901635964789e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.11                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3946.8MB, alloc=48.3MB, time=23.64
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y[1] (closed_form)                = 0.6254022549066664477393041602318            
y[1] (numeric)                    = 0.62540225672062104893407222570473           
absolute error                    = 1.81395460119476806547293e-09                
relative error                    = 2.9004606026971846411312620474823e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.12                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3989.6MB, alloc=48.3MB, time=23.88
 
TOP MAIN SOLVE Loop
x[1]                              = 0.13                                         
y[1] (closed_form)                = 0.6297217036931644783307469948105            
y[1] (numeric)                    = 0.62972170551941702421023803298473           
absolute error                    = 1.82625254587949103817423e-09                
relative error                    = 2.9000946531919806498786371157221e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.13                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4032.4MB, alloc=48.3MB, time=24.11
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y[1] (closed_form)                = 0.6340500838930149926756156872219            
y[1] (numeric)                    = 0.63405008573151643034748274075308           
absolute error                    = 1.83850143767186705353118e-09                
relative error                    = 2.8996154789281321769877793248661e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.14                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4075.1MB, alloc=48.3MB, time=24.38
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y[1] (closed_form)                = 0.6383873672740593717916165913415            
y[1] (numeric)                    = 0.63838736912476099446649760572792           
absolute error                    = 1.85070162267488101438642e-09                
relative error                    = 2.8990260734285109214811347370141e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.15                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.16                                         
y[1] (closed_form)                = 0.6427335257963035422182819650782            
y[1] (numeric)                    = 0.64273352765915698536685214515572           
absolute error                    = 1.86285344314857018007752e-09                
relative error                    = 2.8983293517179149022751342434284e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.16                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4118.0MB, alloc=48.3MB, time=24.61
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y[1] (closed_form)                = 0.6470885316097570440313462657759            
y[1] (numeric)                    = 0.64708853348471428160155298979726           
absolute error                    = 1.87495723757020672402136e-09                
relative error                    = 2.8975281526097988015312258868929e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.17                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4160.8MB, alloc=48.3MB, time=24.86
 
TOP MAIN SOLVE Loop
x[1]                              = 0.18                                         
y[1] (closed_form)                = 0.6514523570523064180387991596377            
y[1] (numeric)                    = 0.65145235893931975873205686673195           
absolute error                    = 1.88701334069325770709425e-09                
relative error                    = 2.8966252409180332681504965726991e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.18                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4203.6MB, alloc=48.3MB, time=25.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y[1] (closed_form)                = 0.65582497464762220926540651484              
y[1] (numeric)                    = 0.65582497654664429287055943692776           
absolute error                    = 1.89902208360515292208776e-09                
relative error                    = 2.8956233095964457082820722849818e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.19                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4246.4MB, alloc=48.3MB, time=25.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.2                                          
y[1] (closed_form)                = 0.6602063571030989014115356583662            
y[1] (numeric)                    = 0.6602063590140826951954258266295            
absolute error                    = 1.91098379378389016826330e-09                
relative error                    = 2.8945249818087828901813637759756e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.2                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4289.2MB, alloc=48.3MB, time=25.59
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y[1] (closed_form)                = 0.6645964773078271140329936978712            
y[1] (numeric)                    = 0.66459647923072590918650034700839           
absolute error                    = 1.92289879515350664913719e-09                
relative error                    = 2.8933328129316285247107669564844e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.21                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y[1] (closed_form)                = 0.6689953083305974107488498468797            
y[1] (numeric)                    = 0.66899531026536481888729419682224           
absolute error                    = 1.93476740813844434994254e-09                
relative error                    = 2.8920492924927066036857886050822e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.22                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4332.0MB, alloc=48.3MB, time=25.84
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y[1] (closed_form)                = 0.673402823417935082860754583296             
y[1] (numeric)                    = 0.67340282536452503257759102591394           
absolute error                    = 1.94658994971683644261794e-09                
relative error                    = 2.8906768460469034526777781054781e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.23                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4374.9MB, alloc=48.3MB, time=26.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y[1] (closed_form)                = 0.67781899599216528837633690935              
y[1] (numeric)                    = 0.67781899795053202184907789394646           
absolute error                    = 1.95836673347274098459646e-09                
relative error                    = 2.8892178369922479616774238321875e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.24                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4417.7MB, alloc=48.3MB, time=26.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.25                                         
y[1] (closed_form)                = 0.6822437996495079415864866874361            
y[1] (numeric)                    = 0.68224380161960601123383410954431           
absolute error                    = 1.97009806964734742210821e-09                
relative error                    = 2.8876745683280000867576139875330e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.25                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4460.5MB, alloc=48.3MB, time=26.59
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y[1] (closed_form)                = 0.6866772081582017630667526566934            
y[1] (numeric)                    = 0.68667721013998602825593333485533           
absolute error                    = 1.98178426518918067816193e-09                
relative error                    = 2.8860492843569122700212392961314e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.26                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=4503.2MB, alloc=48.3MB, time=26.84
x[1]                              = 0.27                                         
y[1] (closed_form)                = 0.6911191954566569142711836756123            
y[1] (numeric)                    = 0.69111919745008253807451057453558           
absolute error                    = 1.99342562380332689892328e-09                
relative error                    = 2.8843441723336467155847489637594e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.27                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y[1] (closed_form)                = 0.6955697356516356547766447517033            
y[1] (numeric)                    = 0.69556973765665810077634900065402           
absolute error                    = 2.00502244599970424895072e-09                
relative error                    = 2.8825613640612533077604461181408e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.28                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4546.0MB, alloc=48.3MB, time=27.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y[1] (closed_form)                = 0.700028803016460473730365214875             
y[1] (numeric)                    = 0.70002880503303550287076669969365           
absolute error                    = 2.01657502914040148481865e-09                
relative error                    = 2.8807029374375381948276398185075e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.29                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4588.8MB, alloc=48.3MB, time=27.33
 
TOP MAIN SOLVE Loop
x[1]                              = 0.3                                          
y[1] (closed_form)                = 0.7044963719892491601661411360971            
y[1] (numeric)                    = 0.70449637401733282765224753334076           
absolute error                    = 2.02808366748610639724366e-09                
relative error                    = 2.8787709179530815274389297155052e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.3                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4631.6MB, alloc=48.3MB, time=27.58
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y[1] (closed_form)                = 0.7089724171711762895976579646094            
y[1] (numeric)                    = 0.70897241921072494183930355773216           
absolute error                    = 2.03954865224164559312276e-09                
relative error                    = 2.8767672801425943825851329635746e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.31                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4674.4MB, alloc=48.3MB, time=27.81
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y[1] (closed_form)                = 0.7134569133247606166828051500266            
y[1] (numeric)                    = 0.71345691537573088828346164017579           
absolute error                    = 2.05097027160065649014919e-09                
relative error                    = 2.8746939489912393777596863623827e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.32                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y[1] (closed_form)                = 0.7179498353721778757921663639591            
y[1] (numeric)                    = 0.71794983743452668658157818111554           
absolute error                    = 2.06234881078941181715644e-09                
relative error                    = 2.8725528012974767484537525564223e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.33                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4717.3MB, alloc=48.3MB, time=28.06
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y[1] (closed_form)                = 0.7224511583935985030192101903542            
y[1] (numeric)                    = 0.72245116046728305512902654271256           
absolute error                    = 2.07368455210981635235836e-09                
relative error                    = 2.8703456669939375952690628337001e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.34                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4760.2MB, alloc=48.3MB, time=28.30
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y[1] (closed_form)                = 0.7269608576255498045497964592503            
y[1] (numeric)                    = 0.72696085971052757953139154778294           
absolute error                    = 2.08497777498159508853264e-09                
relative error                    = 2.8680743304277684812117209753493e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.35                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4802.9MB, alloc=48.3MB, time=28.55
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y[1] (closed_form)                = 0.7314789084593021073747850062784            
y[1] (numeric)                    = 0.73147891055553086335847649457338           
absolute error                    = 2.09622875598369148829498e-09                
relative error                    = 2.8657405316018364577928743869367e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.36                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4845.7MB, alloc=48.3MB, time=28.78
 
TOP MAIN SOLVE Loop
x[1]                              = 0.37                                         
y[1] (closed_form)                = 0.7360052864392784390917469954383            
y[1] (numeric)                    = 0.73600528854671620798664097875092           
absolute error                    = 2.10743776889489398331262e-09                
relative error                    = 2.8633459673781308089451770406190e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.37                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4888.5MB, alloc=48.3MB, time=29.03
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y[1] (closed_form)                = 0.7405399672614872940096375819502            
y[1] (numeric)                    = 0.74053996938009237874334595996892           
absolute error                    = 2.11860508473370837801872e-09                
relative error                    = 2.8608922926446472185640225023966e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.38                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y[1] (closed_form)                = 0.7450829267719780529530534828622            
y[1] (numeric)                    = 0.74508292890170902475054682340337           
absolute error                    = 2.12973097179749334054117e-09                
relative error                    = 2.8583811214469915900458520611884e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.39                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4931.3MB, alloc=48.3MB, time=29.26
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y[1] (closed_form)                = 0.7496341409653186340693017784447            
y[1] (numeric)                    = 0.74963414310613432977017747905456           
absolute error                    = 2.14081569570087570060986e-09                
relative error                    = 2.8558140280858942788571954700615e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.4                                          
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4974.2MB, alloc=48.3MB, time=29.52
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y[1] (closed_form)                = 0.7541935859830949615805627642576            
y[1] (numeric)                    = 0.75419358813495448099402458987873           
absolute error                    = 2.15185951941346182562113e-09                
relative error                    = 2.8531925481817809509536123704634e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.41                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5017.0MB, alloc=48.3MB, time=29.75
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y[1] (closed_form)                = 0.758761238112431848803252105015             
y[1] (numeric)                    = 0.75876124027529455210011301634204           
absolute error                    = 2.16286270329686091132704e-09                
relative error                    = 2.8505181797075035642967894289902e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.42                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5059.7MB, alloc=48.3MB, time=30.00
 
TOP MAIN SOLVE Loop
x[1]                              = 0.43                                         
y[1] (closed_form)                = 0.7633370737845349008852964273041            
y[1] (numeric)                    = 0.76333707595836040602633202958032           
absolute error                    = 2.17382550514103560227622e-09                
relative error                    = 2.8477923839902940054904062915618e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.43                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=5102.4MB, alloc=48.3MB, time=30.23
x[1]                              = 0.44                                         
y[1] (closed_form)                = 0.7679210695732530515971720734509            
y[1] (numeric)                    = 0.76792107175800123179716702217324           
absolute error                    = 2.18474818019999494872234e-09                
relative error                    = 2.8450165866839636204345207615871e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.44                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y[1] (closed_form)                = 0.7725132021936613571616898989715            
y[1] (numeric)                    = 0.77251320438929233838853420972854           
absolute error                    = 2.19563098122684431075704e-09                
relative error                    = 2.8421921787123341823655579200988e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.45                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5145.2MB, alloc=48.3MB, time=30.48
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y[1] (closed_form)                = 0.777113448500663678527851676856             
y[1] (numeric)                    = 0.77711345070713783703605811337444           
absolute error                    = 2.20647415850820643651844e-09                
relative error                    = 2.8393205171848496718655045862481e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.46                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5188.0MB, alloc=48.3MB, time=30.73
 
TOP MAIN SOLVE Loop
x[1]                              = 0.47                                         
y[1] (closed_form)                = 0.7817217854876148916926188832159            
y[1] (numeric)                    = 0.78172178770489285159064645224823           
absolute error                    = 2.21727795989802756903233e-09                
relative error                    = 2.8364029262852835338791334919359e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.47                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5230.8MB, alloc=48.3MB, time=30.97
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y[1] (closed_form)                = 0.7863381902849622736578460233979            
y[1] (numeric)                    = 0.78633819251300490450862809858154           
absolute error                    = 2.22804263085078207518364e-09                
relative error                    = 2.8334406981344227622577765609001e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.48                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5273.7MB, alloc=48.3MB, time=31.22
 
TOP MAIN SOLVE Loop
x[1]                              = 0.49                                         
y[1] (closed_form)                = 0.790962640158905719384431655433             
y[1] (numeric)                    = 0.79096264239767413383852039552857           
absolute error                    = 2.23876841445408874009557e-09                
relative error                    = 2.8304350936275781816594251811638e-07      % 
Desired digits                    = 12                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.001                                        
Radius of convergence (given) for eq  1            = 2.49                                         
Order of pole (given)                              = 0.5                                          
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =  arctan ( sqrt ( 0.1  *  x  +  0.2 )  )  ; 
Iterations                       = 1500                                
Total Elapsed Time               = 31 Seconds
Elapsed Time(since restart)      = 31 Seconds
Time to Timeout                  = 2 Minutes 28 Seconds
Percent Done                     = 100.1                                      % 
> quit
memory used=5313.1MB, alloc=48.3MB, time=31.42