|\^/|     Maple 2016 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
 \  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(cos(c(x)) - sin(c(x))) ;
> end;
         exact_soln_y := proc(x) return cos(c(x)) - sin(c(x)) end proc

#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
>     local rad_given;
>     global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 1
>         rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) +  array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
>         omniout_float(ALWAYS,"Radius of convergence (given) for eq  1           ",4,rad_given,4," ");
>         omniout_float(ALWAYS,"Order of pole (given)                             ",4,array_given_ord_poles[1,1],4," ");
>         if (rad_given < glob_least_given_sing)  then # if number 2
>             glob_least_given_sing :=  rad_given;
>         fi;# end if 2;
>     elif
>     (glob_type_given_pole = 3) then # if number 2
>         omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
>     elif
>     (glob_type_given_pole = 5) then # if number 3
>         omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
>     else
>         omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
>     fi;# end if 3;
>     if (array_rad_test_poles[1,1] < glob_large_float)  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq  1      ",4,array_rad_test_poles[1,1],4," ");
>         if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
>             glob_least_ratio_sing := array_rad_test_poles[1,1];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (ratio test)                        ",4, array_ord_test_poles[1,1],4," ");
>     else
>         omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
>     fi;# end if 3;
>     if ((array_rad_test_poles[1,2] >  glob__small) and (array_rad_test_poles[1,2] < glob_large_float))  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1  ",4,array_rad_test_poles[1,2],4," ");
>         if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
>             glob_least_3_sing := array_rad_test_poles[1,2];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (three term test)                   ",4, array_ord_test_poles[1,2],4," ");
>     else
>         omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
>     fi;# end if 3;
>     if ((array_rad_test_poles[1,3] >  glob__small) and (array_rad_test_poles[1,3] < glob_large_float))  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1    ",4,array_rad_test_poles[1,3],4," ");
>         if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
>             glob_least_6_sing := array_rad_test_poles[1,3];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (six term test)                     ",4, array_ord_test_poles[1,3],4," ");
>     else
>         omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
>     fi;# end if 3
>     ;
> 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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 6
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 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)*25*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,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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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*glob__100/float_abs(closed_form_val_y);
                if c(glob_prec) < c(relerr) then
                    glob_good_digits := -int_trunc(log10(c(relerr))) + 3
                else glob_good_digits := Digits
                end if
            else relerr := glob__m1; glob_good_digits := -16
            end if;
            if glob_good_digits < glob_min_good_digits then
                glob_min_good_digits := glob_good_digits
            end if;
            if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
            then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
            end if;
            if glob_prec < evalf(float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[1]*100.0*
                    sqrt(glob_iter)*25*ATS_MAX_TERMS/float_abs(numeric_val))
                    ;
                if glob_prec < evalf(est_rel_err) then
                    glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
                else glob_est_digits := Digits
                end if
            else relerr := glob__m1; glob_est_digits := -16
            end if;
            array_est_digits[1] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[1] := relerr
            else array_last_rel_error[1] := relerr
            end if;
            array_est_rel_error[1] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ")
        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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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,
#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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> 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 sin 1 $eq_no = 1
>     array_tmp1[1] :=  sin(array_x[1]);
>     array_tmp1_g[1] :=  cos(array_x[1]);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[1] :=  neg(array_tmp1[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
>     #emit pre cos 1 $eq_no = 1
>     array_tmp4[1] :=  cos(array_x[1]);
>     array_tmp4_g[1] :=  sin(array_x[1]);
>     #emit pre sub FULL FULL $eq_no = 1 i = 1
>     array_tmp5[1] := array_tmp3[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 sin ID_LINEAR iii = 2 $eq_no = 1
>     array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1);
>     array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[2] :=  neg(array_tmp1[2]);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp3[2] := array_tmp2[2];
>     #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
>     array_tmp4[2] := neg(array_tmp4_g[1]) * array_x[2] / c(1);
>     array_tmp4_g[2] := array_tmp4[1] * array_x[2] / c(1);
>     #emit pre sub FULL FULL $eq_no = 1 i = 2
>     array_tmp5[2] := array_tmp3[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 sin ID_LINEAR iii = 3 $eq_no = 1
>     array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2);
>     array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[3] :=  neg(array_tmp1[3]);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp3[3] := array_tmp2[3];
>     #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
>     array_tmp4[3] := neg(array_tmp4_g[2]) * array_x[2] / c(2);
>     array_tmp4_g[3] := array_tmp4[2] * array_x[2] / c(2);
>     #emit pre sub FULL FULL $eq_no = 1 i = 3
>     array_tmp5[3] := array_tmp3[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 sin ID_LINEAR iii = 4 $eq_no = 1
>     array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3);
>     array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[4] :=  neg(array_tmp1[4]);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp3[4] := array_tmp2[4];
>     #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
>     array_tmp4[4] := neg(array_tmp4_g[3]) * array_x[2] / c(3);
>     array_tmp4_g[4] := array_tmp4[3] * array_x[2] / c(3);
>     #emit pre sub FULL FULL $eq_no = 1 i = 4
>     array_tmp5[4] := array_tmp3[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 sin ID_LINEAR iii = 5 $eq_no = 1
>     array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4);
>     array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[5] :=  neg(array_tmp1[5]);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp3[5] := array_tmp2[5];
>     #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
>     array_tmp4[5] := neg(array_tmp4_g[4]) * array_x[2] / c(4);
>     array_tmp4_g[5] := array_tmp4[4] * array_x[2] / c(4);
>     #emit pre sub FULL FULL $eq_no = 1 i = 5
>     array_tmp5[5] := array_tmp3[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 sin LINEAR $eq_no = 1
>         array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1);
>         array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
>         #emit neg FULL $eq_no = 1
>         array_tmp2[kkk] := neg(array_tmp1[kkk]);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp3[kkk] := array_tmp2[kkk];
>         #emit cos LINEAR $eq_no = 1
>         array_tmp4[kkk] := neg(array_tmp4_g[kkk - 1]) * array_x[2] / c(kkk - 1);
>         array_tmp4_g[kkk] := array_tmp4[kkk - 1] * array_x[2] / c(kkk - 1);
>         #emit FULL - FULL sub $eq_no = 1
>         array_tmp5[kkk] := array_tmp3[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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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] := sin(array_x[1]);
    array_tmp1_g[1] := cos(array_x[1]);
    array_tmp2[1] := neg(array_tmp1[1]);
    array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
    array_tmp4[1] := cos(array_x[1]);
    array_tmp4_g[1] := sin(array_x[1]);
    array_tmp5[1] := array_tmp3[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_tmp1_g[1]*array_x[2]/c(1);
    array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
    array_tmp2[2] := neg(array_tmp1[2]);
    array_tmp3[2] := array_tmp2[2];
    array_tmp4[2] := neg(array_tmp4_g[1])*array_x[2]/c(1);
    array_tmp4_g[2] := array_tmp4[1]*array_x[2]/c(1);
    array_tmp5[2] := array_tmp3[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_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
    array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
    array_tmp2[3] := neg(array_tmp1[3]);
    array_tmp3[3] := array_tmp2[3];
    array_tmp4[3] := neg(array_tmp4_g[2])*array_x[2]/c(2);
    array_tmp4_g[3] := array_tmp4[2]*array_x[2]/c(2);
    array_tmp5[3] := array_tmp3[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_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
    array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
    array_tmp2[4] := neg(array_tmp1[4]);
    array_tmp3[4] := array_tmp2[4];
    array_tmp4[4] := neg(array_tmp4_g[3])*array_x[2]/c(3);
    array_tmp4_g[4] := array_tmp4[3]*array_x[2]/c(3);
    array_tmp5[4] := array_tmp3[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_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
    array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
    array_tmp2[5] := neg(array_tmp1[5]);
    array_tmp3[5] := array_tmp2[5];
    array_tmp4[5] := neg(array_tmp4_g[4])*array_x[2]/c(4);
    array_tmp4_g[5] := array_tmp4[4]*array_x[2]/c(4);
    array_tmp5[5] := array_tmp3[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_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
        array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
            ;
        array_tmp2[kkk] := neg(array_tmp1[kkk]);
        array_tmp3[kkk] := array_tmp2[kkk];
        array_tmp4[kkk] := neg(array_tmp4_g[kkk - 1])*array_x[2]/c(kkk - 1)
            ;
        array_tmp4_g[kkk] := array_tmp4[kkk - 1]*array_x[2]/c(kkk - 1);
        array_tmp5[kkk] := array_tmp3[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,
>     #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_g,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4_g,
>     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_g:= Array(0..(40),[]);
>     array_tmp1:= Array(0..(40),[]);
>     array_tmp2:= Array(0..(40),[]);
>     array_tmp3:= Array(0..(40),[]);
>     array_tmp4_g:= 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_g[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4_g[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_g);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4_g);
>     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_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,"##############temp/sub_sin_cospostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =  neg ( sin ( x )  )   -  cos ( x )  ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=40;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(0.1);");
>     omniout_str(ALWAYS,"x_end := c(5.0) ;");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 3;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
>     omniout_str(ALWAYS,"glob_look_poles:=false;");
>     omniout_str(ALWAYS,"glob_h:=c(0.001);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y := proc(x)");
>     omniout_str(ALWAYS,"return(cos(c(x)) - sin(c(x))) ;");
>     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(0.1);
>     x_end := c(5.0) ;
>     array_y_init[0 + 1] := exact_soln_y(x_start);
>     glob_look_poles := true;
>     glob_type_given_pole := 3;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=8;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=3;
>     glob_max_iter:=100000;
>     glob_upper_ratio_limit:=c(1.000001);
>     glob_lower_ratio_limit:=c(0.999999);
>     glob_look_poles:=false;
>     glob_h:=c(0.001);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(x_start,x_end));
>     glob__pi := arccos(glob__m1);
>     glob_prec = expt(10.0,c(-Digits));
>     if (glob_optimize)  then # if number 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  )   =  neg ( sin ( x )  )   -  cos ( x )  ; ");
>         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,"2016-08-26T17:03:53-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"sub_sin_cos.ode.txt\">sub_sin_cos</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =  neg ( sin ( x )  )   -  cos ( x )  ; ")
>             ;
>             logitem_float(html_log_file,x_start)
>             ;
>             logitem_float(html_log_file,x_end)
>             ;
>             logitem_float(html_log_file,array_x[1])
>             ;
>             logitem_float(html_log_file,glob_h)
>             ;
>             logitem_h_reason(html_log_file)
>             ;
>             logitem_integer(html_log_file,Digits)
>             ;
>             ;
>             logitem_float(html_log_file,glob_desired_digits_correct)
>             ;
>             if (array_est_digits[1] <> -16) then # if number 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> 308.maple.seems.ok </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.sub_sin_cos.mxt.txt\">sub_sin_cos diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.sub_sin_cos.mxt.txt\">sub_sin_cos 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_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_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, 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_g := Array(0 .. 40, []);
    array_tmp1 := Array(0 .. 40, []);
    array_tmp2 := Array(0 .. 40, []);
    array_tmp3 := Array(0 .. 40, []);
    array_tmp4_g := 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_g[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp4_g[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_g);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4_g);
    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_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,
        "##############temp/sub_sin_cospostode.ode#################");
    omniout_str(ALWAYS, "diff  (  y  ,  x  ,  1  )   =  neg ( sin ( x )  \
        )   -  cos ( x )  ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=40;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(0.1);");
    omniout_str(ALWAYS, "x_end := c(5.0) ;");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 3;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
    omniout_str(ALWAYS, "glob_look_poles:=false;");
    omniout_str(ALWAYS, "glob_h:=c(0.001);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y := proc(x)");
    omniout_str(ALWAYS, "return(cos(c(x)) - sin(c(x))) ;");
    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(0.1);
    x_end := c(5.0);
    array_y_init[1] := exact_soln_y(x_start);
    glob_look_poles := true;
    glob_type_given_pole := 3;
    glob_desired_digits_correct := 8;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000;
    glob_upper_ratio_limit := c(1.000001);
    glob_lower_ratio_limit := c(0.999999);
    glob_look_poles := false;
    glob_h := c(0.001);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(x_start, x_end));
    glob__pi := arccos(glob__m1);
    glob_prec = expt(10.0, c(-Digits));
    if glob_optimize then
        omniout_str(ALWAYS, "START of Optimize");
        found_h := false;
        glob_min_pole_est := glob_larger_float;
        last_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        glob_min_h := float_abs(glob_min_h)*glob_check_sign;
        glob_max_h := float_abs(glob_max_h)*glob_check_sign;
        glob_h := float_abs(glob_min_h)*glob_check_sign;
        glob_display_interval :=
            c(float_abs(c(glob_display_interval))*glob_check_sign);
        display_max := c(x_end) - c(x_start)/glob__10;
        if display_max < glob_display_interval then
            glob_display_interval := c(display_max)
        end if;
        chk_data();
        min_value := glob_larger_float;
        est_answer := est_size_answer();
        opt_iter := 1;
        est_needed_step_err :=
            estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
            ;
        omniout_float(ALWAYS, "est_needed_step_err", 32,
            est_needed_step_err, 16, "");
        estimated_step_error := glob_small_float;
        while opt_iter <= 100 and not found_h do
            omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
            array_x[1] := c(x_start);
            array_x[2] := c(glob_h);
            glob_next_display := c(x_start);
            order_diff := 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  )   =  neg ( sin ( x )\
              )   -  cos ( x )  ; ");
        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, "2016-08-26T17:03:53-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"sub_sin_cos.ode.txt\">sub_sin_cos</a>");
            logitem_str(html_log_file, "diff  (  y  ,  x  ,  1  )   =  ne\
                g ( sin ( x )  )   -  cos ( x )  ; ");
            logitem_float(html_log_file, x_start);
            logitem_float(html_log_file, x_end);
            logitem_float(html_log_file, array_x[1]);
            logitem_float(html_log_file, glob_h);
            logitem_h_reason(html_log_file);
            logitem_integer(html_log_file, Digits);
            logitem_float(html_log_file, glob_desired_digits_correct);
            if array_est_digits[1] <> -16 then
                logitem_integer(html_log_file, array_est_digits[1])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_min_good_digits <> -16 then
                logitem_integer(html_log_file, glob_min_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_good_digits <> -16 then
                logitem_integer(html_log_file, glob_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            logitem_integer(html_log_file, ATS_MAX_TERMS);
            if glob_type_given_pole = 0 then
                logitem_str(html_log_file, "Not Given");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 4 then
                logitem_str(html_log_file, "No Solution");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 5 then
                logitem_str(html_log_file, "Some Pole");
                logitem_str(html_log_file, "????")
            elif glob_type_given_pole = 3 then
                logitem_str(html_log_file, "No Pole");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 1 then
                logitem_str(html_log_file, "Real Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            elif glob_type_given_pole = 2 then
                logitem_str(html_log_file, "Complex Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_ratio_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_3_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_3_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_6_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_6_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            logitem_integer(html_log_file, glob_iter);
            logitem_time(html_log_file, glob_clock_sec);
            if c(glob_percent_done) < glob__100 then
                logitem_time(html_log_file, glob_total_exp_sec); 0
            else logitem_str(html_log_file, "Done"); 0
            end if;
            log_revs(html_log_file, "<td> 308.maple.seems.ok </td>");
            logitem_str(html_log_file, "<a href=\"diffeq.sub_sin_cos.mxt.\
                txt\">sub_sin_cos diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.sub_sin_cos.mxt\
                .txt\">sub_sin_cos 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#################
##############temp/sub_sin_cospostode.ode#################
diff  (  y  ,  x  ,  1  )   =  neg ( sin ( x )  )   -  cos ( x )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;







glob_type_given_pole := 3;

#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(cos(c(x)) - sin(c(x))) ;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0.1                                          
y[1] (closed_form)                = 0.89517074863119761378874778939325           
y[1] (numeric)                    = 0.89517074863119761378874778939325           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4.1MB, alloc=40.3MB, time=0.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.11                                         
y[1] (closed_form)                = 0.8841777971195220416928901213364            
y[1] (numeric)                    = 0.88417779711952204169289012133639           
absolute error                    = 1e-32                                        
relative error                    = 1.1309942448880801953773423004260e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y[1] (closed_form)                = 0.87309642856494689228074755358666           
y[1] (numeric)                    = 0.87309642856494689228074755358666           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.13                                         
y[1] (closed_form)                = 0.8619277510950931800533063604435            
y[1] (numeric)                    = 0.8619277510950931800533063604435            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y[1] (closed_form)                = 0.85067288156840069018095987530603           
y[1] (numeric)                    = 0.85067288156840069018095987530601           
absolute error                    = 2e-32                                        
relative error                    = 2.3510800018834084641036278497237e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y[1] (closed_form)                = 0.8393329454624430652372555599667            
y[1] (numeric)                    = 0.83933294546244306523725555996667           
absolute error                    = 3e-32                                        
relative error                    = 3.5742669416450763046474484172780e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.16                                         
y[1] (closed_form)                = 0.82790907676138098572948936433235           
y[1] (numeric)                    = 0.82790907676138098572948936433232           
absolute error                    = 3e-32                                        
relative error                    = 3.6235863142549608674379004834396e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y[1] (closed_form)                = 0.81640241784256469901430561354165           
y[1] (numeric)                    = 0.81640241784256469901430561354162           
absolute error                    = 3e-32                                        
relative error                    = 3.6746583969310597396349830794283e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.18                                         
y[1] (closed_form)                = 0.80481411936229723625091328491232           
y[1] (numeric)                    = 0.8048141193622972362509132849123            
absolute error                    = 2e-32                                        
relative error                    = 2.4850458657270086372457720499439e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=34.0MB, alloc=40.3MB, time=0.45
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y[1] (closed_form)                = 0.7931453401407697409750263512086            
y[1] (numeric)                    = 0.79314534014076974097502635120859           
absolute error                    = 1e-32                                        
relative error                    = 1.2608029693807658159849057629899e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.2                                          
y[1] (closed_form)                = 0.78139724704618041566478388962978           
y[1] (numeric)                    = 0.78139724704618041566478388962975           
absolute error                    = 3e-32                                        
relative error                    = 3.8392763877023239890732769517162e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y[1] (closed_form)                = 0.76957101487804867430742614187171           
y[1] (numeric)                    = 0.76957101487804867430742614187166           
absolute error                    = 5e-32                                        
relative error                    = 6.4971261954198380934648350064117e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y[1] (closed_form)                = 0.75766782624973616945423197558769           
y[1] (numeric)                    = 0.75766782624973616945423197558765           
absolute error                    = 4e-32                                        
relative error                    = 5.2793583961443721868834730287484e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y[1] (closed_form)                = 0.74568887147018644156311343571153           
y[1] (numeric)                    = 0.74568887147018644156311343571149           
absolute error                    = 4e-32                                        
relative error                    = 5.3641674873244033934179384748806e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y[1] (closed_form)                = 0.73363534842489501656538316247356           
y[1] (numeric)                    = 0.73363534842489501656538316247351           
absolute error                    = 5e-32                                        
relative error                    = 6.8153749825917345709361689002387e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.25                                         
y[1] (closed_form)                = 0.7215084624561218545477467446448            
y[1] (numeric)                    = 0.72150846245612185454774674464476           
absolute error                    = 4e-32                                        
relative error                    = 5.5439405192607256889696738129625e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y[1] (closed_form)                = 0.70930942624235812820482918208484           
y[1] (numeric)                    = 0.70930942624235812820482918208482           
absolute error                    = 2e-32                                        
relative error                    = 2.8196439043468123616030306899894e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y[1] (closed_form)                = 0.69703945967705938428394618847166           
y[1] (numeric)                    = 0.69703945967705938428394618847164           
absolute error                    = 2e-32                                        
relative error                    = 2.8692780189612312767829229517267e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y[1] (closed_form)                = 0.68469978974665721460492049513863           
y[1] (numeric)                    = 0.68469978974665721460492049513861           
absolute error                    = 2e-32                                        
relative error                    = 2.9209881906638401106109742205270e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y[1] (closed_form)                = 0.67229165040786163538618457242749           
y[1] (numeric)                    = 0.67229165040786163538618457242745           
absolute error                    = 4e-32                                        
relative error                    = 5.9497987184182718385499783612552e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=74.2MB, alloc=44.3MB, time=0.94
 
TOP MAIN SOLVE Loop
x[1]                              = 0.3                                          
y[1] (closed_form)                = 0.65981628246426644453698948188302           
y[1] (numeric)                    = 0.65981628246426644453698948188299           
absolute error                    = 3e-32                                        
relative error                    = 4.5467201700383477235132552403322e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y[1] (closed_form)                = 0.64727493344226989627716211224325           
y[1] (numeric)                    = 0.64727493344226989627716211224323           
absolute error                    = 2e-32                                        
relative error                    = 3.0898771088875774083825266841152e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y[1] (closed_form)                = 0.63466885746632310091354973034894           
y[1] (numeric)                    = 0.63466885746632310091354973034894           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y[1] (closed_form)                = 0.62199931513351862482921488219599           
y[1] (numeric)                    = 0.62199931513351862482921488219598           
absolute error                    = 1e-32                                        
relative error                    = 1.6077188120140286571020224671770e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y[1] (closed_form)                = 0.60926757338753183172087257299579           
y[1] (numeric)                    = 0.60926757338753183172087257299578           
absolute error                    = 1e-32                                        
relative error                    = 1.6413149881586397774823969664185e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y[1] (closed_form)                = 0.59647490539192757084539745038604           
y[1] (numeric)                    = 0.59647490539192757084539745038605           
absolute error                    = 1e-32                                        
relative error                    = 1.6765164652533487126184174662728e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y[1] (closed_form)                = 0.58362259040284488150099893220401           
y[1] (numeric)                    = 0.58362259040284488150099893220404           
absolute error                    = 3e-32                                        
relative error                    = 5.1403082220125392052160765965881e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.37                                         
y[1] (closed_form)                = 0.57071191364107244516652043536373           
y[1] (numeric)                    = 0.57071191364107244516652043536375           
absolute error                    = 2e-32                                        
relative error                    = 3.5043950409940521116132972581524e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y[1] (closed_form)                = 0.55774416616352757764704534137536           
y[1] (numeric)                    = 0.55774416616352757764704534137539           
absolute error                    = 3e-32                                        
relative error                    = 5.3788101821587071522830127091396e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y[1] (closed_form)                = 0.54472064473415161321949465503394           
y[1] (numeric)                    = 0.54472064473415161321949465503397           
absolute error                    = 3e-32                                        
relative error                    = 5.5074101358213366411818413424548e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y[1] (closed_form)                = 0.53164265169423459113221497525609           
y[1] (numeric)                    = 0.53164265169423459113221497525613           
absolute error                    = 4e-32                                        
relative error                    = 7.5238508183134511219047777278729e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=114.4MB, alloc=44.3MB, time=1.41
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y[1] (closed_form)                = 0.51851149483218221188184441822588           
y[1] (numeric)                    = 0.51851149483218221188184441822592           
absolute error                    = 4e-32                                        
relative error                    = 7.7143902109530125303827376058323e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y[1] (closed_form)                = 0.50532848725273808646330163157933           
y[1] (numeric)                    = 0.50532848725273808646330163157937           
absolute error                    = 4e-32                                        
relative error                    = 7.9156431923051579050411501086764e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.43                                         
y[1] (closed_form)                = 0.49209494724567435625899180503888           
y[1] (numeric)                    = 0.49209494724567435625899180503892           
absolute error                    = 4e-32                                        
relative error                    = 8.1285126425064325832412089118458e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y[1] (closed_form)                = 0.47881219815396381439581663821845           
y[1] (numeric)                    = 0.4788121981539638143958166382185            
absolute error                    = 5e-32                                        
relative error                    = 1.0442507561998726907741636741632e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y[1] (closed_form)                = 0.46548156824144671124799636525455           
y[1] (numeric)                    = 0.46548156824144671124799636525461           
absolute error                    = 6e-32                                        
relative error                    = 1.2889876655412017674475233836762e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y[1] (closed_form)                = 0.45210439056000547729487625957151           
y[1] (numeric)                    = 0.45210439056000547729487625957156           
absolute error                    = 5e-32                                        
relative error                    = 1.1059392707526417755488272476206e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.47                                         
y[1] (closed_form)                = 0.43868200281626064575074447613698           
y[1] (numeric)                    = 0.43868200281626064575074447613704           
absolute error                    = 6e-32                                        
relative error                    = 1.3677333379261205759920909816959e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y[1] (closed_form)                = 0.4252157472378013052633118885701            
y[1] (numeric)                    = 0.42521574723780130526331188857016           
absolute error                    = 6e-32                                        
relative error                    = 1.4110484004828044352164612004616e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.49                                         
y[1] (closed_form)                = 0.4117069704389634595241098219487            
y[1] (numeric)                    = 0.41170697043896345952410982194876           
absolute error                    = 6e-32                                        
relative error                    = 1.4573471985676556119245978913354e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y[1] (closed_form)                = 0.39815702328616971584299364738826           
y[1] (numeric)                    = 0.39815702328616971584299364738832           
absolute error                    = 6e-32                                        
relative error                    = 1.5069431528494186730885239605061e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.51                                         
y[1] (closed_form)                = 0.38456726076284376860567823590094           
y[1] (numeric)                    = 0.38456726076284376860567823590099           
absolute error                    = 5e-32                                        
relative error                    = 1.3001626789763096374071400037513e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=154.6MB, alloc=44.3MB, time=1.88
 
TOP MAIN SOLVE Loop
x[1]                              = 0.52                                         
y[1] (closed_form)                = 0.37093904183391318605338862944076           
y[1] (numeric)                    = 0.37093904183391318605338862944082           
absolute error                    = 6e-32                                        
relative error                    = 1.6175164443020482938012727943919e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.53                                         
y[1] (closed_form)                = 0.35727372930991404999303399609812           
y[1] (numeric)                    = 0.35727372930991404999303399609818           
absolute error                    = 6e-32                                        
relative error                    = 1.6793846028335744670437385017973e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.54                                         
y[1] (closed_form)                = 0.34357268971071103786068809595956           
y[1] (numeric)                    = 0.34357268971071103786068809595962           
absolute error                    = 6e-32                                        
relative error                    = 1.7463553360577097169585396997463e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.55                                         
y[1] (closed_form)                = 0.32983729312884657501660368986048           
y[1] (numeric)                    = 0.32983729312884657501660368986055           
absolute error                    = 7e-32                                        
relative error                    = 2.1222585031540210359679988340416e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.56                                         
y[1] (closed_form)                = 0.31606891309253272224265606275429           
y[1] (numeric)                    = 0.31606891309253272224265606275436           
absolute error                    = 7e-32                                        
relative error                    = 2.2147068914527103219553582771909e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.57                                         
y[1] (closed_form)                = 0.30226892642829949913929287083718           
y[1] (numeric)                    = 0.30226892642829949913929287083726           
absolute error                    = 8e-32                                        
relative error                    = 2.6466498209162300967201619558800e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y[1] (closed_form)                = 0.28843871312331337847519126847356           
y[1] (numeric)                    = 0.28843871312331337847519126847363           
absolute error                    = 7e-32                                        
relative error                    = 2.4268586987514947578310916100806e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.59                                         
y[1] (closed_form)                = 0.27457965618737971952545314361491           
y[1] (numeric)                    = 0.27457965618737971952545314361498           
absolute error                    = 7e-32                                        
relative error                    = 2.5493512874176784269546267206793e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y[1] (closed_form)                = 0.26069314151464294004000705329672           
y[1] (numeric)                    = 0.26069314151464294004000705329677           
absolute error                    = 5e-32                                        
relative error                    = 1.9179637680338259744580763725104e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.61                                         
y[1] (closed_form)                = 0.2467805577449982567097705464921            
y[1] (numeric)                    = 0.24678055774499825670977054649217           
absolute error                    = 7e-32                                        
relative error                    = 2.8365281543909938977507319014064e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.62                                         
y[1] (closed_form)                = 0.23284329612522885284103642677849           
y[1] (numeric)                    = 0.23284329612522885284103642677855           
absolute error                    = 6e-32                                        
relative error                    = 2.5768403470688940916815755352976e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=195.0MB, alloc=44.3MB, time=2.36
 
TOP MAIN SOLVE Loop
x[1]                              = 0.63                                         
y[1] (closed_form)                = 0.21888275036988235940559687498244           
y[1] (numeric)                    = 0.21888275036988235940559687498251           
absolute error                    = 7e-32                                        
relative error                    = 3.1980592295057253560254386049651e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.64                                         
y[1] (closed_form)                = 0.20490031652190056170256454005239           
y[1] (numeric)                    = 0.20490031652190056170256454005246           
absolute error                    = 7e-32                                        
relative error                    = 3.4162953570898032885072190914119e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y[1] (closed_form)                = 0.19089739281301626854508289207397           
y[1] (numeric)                    = 0.19089739281301626854508289207404           
absolute error                    = 7e-32                                        
relative error                    = 3.6668913581530630383582483377359e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.66                                         
y[1] (closed_form)                = 0.17687537952393130416867161183394           
y[1] (numeric)                    = 0.17687537952393130416867161183402           
absolute error                    = 8e-32                                        
relative error                    = 4.5229584928848715463222262811943e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.67                                         
y[1] (closed_form)                = 0.16283567884428960494549823071153           
y[1] (numeric)                    = 0.1628356788442896049454982307116            
absolute error                    = 7e-32                                        
relative error                    = 4.2988121827364980818424024076345e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.68                                         
y[1] (closed_form)                = 0.14877969473245942347821589662407           
y[1] (numeric)                    = 0.14877969473245942347821589662415           
absolute error                    = 8e-32                                        
relative error                    = 5.3770778427700534408086484790621e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.69                                         
y[1] (closed_form)                = 0.13470883277513866173611010848905           
y[1] (numeric)                    = 0.13470883277513866173611010848912           
absolute error                    = 7e-32                                        
relative error                    = 5.1963927351999836906153254656297e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y[1] (closed_form)                = 0.12062450004679737258324563879314           
y[1] (numeric)                    = 0.12062450004679737258324563879322           
absolute error                    = 8e-32                                        
relative error                    = 6.6321518405434444850708613047924e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.71                                         
y[1] (closed_form)                = 0.10652810496897148533132997128671           
y[1] (numeric)                    = 0.10652810496897148533132997128681           
absolute error                    = 1.0e-31                                      
relative error                    = 9.3871941145603847011198580756168e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y[1] (closed_form)                = 0.09242105716942182582748312960378           
y[1] (numeric)                    = 0.092421057169421825827483129603862          
absolute error                    = 8.2e-32                                      
relative error                    = 8.8724369219972839862245422121078e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.73                                         
y[1] (closed_form)                = 0.0783047673411725150575380277888            
y[1] (numeric)                    = 0.078304767341172515057538027788886          
absolute error                    = 8.6e-32                                      
relative error                    = 1.0982728500462748267969700643492e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=235.2MB, alloc=44.3MB, time=2.83
 
TOP MAIN SOLVE Loop
x[1]                              = 0.74                                         
y[1] (closed_form)                = 0.06418064710144284230754340309066           
y[1] (numeric)                    = 0.064180647101442842307543403090744          
absolute error                    = 8.4e-32                                      
relative error                    = 1.3088057505439455080028181590028e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.75                                         
y[1] (closed_form)                = 0.05005010885048671957859680022019           
y[1] (numeric)                    = 0.050050108850486719578596800220276          
absolute error                    = 8.6e-32                                      
relative error                    = 1.7182779813107974981961352533051e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.76                                         
y[1] (closed_form)                = 0.03591456563035383319193272789728           
y[1] (numeric)                    = 0.035914565630353833191932727897366          
absolute error                    = 8.6e-32                                      
relative error                    = 2.3945716310519866665159864028287e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y[1] (closed_form)                = 0.02177543098358661635140683087213           
y[1] (numeric)                    = 0.021775430983586616351406830872218          
absolute error                    = 8.8e-32                                      
relative error                    = 4.0412518156968106152114962451253e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y[1] (closed_form)                = 0.00763411881186717284836769864664           
y[1] (numeric)                    = 0.0076341188118671728483676986467229         
absolute error                    = 8.29e-32                                     
relative error                    = 1.0859144590615049658089433230684e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.79                                         
y[1] (closed_form)                = -0.00650795676537171290124801388425          
y[1] (numeric)                    = -0.0065079567653717129012480138841611        
absolute error                    = 8.89e-32                                     
relative error                    = 1.3660201381949765751506697960041e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y[1] (closed_form)                = -0.02064938155235734070642462893907          
y[1] (numeric)                    = -0.020649381552357340706424628938976         
absolute error                    = 9.4e-32                                      
relative error                    = 4.5521944452263233390013032672418e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.81                                         
y[1] (closed_form)                = -0.03478874141839549337853761183444          
y[1] (numeric)                    = -0.034788741418395493378537611834357         
absolute error                    = 8.3e-32                                      
relative error                    = 2.3858293406415528491038643382537e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y[1] (closed_form)                = -0.04892462243928232771475538625079          
y[1] (numeric)                    = -0.048924622439282327714755386250709         
absolute error                    = 8.1e-32                                      
relative error                    = 1.6556080754741575892475088793775e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.83                                         
y[1] (closed_form)                = -0.06305561103869561661611730827363          
y[1] (numeric)                    = -0.063055611038695616616117308273544         
absolute error                    = 8.6e-32                                      
relative error                    = 1.3638754518963268534704388484123e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.84                                         
y[1] (closed_form)                = -0.07718029412955120333390163375879          
y[1] (numeric)                    = -0.077180294129551203333901633758706         
absolute error                    = 8.4e-32                                      
relative error                    = 1.0883607136687191147895015118374e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=275.4MB, alloc=44.3MB, time=3.30
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y[1] (closed_form)                = -0.091297259255310532316655494774            
y[1] (numeric)                    = -0.09129725925531053231665549477392          
absolute error                    = 8.0e-32                                      
relative error                    = 8.7625850603337362381955081006253e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.86                                         
y[1] (closed_form)                = -0.10540509473122512602255806530479          
y[1] (numeric)                    = -0.10540509473122512602255806530471          
absolute error                    = 8e-32                                        
relative error                    = 7.5897659599845566233124481525610e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y[1] (closed_form)                = -0.11950238978550388336713901824002          
y[1] (numeric)                    = -0.11950238978550388336713901823994          
absolute error                    = 8e-32                                        
relative error                    = 6.6944267929363467138006538433048e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.88                                         
y[1] (closed_form)                = -0.1335877347003890831941465250339           
y[1] (numeric)                    = -0.13358773470038908319414652503382          
absolute error                    = 8e-32                                        
relative error                    = 5.9885737399039071107244113377276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.89                                         
y[1] (closed_form)                = -0.14765972095312698528678065559293          
y[1] (numeric)                    = -0.14765972095312698528678065559287          
absolute error                    = 6e-32                                        
relative error                    = 4.0633965452939169921173454295423e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y[1] (closed_form)                = -0.16171694135681893197666616430642          
y[1] (numeric)                    = -0.16171694135681893197666616430634          
absolute error                    = 8e-32                                        
relative error                    = 4.9469152290906058591399227199976e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y[1] (closed_form)                = -0.17575799020113886535777929169687          
y[1] (numeric)                    = -0.17575799020113886535777929169679          
absolute error                    = 8e-32                                        
relative error                    = 4.5517134048043763491142189104931e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.92                                         
y[1] (closed_form)                = -0.18978146339290318847087139580724          
y[1] (numeric)                    = -0.18978146339290318847087139580716          
absolute error                    = 8e-32                                        
relative error                    = 4.2153748089915704620077751228526e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.93                                         
y[1] (closed_form)                = -0.20378595859647891358941213147767          
y[1] (numeric)                    = -0.20378595859647891358941213147759          
absolute error                    = 8e-32                                        
relative error                    = 3.9256875474138907874461036082126e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y[1] (closed_form)                = -0.21777007537401605690922998341013          
y[1] (numeric)                    = -0.21777007537401605690922998341006          
absolute error                    = 7e-32                                        
relative error                    = 3.2143994017440780622787225796248e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.95                                         
y[1] (closed_form)                = -0.2317324153254902565192411283421           
y[1] (numeric)                    = -0.23173241532549025651924112834202          
absolute error                    = 8e-32                                        
relative error                    = 3.4522576346357231763709442506868e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=315.6MB, alloc=44.3MB, time=3.78
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y[1] (closed_form)                = -0.24567158222854160950817134607857          
y[1] (numeric)                    = -0.24567158222854160950817134607848          
absolute error                    = 9e-32                                        
relative error                    = 3.6634273766460884801279339420864e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.97                                         
y[1] (closed_form)                = -0.25958618217809574444009228300648          
y[1] (numeric)                    = -0.2595861821780957444400922830064           
absolute error                    = 8e-32                                        
relative error                    = 3.0818281361799894412353685384763e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.98                                         
y[1] (closed_form)                = -0.27347482372575316720787502035921          
y[1] (numeric)                    = -0.27347482372575316720787502035912          
absolute error                    = 9e-32                                        
relative error                    = 3.2909793586796152976119774588142e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.99                                         
y[1] (closed_form)                = -0.2873361180189329414461330028935           
y[1] (numeric)                    = -0.28733611801893294144613300289343          
absolute error                    = 7e-32                                        
relative error                    = 2.4361712854834215853754654383210e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y[1] (closed_form)                = -0.30116867893975678925156571418732          
y[1] (numeric)                    = -0.30116867893975678925156571418726          
absolute error                    = 6e-32                                        
relative error                    = 1.9922390406341652691785474645290e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y[1] (closed_form)                = -0.31497112324365972391636742900283          
y[1] (numeric)                    = -0.31497112324365972391636742900278          
absolute error                    = 5e-32                                        
relative error                    = 1.5874471121379691525709411452115e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y[1] (closed_form)                = -0.32874207069771335372693617742157          
y[1] (numeric)                    = -0.32874207069771335372693617742152          
absolute error                    = 5e-32                                        
relative error                    = 1.5209492321406061913364762408581e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y[1] (closed_form)                = -0.34248014421864802461277208545707          
y[1] (numeric)                    = -0.34248014421864802461277208545702          
absolute error                    = 5e-32                                        
relative error                    = 1.4599386517449820324185739492886e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y[1] (closed_form)                = -0.356183970010559999546318271124            
y[1] (numeric)                    = -0.35618397001055999954631827112394          
absolute error                    = 6e-32                                        
relative error                    = 1.6845227481242669077556885397006e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y[1] (closed_form)                = -0.36985217770228990409055991218817          
y[1] (numeric)                    = -0.36985217770228990409055991218811          
absolute error                    = 6e-32                                        
relative error                    = 1.6222697503838035610479643812303e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y[1] (closed_form)                = -0.38348340048445870036430838204101          
y[1] (numeric)                    = -0.38348340048445870036430838204095          
absolute error                    = 6e-32                                        
relative error                    = 1.5646048805294141884500502966825e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=356.0MB, alloc=44.3MB, time=4.26
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y[1] (closed_form)                = -0.3970762752461474859419701896009           
y[1] (numeric)                    = -0.39707627524614748594197018960084          
absolute error                    = 6e-32                                        
relative error                    = 1.5110446969617113152804925420316e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y[1] (closed_form)                = -0.41062944271120744982181019909873          
y[1] (numeric)                    = -0.41062944271120744982181019909867          
absolute error                    = 6e-32                                        
relative error                    = 1.4611714056314647083885820998536e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y[1] (closed_form)                = -0.42414154757418635458070355476091          
y[1] (numeric)                    = -0.42414154757418635458070355476087          
absolute error                    = 4e-32                                        
relative error                    = 9.4308138942704317276416501673393e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y[1] (closed_form)                = -0.43761123863585795218043252608698          
y[1] (numeric)                    = -0.43761123863585795218043252608697          
absolute error                    = 1e-32                                        
relative error                    = 2.2851332683256636099986643849762e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y[1] (closed_form)                = -0.4510371689383407805968884474058           
y[1] (numeric)                    = -0.45103716893834078059688844740579          
absolute error                    = 1e-32                                        
relative error                    = 2.2171121780358314687515738968785e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y[1] (closed_form)                = -0.46441799589979282950511445337802          
y[1] (numeric)                    = -0.464417995899792829505114453378            
absolute error                    = 2e-32                                        
relative error                    = 4.3064653343698996237680652355472e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y[1] (closed_form)                = -0.47775238144866860566586568675786          
y[1] (numeric)                    = -0.47775238144866860566586568675784          
absolute error                    = 2e-32                                        
relative error                    = 4.1862690332081306988364677976248e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y[1] (closed_form)                = -0.49103899215752517241902883727962          
y[1] (numeric)                    = -0.4910389921575251724190288372796           
absolute error                    = 2e-32                                        
relative error                    = 4.0729963036385520989487326689207e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y[1] (closed_form)                = -0.50427649937636378279145633094376          
y[1] (numeric)                    = -0.50427649937636378279145633094374          
absolute error                    = 2e-32                                        
relative error                    = 3.9660781386271023288352880945667e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y[1] (closed_form)                = -0.51746357936549377216702204348032          
y[1] (numeric)                    = -0.51746357936549377216702204348032          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.17                                         
y[1] (closed_form)                = -0.53059891342790542424035107391153          
y[1] (numeric)                    = -0.53059891342790542424035107391151          
absolute error                    = 2e-32                                        
relative error                    = 3.7693254723782013941706737323486e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=396.4MB, alloc=44.3MB, time=4.74
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y[1] (closed_form)                = -0.543681188041138573077938559162            
y[1] (numeric)                    = -0.54368118804113857307793855916198          
absolute error                    = 2e-32                                        
relative error                    = 3.6786264523992810228731590895100e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y[1] (closed_form)                = -0.5567090949886337545363415532522           
y[1] (numeric)                    = -0.55670909498863375453634155325218          
absolute error                    = 2e-32                                        
relative error                    = 3.5925405530528178235783009760782e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y[1] (closed_form)                = -0.56968133149055277203176107987175          
y[1] (numeric)                    = -0.56968133149055277203176107987171          
absolute error                    = 4e-32                                        
relative error                    = 7.0214693353811145933318062540009e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y[1] (closed_form)                = -0.58259660033405559471345417487882          
y[1] (numeric)                    = -0.58259660033405559471345417487875          
absolute error                    = 7e-32                                        
relative error                    = 1.2015174815620729045417876187256e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.22                                         
y[1] (closed_form)                = -0.59545361000302056045972229745317          
y[1] (numeric)                    = -0.59545361000302056045972229745313          
absolute error                    = 4e-32                                        
relative error                    = 6.7175678051220634640242500088545e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y[1] (closed_form)                = -0.60825107480719491178427631989158          
y[1] (numeric)                    = -0.60825107480719491178427631989153          
absolute error                    = 5e-32                                        
relative error                    = 8.2202896256038900817780818717861e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y[1] (closed_form)                = -0.62098771501076274970701254738441          
y[1] (numeric)                    = -0.62098771501076274970701254738437          
absolute error                    = 4e-32                                        
relative error                    = 6.4413512591479742052913884736705e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y[1] (closed_form)                = -0.63366225696031754890095229459801          
y[1] (numeric)                    = -0.63366225696031754890095229459799          
absolute error                    = 2e-32                                        
relative error                    = 3.1562555257654362007508457727495e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y[1] (closed_form)                = -0.64627343321222643697047373224894          
y[1] (numeric)                    = -0.64627343321222643697047373224893          
absolute error                    = 1e-32                                        
relative error                    = 1.5473326747002690108110460170304e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.27                                         
y[1] (closed_form)                = -0.65881998265937350153904472609493          
y[1] (numeric)                    = -0.65881998265937350153904472609491          
absolute error                    = 2e-32                                        
relative error                    = 3.0357306284591709086679639557115e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y[1] (closed_form)                = -0.6713006506572694509213669655677           
y[1] (numeric)                    = -0.67130065065726945092136696556768          
absolute error                    = 2e-32                                        
relative error                    = 2.9792910196672728193668992941998e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=436.8MB, alloc=44.3MB, time=5.22
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y[1] (closed_form)                = -0.68371418914951501751895520122419          
y[1] (numeric)                    = -0.68371418914951501751895520122417          
absolute error                    = 2e-32                                        
relative error                    = 2.9251989087543111291364037120934e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y[1] (closed_form)                = -0.69605935679260555770336452074668          
y[1] (numeric)                    = -0.69605935679260555770336452074669          
absolute error                    = 1e-32                                        
relative error                    = 1.4366590869605321750032491887643e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.31                                         
y[1] (closed_form)                = -0.7083349190800643678310808273213           
y[1] (numeric)                    = -0.70833491908006436783108082732131          
absolute error                    = 1e-32                                        
relative error                    = 1.4117615453699921355165067695447e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.32                                         
y[1] (closed_form)                = -0.72053964846589230316191711654542          
y[1] (numeric)                    = -0.72053964846589230316191711654542          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y[1] (closed_form)                = -0.73267232448732135482189805175322          
y[1] (numeric)                    = -0.73267232448732135482189805175323          
absolute error                    = 1e-32                                        
relative error                    = 1.3648666212412731301496743865412e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y[1] (closed_form)                = -0.74473173388685990955523085578941          
y[1] (numeric)                    = -0.74473173388685990955523085578943          
absolute error                    = 2e-32                                        
relative error                    = 2.6855307877935025610486057405073e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y[1] (closed_form)                = -0.75671667073361748784109136625459          
y[1] (numeric)                    = -0.75671667073361748784109136625461          
absolute error                    = 2e-32                                        
relative error                    = 2.6429971445733461566624718681458e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y[1] (closed_form)                = -0.76862593654389682800251718703477          
y[1] (numeric)                    = -0.76862593654389682800251718703478          
absolute error                    = 1e-32                                        
relative error                    = 1.3010229715854627791225844678850e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.37                                         
y[1] (closed_form)                = -0.78045834040104125719949011524662          
y[1] (numeric)                    = -0.78045834040104125719949011524662          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y[1] (closed_form)                = -0.79221269907452536466898101160785          
y[1] (numeric)                    = -0.79221269907452536466898101160784          
absolute error                    = 1e-32                                        
relative error                    = 1.2622872634687816098400853044583e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y[1] (closed_form)                = -0.80388783713827706824387500663886          
y[1] (numeric)                    = -0.80388783713827706824387500663885          
absolute error                    = 1e-32                                        
relative error                    = 1.2439546337208602401340923273596e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=477.2MB, alloc=44.3MB, time=5.70
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y[1] (closed_form)                = -0.81548258708821924204272654360245          
y[1] (numeric)                    = -0.81548258708821924204272654360244          
absolute error                    = 1e-32                                        
relative error                    = 1.2262677533932672289594932264619e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y[1] (closed_form)                = -0.82699578945901915126552631258132          
y[1] (numeric)                    = -0.82699578945901915126552631258131          
absolute error                    = 1e-32                                        
relative error                    = 1.2091959992373744465540324283418e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y[1] (closed_form)                = -0.83842629294003401924929137035979          
y[1] (numeric)                    = -0.83842629294003401924929137035978          
absolute error                    = 1e-32                                        
relative error                    = 1.1927106871772711284812208322207e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y[1] (closed_form)                = -0.84977295449044113232339387090691          
y[1] (numeric)                    = -0.84977295449044113232339387090688          
absolute error                    = 3e-32                                        
relative error                    = 3.5303547661138775322847231599097e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y[1] (closed_form)                = -0.86103463945354096955008430782881          
y[1] (numeric)                    = -0.86103463945354096955008430782878          
absolute error                    = 3e-32                                        
relative error                    = 3.4841803831538784944713539185400e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y[1] (closed_form)                = -0.87221022167022192713248750707499          
y[1] (numeric)                    = -0.87221022167022192713248750707496          
absolute error                    = 3e-32                                        
relative error                    = 3.4395377690658206216683729146477e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.46                                         
y[1] (closed_form)                = -0.88329858359157529111218419212666          
y[1] (numeric)                    = -0.88329858359157529111218419212664          
absolute error                    = 2e-32                                        
relative error                    = 2.2642400170821190514089033856957e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y[1] (closed_form)                = -0.89429861639064919695295386127316          
y[1] (numeric)                    = -0.89429861639064919695295386127315          
absolute error                    = 1e-32                                        
relative error                    = 1.1181947301181757913425079664933e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y[1] (closed_form)                = -0.90520922007333040070784859191485          
y[1] (numeric)                    = -0.90520922007333040070784859191484          
absolute error                    = 1e-32                                        
relative error                    = 1.1047169845651711997068145283232e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.49                                         
y[1] (closed_form)                = -0.91602930358834277368488223247999          
y[1] (numeric)                    = -0.91602930358834277368488223247999          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y[1] (closed_form)                = -0.92675778493635152085353351970722          
y[1] (numeric)                    = -0.92675778493635152085353351970723          
absolute error                    = 1e-32                                        
relative error                    = 1.0790305905751616168431998494850e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=517.6MB, alloc=44.3MB, time=6.18
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y[1] (closed_form)                = -0.93739359127816221266114234992052          
y[1] (numeric)                    = -0.93739359127816221266114234992052          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.52                                         
y[1] (closed_form)                = -0.94793565904200381044618312396412          
y[1] (numeric)                    = -0.94793565904200381044618312396413          
absolute error                    = 1e-32                                        
relative error                    = 1.0549239185817876017772487600630e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y[1] (closed_form)                = -0.95838293402988495723527606163286          
y[1] (numeric)                    = -0.95838293402988495723527606163287          
absolute error                    = 1e-32                                        
relative error                    = 1.0434242561009723809712295055839e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y[1] (closed_form)                = -0.96873437152301289838348673136363          
y[1] (numeric)                    = -0.96873437152301289838348673136365          
absolute error                    = 2e-32                                        
relative error                    = 2.0645494356266770840289508602196e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.55                                         
y[1] (closed_form)                = -0.97898893638626449025369857293891          
y[1] (numeric)                    = -0.97898893638626449025369857293894          
absolute error                    = 3e-32                                        
relative error                    = 3.0643860093801269477740243745401e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.56                                         
y[1] (closed_form)                = -0.98914560317169884992124935965257          
y[1] (numeric)                    = -0.98914560317169884992124935965261          
absolute error                    = 4e-32                                        
relative error                    = 4.0438940305390692271550603839961e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.57                                         
y[1] (closed_form)                = -0.99920335622110129472512139017798          
y[1] (numeric)                    = -0.99920335622110129472512139017802          
absolute error                    = 4e-32                                        
relative error                    = 4.0031891157047812232209507239022e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.58                                         
y[1] (closed_form)                = -1.0091611897675483173571832892344           
y[1] (numeric)                    = -1.0091611897675483173571832892346           
absolute error                    = 2e-31                                        
relative error                    = 1.9818439514709072009149511219846e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.59                                         
y[1] (closed_form)                = -1.0190181080359834400766116899889           
y[1] (numeric)                    = -1.0190181080359834400766116899891           
absolute error                    = 2e-31                                        
relative error                    = 1.9626736602892401691796413079200e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y[1] (closed_form)                = -1.0287731253427938905478842884927           
y[1] (numeric)                    = -1.0287731253427938905478842884929           
absolute error                    = 2e-31                                        
relative error                    = 1.9440632251484864591309019684655e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.61                                         
y[1] (closed_form)                = -1.0384252661943781417177407574453           
y[1] (numeric)                    = -1.0384252661943781417177407574457           
absolute error                    = 4e-31                                        
relative error                    = 3.8519863973063787550115051377104e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=557.9MB, alloc=44.3MB, time=6.65
 
TOP MAIN SOLVE Loop
x[1]                              = 1.62                                         
y[1] (closed_form)                = -1.0479735653846944590592631659591           
y[1] (numeric)                    = -1.0479735653846944590592631659594           
absolute error                    = 3e-31                                        
relative error                    = 2.8626676274021736660982059021764e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.63                                         
y[1] (closed_form)                = -1.0574170680917807004096416823529           
y[1] (numeric)                    = -1.0574170680917807004096416823532           
absolute error                    = 3e-31                                        
relative error                    = 2.8371019255569731338390292657005e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.64                                         
y[1] (closed_form)                = -1.0667548299732357165020746818245           
y[1] (numeric)                    = -1.0667548299732357165020746818248           
absolute error                    = 3e-31                                        
relative error                    = 2.8122675573686114232802971885744e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.65                                         
y[1] (closed_form)                = -1.0759859172606528041313176375435           
y[1] (numeric)                    = -1.0759859172606528041313176375437           
absolute error                    = 2e-31                                        
relative error                    = 1.8587603870242001437960539718466e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.66                                         
y[1] (closed_form)                = -1.0851094068529957686862585222636           
y[1] (numeric)                    = -1.0851094068529957686862585222638           
absolute error                    = 2e-31                                        
relative error                    = 1.8431321186315623013570470161839e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.67                                         
y[1] (closed_form)                = -1.0941243864089082585210795889829           
y[1] (numeric)                    = -1.0941243864089082585210795889831           
absolute error                    = 2e-31                                        
relative error                    = 1.8279457297943251353130507787341e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.68                                         
y[1] (closed_form)                = -1.1030299544379471403084926033664           
y[1] (numeric)                    = -1.1030299544379471403084926033665           
absolute error                    = 1e-31                                        
relative error                    = 9.0659369310559981826448875659894e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.69                                         
y[1] (closed_form)                = -1.1118252203907307921135397637787           
y[1] (numeric)                    = -1.1118252203907307921135397637788           
absolute error                    = 1e-31                                        
relative error                    = 8.9942194299978925803409400303914e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.7                                          
y[1] (closed_form)                = -1.1205093047479932994337762559828           
y[1] (numeric)                    = -1.1205093047479932994337762559828           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.71                                         
y[1] (closed_form)                = -1.1290813391085356488604420069122           
y[1] (numeric)                    = -1.1290813391085356488604420069123           
absolute error                    = 1e-31                                        
relative error                    = 8.8567578380982577210428946976219e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=598.3MB, alloc=44.3MB, time=7.13
 
TOP MAIN SOLVE Loop
x[1]                              = 1.72                                         
y[1] (closed_form)                = -1.1375404662760651243145489374167           
y[1] (numeric)                    = -1.1375404662760651243145489374168           
absolute error                    = 1e-31                                        
relative error                    = 8.7908960572951962019314427994570e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.73                                         
y[1] (closed_form)                = -1.1458858403449142219906260275646           
y[1] (numeric)                    = -1.1458858403449142219906260275648           
absolute error                    = 2e-31                                        
relative error                    = 1.7453745648850984055012224054831e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.74                                         
y[1] (closed_form)                = -1.1541166267846305121880600110106           
y[1] (numeric)                    = -1.1541166267846305121880600110108           
absolute error                    = 2e-31                                        
relative error                    = 1.7329271180955090995666342106718e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.75                                         
y[1] (closed_form)                = -1.1622320025234289891143398809106           
y[1] (numeric)                    = -1.1622320025234289891143398809108           
absolute error                    = 2e-31                                        
relative error                    = 1.7208268191356077954726665873958e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.76                                         
y[1] (closed_form)                = -1.1702311560304985634947682759601           
y[1] (numeric)                    = -1.1702311560304985634947682759603           
absolute error                    = 2e-31                                        
relative error                    = 1.7090640508872898283417332902630e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.77                                         
y[1] (closed_form)                = -1.1781132873971544674079672906288           
y[1] (numeric)                    = -1.178113287397154467407967290629            
absolute error                    = 2e-31                                        
relative error                    = 1.6976296094738627768259883195514e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.78                                         
y[1] (closed_form)                = -1.1858776084168284561743219376182           
y[1] (numeric)                    = -1.1858776084168284561743219376183           
absolute error                    = 1e-31                                        
relative error                    = 8.4325734199081558506019629618642e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.79                                         
y[1] (closed_form)                = -1.1935233426638888083438306975732           
y[1] (numeric)                    = -1.1935233426638888083438306975733           
absolute error                    = 1e-31                                        
relative error                    = 8.3785541870345520608388889362273e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y[1] (closed_form)                = -1.2010497255712822418490474853739           
y[1] (numeric)                    = -1.2010497255712822418490474853741           
absolute error                    = 2e-31                                        
relative error                    = 1.6652099887443836719422098582689e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.81                                         
y[1] (closed_form)                = -1.2084560045069899821962011199324           
y[1] (numeric)                    = -1.2084560045069899821962011199326           
absolute error                    = 2e-31                                        
relative error                    = 1.6550043961392982169888765031620e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.82                                         
y[1] (closed_form)                = -1.2157414388492903371513863633289           
y[1] (numeric)                    = -1.2157414388492903371513863633292           
absolute error                    = 3e-31                                        
relative error                    = 2.4676299615480127428148300807152e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=638.7MB, alloc=44.3MB, time=7.61
 
TOP MAIN SOLVE Loop
x[1]                              = 1.83                                         
y[1] (closed_form)                = -1.2229053000608202517270765133613           
y[1] (numeric)                    = -1.2229053000608202517270765133615           
absolute error                    = 2e-31                                        
relative error                    = 1.6354496132288669799995718288786e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.84                                         
y[1] (closed_form)                = -1.2299468717614284373751766550087           
y[1] (numeric)                    = -1.2299468717614284373751766550088           
absolute error                    = 1e-31                                        
relative error                    = 8.1304324841924472836656122477344e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.85                                         
y[1] (closed_form)                = -1.2368654497998127901344090041109           
y[1] (numeric)                    = -1.2368654497998127901344090041111           
absolute error                    = 2e-31                                        
relative error                    = 1.6169907570170230464645023829150e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.86                                         
y[1] (closed_form)                = -1.2436603423239349340499132541923           
y[1] (numeric)                    = -1.2436603423239349340499132541924           
absolute error                    = 1e-31                                        
relative error                    = 8.0407806373513116771313621168748e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.87                                         
y[1] (closed_form)                = -1.2503308698502048484693985569825           
y[1] (numeric)                    = -1.2503308698502048484693985569825           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.88                                         
y[1] (closed_form)                = -1.2568763653314286608107711853374           
y[1] (numeric)                    = -1.2568763653314286608107711853374           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.89                                         
y[1] (closed_form)                = -1.2632961742235128100785840876896           
y[1] (numeric)                    = -1.2632961742235128100785840876896           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y[1] (closed_form)                = -1.2695896545509179107685433067153           
y[1] (numeric)                    = -1.2695896545509179107685433067152           
absolute error                    = 1e-31                                        
relative error                    = 7.8765607172005685119093477784956e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.91                                         
y[1] (closed_form)                = -1.2757561769708557718282255163457           
y[1] (numeric)                    = -1.2757561769708557718282255163457           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.92                                         
y[1] (closed_form)                = -1.2817951248362231510256079428461           
y[1] (numeric)                    = -1.2817951248362231510256079428462           
absolute error                    = 1e-31                                        
relative error                    = 7.8015587719431486469082776558281e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.93                                         
y[1] (closed_form)                = -1.2877058942572659514024184374606           
y[1] (numeric)                    = -1.2877058942572659514024184374609           
absolute error                    = 3e-31                                        
relative error                    = 2.3297245227959181835797070813174e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=679.0MB, alloc=44.3MB, time=8.09
 
TOP MAIN SOLVE Loop
x[1]                              = 1.94                                         
y[1] (closed_form)                = -1.2934878941619676934440470247064           
y[1] (numeric)                    = -1.2934878941619676934440470247067           
absolute error                    = 3e-31                                        
relative error                    = 2.3193104578250862506838537711765e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.95                                         
y[1] (closed_form)                = -1.2991405463551562241691254942222           
y[1] (numeric)                    = -1.2991405463551562241691254942224           
absolute error                    = 2e-31                                        
relative error                    = 1.5394793162380787850942932955522e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.96                                         
y[1] (closed_form)                = -1.3046632855763227525171215049375           
y[1] (numeric)                    = -1.3046632855763227525171215049376           
absolute error                    = 1e-31                                        
relative error                    = 7.6648129142245264637345423369184e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.97                                         
y[1] (closed_form)                = -1.3100555595561474291785908110325           
y[1] (numeric)                    = -1.3100555595561474291785908110327           
absolute error                    = 2e-31                                        
relative error                    = 1.5266528090439223616179078914762e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.98                                         
y[1] (closed_form)                = -1.3153168290717258183572090773092           
y[1] (numeric)                    = -1.3153168290717258183572090773092           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.99                                         
y[1] (closed_form)                = -1.3204465680004907388624289871879           
y[1] (numeric)                    = -1.320446568000490738862428987188            
absolute error                    = 1e-31                                        
relative error                    = 7.5731954948716134181795187745577e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2                                            
y[1] (closed_form)                = -1.3254442633728240823935880954125           
y[1] (numeric)                    = -1.3254442633728240823935880954126           
absolute error                    = 1e-31                                        
relative error                    = 7.5446401454507457178397389208891e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.01                                         
y[1] (closed_form)                = -1.3303094154233533478774820504392           
y[1] (numeric)                    = -1.3303094154233533478774820504391           
absolute error                    = 1e-31                                        
relative error                    = 7.5170482025173312610945319928542e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.02                                         
y[1] (closed_form)                = -1.3350415376409277622487163986439           
y[1] (numeric)                    = -1.3350415376409277622487163986438           
absolute error                    = 1e-31                                        
relative error                    = 7.4904036451707737040702035348177e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.03                                         
y[1] (closed_form)                = -1.3396401568172689901024055636637           
y[1] (numeric)                    = -1.3396401568172689901024055636636           
absolute error                    = 1e-31                                        
relative error                    = 7.4646911329965682338873642296035e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.04                                         
y[1] (closed_form)                = -1.3441048130942915671887958538756           
y[1] (numeric)                    = -1.3441048130942915671887958538755           
absolute error                    = 1e-31                                        
relative error                    = 7.4398959832446344703463510003416e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=719.5MB, alloc=44.3MB, time=8.57
 
TOP MAIN SOLVE Loop
x[1]                              = 2.05                                         
y[1] (closed_form)                = -1.3484350600100883257458965988477           
y[1] (numeric)                    = -1.3484350600100883257458965988476           
absolute error                    = 1e-31                                        
relative error                    = 7.4160041492285026573023561801929e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.06                                         
y[1] (closed_form)                = -1.3526304645435762131659072116878           
y[1] (numeric)                    = -1.3526304645435762131659072116877           
absolute error                    = 1e-31                                        
relative error                    = 7.3930021998834264465155101147823e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.07                                         
y[1] (closed_form)                = -1.3566906071577980394507782594556           
y[1] (numeric)                    = -1.3566906071577980394507782594556           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.08                                         
y[1] (closed_form)                = -1.360615081841875823318245654797            
y[1] (numeric)                    = -1.3606150818418758233182456547971           
absolute error                    = 1e-31                                        
relative error                    = 7.3496171940582326778415966403552e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.09                                         
y[1] (closed_form)                = -1.364403496151611541658688370598            
y[1] (numeric)                    = -1.364403496151611541658688370598            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.1                                          
y[1] (closed_form)                = -1.3680554712487312223016978369882           
y[1] (numeric)                    = -1.3680554712487312223016978369882           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.11                                         
y[1] (closed_form)                = -1.3715706419387684557157856653824           
y[1] (numeric)                    = -1.3715706419387684557157856653823           
absolute error                    = 1e-31                                        
relative error                    = 7.2909113786983738625086812467245e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.12                                         
y[1] (closed_form)                = -1.374948656707583537321629216638            
y[1] (numeric)                    = -1.3749486567075835373216292166378           
absolute error                    = 2e-31                                        
relative error                    = 1.4545997701391615813599539104936e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.13                                         
y[1] (closed_form)                = -1.3781891777565145885350562059256           
y[1] (numeric)                    = -1.3781891777565145885350562059254           
absolute error                    = 2e-31                                        
relative error                    = 1.4511795857051353646131602054450e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.14                                         
y[1] (closed_form)                = -1.3812918810361571414569565490775           
y[1] (numeric)                    = -1.3812918810361571414569565490773           
absolute error                    = 2e-31                                        
relative error                    = 1.4479198983633549319447089593049e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.15                                         
y[1] (closed_form)                = -1.3842564562787688092798020193078           
y[1] (numeric)                    = -1.3842564562787688092798020193077           
absolute error                    = 1e-31                                        
relative error                    = 7.2240948955965336439292421346629e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=759.6MB, alloc=44.3MB, time=9.05
 
TOP MAIN SOLVE Loop
x[1]                              = 2.16                                         
y[1] (closed_form)                = -1.3870826070292958019707368643297           
y[1] (numeric)                    = -1.3870826070292958019707368643295           
absolute error                    = 2e-31                                        
relative error                    = 1.4418751917619273485098384876625e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.17                                         
y[1] (closed_form)                = -1.3897700506750181846055264183599           
y[1] (numeric)                    = -1.3897700506750181846055264183597           
absolute error                    = 2e-31                                        
relative error                    = 1.4390869907065489805625292033331e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.18                                         
y[1] (closed_form)                = -1.3923185184738109138522346137464           
y[1] (numeric)                    = -1.3923185184738109138522346137461           
absolute error                    = 3e-31                                        
relative error                    = 2.1546793784574869775843153840881e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.19                                         
y[1] (closed_form)                = -1.394727755581017826524532809702            
y[1] (numeric)                    = -1.3947277555810178265245328097017           
absolute error                    = 3e-31                                        
relative error                    = 2.1509574094266557425955037658735e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.2                                          
y[1] (closed_form)                = -1.396997521074935892828179523071            
y[1] (numeric)                    = -1.3969975210749358928281795230708           
absolute error                    = 2e-31                                        
relative error                    = 1.4316417673104221964875488678479e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.21                                         
y[1] (closed_form)                = -1.3991275879809071858965832200746           
y[1] (numeric)                    = -1.3991275879809071858965832200742           
absolute error                    = 4e-31                                        
relative error                    = 2.8589244000058877490342465959552e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.22                                         
y[1] (closed_form)                = -1.4011177432940161584385711871093           
y[1] (numeric)                    = -1.401117743294016158438571187109            
absolute error                    = 3e-31                                        
relative error                    = 2.1411476761025272275227056719878e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.23                                         
y[1] (closed_form)                = -1.4029677880003899567896140378742           
y[1] (numeric)                    = -1.402967788000389956789614037874            
absolute error                    = 2e-31                                        
relative error                    = 1.4255494795433208458678605984107e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.24                                         
y[1] (closed_form)                = -1.4046775370970996423528509369149           
y[1] (numeric)                    = -1.4046775370970996423528509369148           
absolute error                    = 1e-31                                        
relative error                    = 7.1190716274042194575898039776831e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.25                                         
y[1] (closed_form)                = -1.4062468196106603303243557329842           
y[1] (numeric)                    = -1.4062468196106603303243557329841           
absolute error                    = 1e-31                                        
relative error                    = 7.1111271937088852671112945824871e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
memory used=799.7MB, alloc=44.3MB, time=9.53
x[1]                              = 2.26                                         
y[1] (closed_form)                = -1.4076754786141283957041882064852           
y[1] (numeric)                    = -1.4076754786141283957041882064852           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.27                                         
y[1] (closed_form)                = -1.408963371242794036886876950059            
y[1] (numeric)                    = -1.408963371242794036886876950059            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.28                                         
y[1] (closed_form)                = -1.4101103687084676275880519267616           
y[1] (numeric)                    = -1.4101103687084676275880519267618           
absolute error                    = 2e-31                                        
relative error                    = 1.4183286956692740478021457369154e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.29                                         
y[1] (closed_form)                = -1.4111163563123584284839392961626           
y[1] (numeric)                    = -1.4111163563123584284839392961628           
absolute error                    = 2e-31                                        
relative error                    = 1.4173175663745824460591498540340e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.3                                          
y[1] (closed_form)                = -1.4119812334565443707032867828095           
y[1] (numeric)                    = -1.4119812334565443707032867828097           
absolute error                    = 2e-31                                        
relative error                    = 1.4164494205804561076967660206759e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.31                                         
y[1] (closed_form)                = -1.4127049136540317642029285155693           
y[1] (numeric)                    = -1.4127049136540317642029285155693           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.32                                         
y[1] (closed_form)                = -1.4132873245374039250645348437329           
y[1] (numeric)                    = -1.4132873245374039250645348437329           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.33                                         
y[1] (closed_form)                = -1.4137284078660578568570246202914           
y[1] (numeric)                    = -1.4137284078660578568570246202915           
absolute error                    = 1e-31                                        
relative error                    = 7.0734944168621665001615992615549e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.34                                         
y[1] (closed_form)                = -1.4140281195320282624025342588554           
y[1] (numeric)                    = -1.4140281195320282624025342588553           
absolute error                    = 1e-31                                        
relative error                    = 7.0719951476703970056381636968309e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.35                                         
y[1] (closed_form)                = -1.4141864295643983035496202942721           
y[1] (numeric)                    = -1.4141864295643983035496202942721           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.36                                         
y[1] (closed_form)                = -1.4142033221322966678813937475778           
y[1] (numeric)                    = -1.4142033221322966678813937475777           
absolute error                    = 1e-31                                        
relative error                    = 7.0711190134402148691382378765367e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=839.8MB, alloc=44.3MB, time=10.00
 
TOP MAIN SOLVE Loop
x[1]                              = 2.37                                         
y[1] (closed_form)                = -1.4140787955464806426544130291116           
y[1] (numeric)                    = -1.4140787955464806426544130291115           
absolute error                    = 1e-31                                        
relative error                    = 7.0717417102173786896467739058675e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.38                                         
y[1] (closed_form)                = -1.4138128622595050376622607143877           
y[1] (numeric)                    = -1.4138128622595050376622607143877           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.39                                         
y[1] (closed_form)                = -1.4134055488644769401316586036311           
y[1] (numeric)                    = -1.4134055488644769401316586036311           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.4                                          
y[1] (closed_form)                = -1.4128568960923964261745937526761           
y[1] (numeric)                    = -1.4128568960923964261745937526762           
absolute error                    = 1e-31                                        
relative error                    = 7.0778576568210565944940895980971e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.41                                         
y[1] (closed_form)                = -1.4121669588080834947230941962227           
y[1] (numeric)                    = -1.4121669588080834947230941962227           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.42                                         
y[1] (closed_form)                = -1.411335806004691631249866675471            
y[1] (numeric)                    = -1.4113358060046916312498666754709           
absolute error                    = 1e-31                                        
relative error                    = 7.0854859328685929426330043640100e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.43                                         
y[1] (closed_form)                = -1.4103635207968085499138522913678           
y[1] (numeric)                    = -1.4103635207968085499138522913678           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.44                                         
y[1] (closed_form)                = -1.4092502004121448040507361655199           
y[1] (numeric)                    = -1.4092502004121448040507361655199           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.45                                         
y[1] (closed_form)                = -1.4079959561818110961404359229703           
y[1] (numeric)                    = -1.4079959561818110961404359229703           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.46                                         
y[1] (closed_form)                = -1.4066009135291852595124700333021           
y[1] (numeric)                    = -1.406600913529185259512470033302            
absolute error                    = 1e-31                                        
relative error                    = 7.1093370577371746837048534336768e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.47                                         
y[1] (closed_form)                = -1.4050652119573700250817579889173           
y[1] (numeric)                    = -1.4050652119573700250817579889172           
absolute error                    = 1e-31                                        
relative error                    = 7.1171073875419542516019167046910e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=879.9MB, alloc=44.3MB, time=10.48
 
TOP MAIN SOLVE Loop
x[1]                              = 2.48                                         
y[1] (closed_form)                = -1.4033890050352428273277269142559           
y[1] (numeric)                    = -1.4033890050352428273277269142559           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.49                                         
y[1] (closed_form)                = -1.4015724603820990445245015723634           
y[1] (numeric)                    = -1.4015724603820990445245015723634           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.5                                          
y[1] (closed_form)                = -1.3996157596508902088853574926535           
y[1] (numeric)                    = -1.3996157596508902088853574926536           
absolute error                    = 1e-31                                        
relative error                    = 7.1448180909982936683283225850453e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.51                                         
y[1] (closed_form)                = -1.3975190985100588627864546629025           
y[1] (numeric)                    = -1.3975190985100588627864546629026           
absolute error                    = 1e-31                                        
relative error                    = 7.1555372736310575954545234419303e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.52                                         
y[1] (closed_form)                = -1.395282686623971877569091842749            
y[1] (numeric)                    = -1.3952826866239718775690918427491           
absolute error                    = 1e-31                                        
relative error                    = 7.1670064395309134763936460234578e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.53                                         
y[1] (closed_form)                = -1.3929067476319541915722957599572           
y[1] (numeric)                    = -1.3929067476319541915722957599573           
absolute error                    = 1e-31                                        
relative error                    = 7.1792315006017086662348455399264e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.54                                         
y[1] (closed_form)                = -1.3903915191259250640044701037886           
y[1] (numeric)                    = -1.3903915191259250640044701037887           
absolute error                    = 1e-31                                        
relative error                    = 7.1922187833010792331930640191566e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.55                                         
y[1] (closed_form)                = -1.3877372526266390810100807575985           
y[1] (numeric)                    = -1.3877372526266390810100807575986           
absolute error                    = 1e-31                                        
relative error                    = 7.2059750367531781334550537402566e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.56                                         
y[1] (closed_form)                = -1.3849442135585342898109715065197           
y[1] (numeric)                    = -1.3849442135585342898109715065198           
absolute error                    = 1e-31                                        
relative error                    = 7.2205074414554046763700731288897e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.57                                         
y[1] (closed_form)                = -1.382012681223189976087936270313            
y[1] (numeric)                    = -1.3820126812231899760879362703131           
absolute error                    = 1e-31                                        
relative error                    = 7.2358236186003829436555336756366e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.58                                         
y[1] (closed_form)                = -1.3789429487713967388026912590409           
y[1] (numeric)                    = -1.3789429487713967388026912590411           
absolute error                    = 2e-31                                        
relative error                    = 1.4503863280072242093740463994384e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=919.9MB, alloc=44.3MB, time=10.95
 
TOP MAIN SOLVE Loop
x[1]                              = 2.59                                         
y[1] (closed_form)                = -1.3757353231738416554294899942842           
y[1] (numeric)                    = -1.3757353231738416554294899942845           
absolute error                    = 3e-31                                        
relative error                    = 2.1806520116667178461159641542377e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.6                                          
y[1] (closed_form)                = -1.3723901251904114690554290868546           
y[1] (numeric)                    = -1.3723901251904114690554290868548           
absolute error                    = 2e-31                                        
relative error                    = 1.4573115641753187084422604264348e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.61                                         
y[1] (closed_form)                = -1.3689076893381168670051541482782           
y[1] (numeric)                    = -1.3689076893381168670051541482785           
absolute error                    = 3e-31                                        
relative error                    = 2.1915283429012920846741024975300e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.62                                         
y[1] (closed_form)                = -1.365288363857641058535373686746            
y[1] (numeric)                    = -1.3652883638576410585353736867464           
absolute error                    = 4e-31                                        
relative error                    = 2.9297839972047699577128108802811e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.63                                         
y[1] (closed_form)                = -1.3615325106785159967135354438066           
y[1] (numeric)                    = -1.361532510678515996713535443807            
absolute error                    = 4e-31                                        
relative error                    = 2.9378659478403574499960668092188e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.64                                         
y[1] (closed_form)                = -1.3576405053829297268294575857988           
y[1] (numeric)                    = -1.3576405053829297268294575857992           
absolute error                    = 4e-31                                        
relative error                    = 2.9462880520582130989561583147072e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.65                                         
y[1] (closed_form)                = -1.3536127371681684805749131444512           
y[1] (numeric)                    = -1.3536127371681684805749131444516           
absolute error                    = 4e-31                                        
relative error                    = 2.9550549357035585440471035579102e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.66                                         
y[1] (closed_form)                = -1.3494496088076972717504515976789           
y[1] (numeric)                    = -1.3494496088076972717504515976794           
absolute error                    = 5e-31                                        
relative error                    = 3.7052143091269166616167967509170e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.67                                         
y[1] (closed_form)                = -1.345151536610882885407454179621            
y[1] (numeric)                    = -1.3451515366108828854074541796215           
absolute error                    = 5e-31                                        
relative error                    = 3.7170533311046345457107010255927e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.68                                         
y[1] (closed_form)                = -1.3407189503813632880929446505501           
y[1] (numeric)                    = -1.3407189503813632880929446505506           
absolute error                    = 5e-31                                        
relative error                    = 3.7293423790107283319267651373637e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.69                                         
y[1] (closed_form)                = -1.3361522933740676222214390030899           
y[1] (numeric)                    = -1.3361522933740676222214390030903           
absolute error                    = 4e-31                                        
relative error                    = 2.9936707213959514654917232962087e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=960.1MB, alloc=44.3MB, time=11.42
 
TOP MAIN SOLVE Loop
x[1]                              = 2.7                                          
y[1] (closed_form)                = -1.3314520222508910825385803678012           
y[1] (numeric)                    = -1.3314520222508910825385803678017           
absolute error                    = 5e-31                                        
relative error                    = 3.7552986637454887225348402574742e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.71                                         
y[1] (closed_form)                = -1.3266186070350291071519752748247           
y[1] (numeric)                    = -1.3266186070350291071519752748253           
absolute error                    = 6e-31                                        
relative error                    = 4.5227769067779788521449517782665e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.72                                         
y[1] (closed_form)                = -1.3216525310639754496720734739945           
y[1] (numeric)                    = -1.3216525310639754496720734739953           
absolute error                    = 8e-31                                        
relative error                    = 6.0530281688786436417895841617850e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.73                                         
y[1] (closed_form)                = -1.3165542909411888326167090827872           
y[1] (numeric)                    = -1.3165542909411888326167090827881           
absolute error                    = 9e-31                                        
relative error                    = 6.8360264836218855920806811144328e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.74                                         
y[1] (closed_form)                = -1.3113243964864330153736849534196           
y[1] (numeric)                    = -1.3113243964864330153736849534203           
absolute error                    = 7e-31                                        
relative error                    = 5.3381146715151670097689310134942e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.75                                         
y[1] (closed_form)                = -1.3059633706847952426732208619045           
y[1] (numeric)                    = -1.3059633706847952426732208619052           
absolute error                    = 7e-31                                        
relative error                    = 5.3600278209407040624911978537577e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.76                                         
y[1] (closed_form)                = -1.3004717496343881716829337895898           
y[1] (numeric)                    = -1.3004717496343881716829337895906           
absolute error                    = 8e-31                                        
relative error                    = 6.1516138295576991805666979799645e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.77                                         
y[1] (closed_form)                = -1.2948500824927405074890592170015           
y[1] (numeric)                    = -1.2948500824927405074890592170022           
absolute error                    = 7e-31                                        
relative error                    = 5.4060312422610090410347606344463e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.78                                         
y[1] (closed_form)                = -1.2890989314218817078556909863449           
y[1] (numeric)                    = -1.2890989314218817078556909863457           
absolute error                    = 8e-31                                        
relative error                    = 6.2058852156335009376190038099896e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.79                                         
y[1] (closed_form)                = -1.2832188715321262487458012151864           
y[1] (numeric)                    = -1.2832188715321262487458012151871           
absolute error                    = 7e-31                                        
relative error                    = 5.4550319943800407904398892819952e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1000.2MB, alloc=44.3MB, time=11.90
 
TOP MAIN SOLVE Loop
x[1]                              = 2.8                                          
y[1] (closed_form)                = -1.2772104908245630721306418700786           
y[1] (numeric)                    = -1.2772104908245630721306418700793           
absolute error                    = 7e-31                                        
relative error                    = 5.4806940988096817435920128966089e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.81                                         
y[1] (closed_form)                = -1.2710743901322559670948217595652           
y[1] (numeric)                    = -1.2710743901322559670948217595658           
absolute error                    = 6e-31                                        
relative error                    = 4.7204160878229139721830328345486e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.82                                         
y[1] (closed_form)                = -1.2648111830601607641499489197846           
y[1] (numeric)                    = -1.2648111830601607641499489197853           
absolute error                    = 7e-31                                        
relative error                    = 5.5344229192089969748879076189750e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.83                                         
y[1] (closed_form)                = -1.2584214959237653509873381905926           
y[1] (numeric)                    = -1.2584214959237653509873381905933           
absolute error                    = 7e-31                                        
relative error                    = 5.5625241802322622423675214075626e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.84                                         
y[1] (closed_form)                = -1.2519059676864586456170755616836           
y[1] (numeric)                    = -1.2519059676864586456170755616842           
absolute error                    = 6e-31                                        
relative error                    = 4.7926922267876809194406871978163e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.85                                         
y[1] (closed_form)                = -1.2452652498956347899439330338666           
y[1] (numeric)                    = -1.2452652498956347899439330338674           
absolute error                    = 8e-31                                        
relative error                    = 6.4243340932146600711042892230658e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.86                                         
y[1] (closed_form)                = -1.238500006617538953307530076146            
y[1] (numeric)                    = -1.2385000066175389533075300761468           
absolute error                    = 8e-31                                        
relative error                    = 6.4594266913641439272211553264924e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.87                                         
y[1] (closed_form)                = -1.2316109143708612613520926797251           
y[1] (numeric)                    = -1.231610914370861261352092679726            
absolute error                    = 9e-31                                        
relative error                    = 7.3075026333275334681472399876092e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.88                                         
y[1] (closed_form)                = -1.2245986620590854907775848248832           
y[1] (numeric)                    = -1.2245986620590854907775848248841           
absolute error                    = 9e-31                                        
relative error                    = 7.3493465890833712587295314045082e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.89                                         
y[1] (closed_form)                = -1.2174639509015992950463613477898           
y[1] (numeric)                    = -1.2174639509015992950463613477907           
absolute error                    = 9e-31                                        
relative error                    = 7.3924160081577798984154800027240e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.9                                          
y[1] (closed_form)                = -1.2102074943635728499653635880851           
y[1] (numeric)                    = -1.210207494363572849965363588086            
absolute error                    = 9e-31                                        
relative error                    = 7.4367412546333172744325868196783e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1040.4MB, alloc=44.3MB, time=12.37
 
TOP MAIN SOLVE Loop
x[1]                              = 2.91                                         
y[1] (closed_form)                = -1.2028300180846129312208653304297           
y[1] (numeric)                    = -1.2028300180846129312208653304305           
absolute error                    = 8e-31                                        
relative error                    = 6.6509813354502106994409016135951e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.92                                         
y[1] (closed_form)                = -1.1953322598061995583985608282228           
y[1] (numeric)                    = -1.1953322598061995583985608282236           
absolute error                    = 8e-31                                        
relative error                    = 6.6926998199622322421169767881427e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.93                                         
y[1] (closed_form)                = -1.1877149692979124617641236389354           
y[1] (numeric)                    = -1.1877149692979124617641236389364           
absolute error                    = 1.0e-30                                      
relative error                    = 8.4195284714743016311769341429060e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.94                                         
y[1] (closed_form)                = -1.1799789082824547490960804757514           
y[1] (numeric)                    = -1.1799789082824547490960804757524           
absolute error                    = 1.0e-30                                      
relative error                    = 8.4747277513254269959728688865036e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.95                                         
y[1] (closed_form)                = -1.1721248503594812701418367187594           
y[1] (numeric)                    = -1.1721248503594812701418367187604           
absolute error                    = 1.0e-30                                      
relative error                    = 8.5315143663519124087766650938184e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.96                                         
y[1] (closed_form)                = -1.1641535809282392957969318317775           
y[1] (numeric)                    = -1.1641535809282392957969318317785           
absolute error                    = 1.0e-30                                      
relative error                    = 8.5899319160505331670256631706306e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.97                                         
y[1] (closed_form)                = -1.1560658971090292478751408734741           
y[1] (numeric)                    = -1.1560658971090292478751408734752           
absolute error                    = 1.1e-30                                      
relative error                    = 9.5150285355771407166208633983239e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.98                                         
y[1] (closed_form)                = -1.1478626076634933333309959189367           
y[1] (numeric)                    = -1.1478626076634933333309959189377           
absolute error                    = 1.0e-30                                      
relative error                    = 8.7118440249180009820177334673668e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.99                                         
y[1] (closed_form)                = -1.1395445329137400540048792228214           
y[1] (numeric)                    = -1.1395445329137400540048792228222           
absolute error                    = 8e-31                                        
relative error                    = 7.0203487173463320026521596380393e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3                                            
y[1] (closed_form)                = -1.1311125046603126793723175975394           
y[1] (numeric)                    = -1.1311125046603126793723175975403           
absolute error                    = 9e-31                                        
relative error                    = 7.9567681931894239542512007244466e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.01                                         
y[1] (closed_form)                = -1.1225673660990098853818436988673           
y[1] (numeric)                    = -1.1225673660990098853818436988682           
absolute error                    = 9e-31                                        
relative error                    = 8.0173362167791758700644335412049e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1080.5MB, alloc=44.3MB, time=12.84
 
TOP MAIN SOLVE Loop
x[1]                              = 3.02                                         
y[1] (closed_form)                = -1.1139099717365668772482245296022           
y[1] (numeric)                    = -1.1139099717365668772482245296031           
absolute error                    = 9e-31                                        
relative error                    = 8.0796475732856144957506800014169e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.03                                         
y[1] (closed_form)                = -1.1051411873052054280185123416257           
y[1] (numeric)                    = -1.1051411873052054280185123416268           
absolute error                    = 1.1e-30                                      
relative error                    = 9.9534793620556140498185840790744e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.04                                         
y[1] (closed_form)                = -1.096261889676061377835853267452            
y[1] (numeric)                    = -1.0962618896760613778358532674532           
absolute error                    = 1.2e-30                                      
relative error                    = 1.0946289488861029306447498449621e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.05                                         
y[1] (closed_form)                = -1.0872729667714982510789837902613           
y[1] (numeric)                    = -1.0872729667714982510789837902628           
absolute error                    = 1.5e-30                                      
relative error                    = 1.3795983583166200780598553005568e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.06                                         
y[1] (closed_form)                = -1.0781753174763157599426293606289           
y[1] (numeric)                    = -1.0781753174763157599426293606303           
absolute error                    = 1.4e-30                                      
relative error                    = 1.2984901224385094048231708388441e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.07                                         
y[1] (closed_form)                = -1.0689698515478620735344544530457           
y[1] (numeric)                    = -1.0689698515478620735344544530472           
absolute error                    = 1.5e-30                                      
relative error                    = 1.4032201168517604124237691589446e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.08                                         
y[1] (closed_form)                = -1.0596574895250588411867481744955           
y[1] (numeric)                    = -1.059657489525058841186748174497            
absolute error                    = 1.5e-30                                      
relative error                    = 1.4155517370733667747356142230662e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.09                                         
y[1] (closed_form)                = -1.0502391626363480674047020286604           
y[1] (numeric)                    = -1.050239162636348067404702028662            
absolute error                    = 1.6e-30                                      
relative error                    = 1.5234625187501316680379645613732e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.1                                          
y[1] (closed_form)                = -1.0407158127065700436870743261381           
y[1] (numeric)                    = -1.0407158127065700436870743261397           
absolute error                    = 1.6e-30                                      
relative error                    = 1.5374033722413711459115978119386e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.11                                         
y[1] (closed_form)                = -1.0310883920627816493484577094202           
y[1] (numeric)                    = -1.0310883920627816493484577094218           
absolute error                    = 1.6e-30                                      
relative error                    = 1.5517583286909683808510714383583e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.12                                         
y[1] (closed_form)                = -1.0213578634390244394345830781775           
y[1] (numeric)                    = -1.0213578634390244394345830781789           
absolute error                    = 1.4e-30                                      
relative error                    = 1.3707242584749343147747004707924e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1120.5MB, alloc=44.3MB, time=13.31
 
TOP MAIN SOLVE Loop
x[1]                              = 3.13                                         
y[1] (closed_form)                = -1.0115251998800520428425087222575           
y[1] (numeric)                    = -1.0115251998800520428425087222589           
absolute error                    = 1.4e-30                                      
relative error                    = 1.3840485636601182034988265222030e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.14                                         
y[1] (closed_form)                = -1.0015913846440264978256557426695           
y[1] (numeric)                    = -1.0015913846440264978256557426709           
absolute error                    = 1.4e-30                                      
relative error                    = 1.3977756013721814071656632410272e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.15                                         
y[1] (closed_form)                = -0.99155741110419325516905314022366          
y[1] (numeric)                    = -0.99155741110419325516905314022504          
absolute error                    = 1.38e-30                                     
relative error                    = 1.3917499728666634310956513568990e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.16                                         
y[1] (closed_form)                = -0.98142428264954468145253782308658          
y[1] (numeric)                    = -0.98142428264954468145253782308796          
absolute error                    = 1.38e-30                                     
relative error                    = 1.4061196817694617007865219542568e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.17                                         
y[1] (closed_form)                = -0.97119301258448199596880307523855          
y[1] (numeric)                    = -0.97119301258448199596880307523991          
absolute error                    = 1.36e-30                                     
relative error                    = 1.4003395642034610690550121176895e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.18                                         
y[1] (closed_form)                = -0.96086462402748567501898890713419          
y[1] (numeric)                    = -0.96086462402748567501898890713555          
absolute error                    = 1.36e-30                                     
relative error                    = 1.4153918939168864628523250081044e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.19                                         
y[1] (closed_form)                = -0.95044014980880445646094368124831          
y[1] (numeric)                    = -0.95044014980880445646094368124968          
absolute error                    = 1.37e-30                                     
relative error                    = 1.4414374227305069251509374525345e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.2                                          
y[1] (closed_form)                = -0.93992063236717317552444330766448          
y[1] (numeric)                    = -0.93992063236717317552444330766584          
absolute error                    = 1.36e-30                                     
relative error                    = 1.4469306802797428829692333060196e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.21                                         
y[1] (closed_form)                = -0.92930712364556976002371830452738          
y[1] (numeric)                    = -0.92930712364556976002371830452873          
absolute error                    = 1.35e-30                                     
relative error                    = 1.4526952023181510757147874559152e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.22                                         
y[1] (closed_form)                = -0.91860068498602180918089858955982          
y[1] (numeric)                    = -0.91860068498602180918089858956116          
absolute error                    = 1.34e-30                                     
relative error                    = 1.4587404754878781227143503425914e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1160.6MB, alloc=44.3MB, time=13.78
 
TOP MAIN SOLVE Loop
x[1]                              = 3.23                                         
y[1] (closed_form)                = -0.90780238702347327531483276605523          
y[1] (numeric)                    = -0.90780238702347327531483276605657          
absolute error                    = 1.34e-30                                     
relative error                    = 1.4760921750752691973086736089416e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.24                                         
y[1] (closed_form)                = -0.89691330957872186163866888430483          
y[1] (numeric)                    = -0.89691330957872186163866888430618          
absolute error                    = 1.35e-30                                     
relative error                    = 1.5051621885665760994573645039470e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.25                                         
y[1] (closed_form)                = -0.88593454155043784233719838261077          
y[1] (numeric)                    = -0.88593454155043784233719838261212          
absolute error                    = 1.35e-30                                     
relative error                    = 1.5238146123498245821936726871740e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.26                                         
y[1] (closed_form)                = -0.87486718080627510295197145683558          
y[1] (numeric)                    = -0.87486718080627510295197145683692          
absolute error                    = 1.34e-30                                     
relative error                    = 1.5316610674148958418837112635092e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.27                                         
y[1] (closed_form)                = -0.86371233407308528987940484974112          
y[1] (numeric)                    = -0.86371233407308528987940484974246          
absolute error                    = 1.34e-30                                     
relative error                    = 1.5514424735384320412983969340083e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.28                                         
y[1] (closed_form)                = -0.85247111682624604747544434554646          
y[1] (numeric)                    = -0.85247111682624604747544434554779          
absolute error                    = 1.33e-30                                     
relative error                    = 1.5601701614848796480325468988372e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.29                                         
y[1] (closed_form)                = -0.84114465317811440985084534179684          
y[1] (numeric)                    = -0.84114465317811440985084534179816          
absolute error                    = 1.32e-30                                     
relative error                    = 1.5692901274621629379391881880848e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.3                                          
y[1] (closed_form)                = -0.82973407576561650192493677350037          
y[1] (numeric)                    = -0.82973407576561650192493677350169          
absolute error                    = 1.32e-30                                     
relative error                    = 1.5908711460138632949063236456965e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.31                                         
y[1] (closed_form)                = -0.81824052563698479067408807626855          
y[1] (numeric)                    = -0.81824052563698479067408807626988          
absolute error                    = 1.33e-30                                     
relative error                    = 1.6254389245321479608986304915027e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.32                                         
y[1] (closed_form)                = -0.80666515213765421275536903242278          
y[1] (numeric)                    = -0.80666515213765421275536903242412          
absolute error                    = 1.34e-30                                     
relative error                    = 1.6611601436469816761908155427292e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.33                                         
y[1] (closed_form)                = -0.79500911279532858879755389072332          
y[1] (numeric)                    = -0.79500911279532858879755389072465          
absolute error                    = 1.33e-30                                     
relative error                    = 1.6729367985778074161741365889129e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1200.6MB, alloc=44.3MB, time=14.25
 
TOP MAIN SOLVE Loop
x[1]                              = 3.34                                         
y[1] (closed_form)                = -0.78327357320422881762226299047719          
y[1] (numeric)                    = -0.78327357320422881762226299047852          
absolute error                    = 1.33e-30                                     
relative error                    = 1.6980018801849951902940544673984e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.35                                         
y[1] (closed_form)                = -0.77145970690853442547936025924602          
y[1] (numeric)                    = -0.77145970690853442547936025924734          
absolute error                    = 1.32e-30                                     
relative error                    = 1.7110420520724635127596913563741e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.36                                         
y[1] (closed_form)                = -0.75956869528503012604455132587279          
y[1] (numeric)                    = -0.75956869528503012604455132587411          
absolute error                    = 1.32e-30                                     
relative error                    = 1.7378283336238160407906372719723e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.37                                         
y[1] (closed_form)                = -0.74760172742496912642538828166228          
y[1] (numeric)                    = -0.7476017274249691264253882816636           
absolute error                    = 1.32e-30                                     
relative error                    = 1.7656460005069717576883975510786e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.38                                         
y[1] (closed_form)                = -0.73556000001516499274663357240094          
y[1] (numeric)                    = -0.73556000001516499274663357240226          
absolute error                    = 1.32e-30                                     
relative error                    = 1.7945510902887400697867038552305e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.39                                         
y[1] (closed_form)                = -0.72344471721832396602933470311454          
y[1] (numeric)                    = -0.72344471721832396602933470311585          
absolute error                    = 1.31e-30                                     
relative error                    = 1.8107810712019659339420398105910e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.4                                          
y[1] (closed_form)                = -0.71125709055262969503229911040195          
y[1] (numeric)                    = -0.71125709055262969503229911040327          
absolute error                    = 1.32e-30                                     
relative error                    = 1.8558690205455690700475274177331e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.41                                         
y[1] (closed_form)                = -0.69899833877059242748233933337885          
y[1] (numeric)                    = -0.69899833877059242748233933338015          
absolute error                    = 1.30e-30                                     
relative error                    = 1.8598041338502424563056001499684e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.42                                         
y[1] (closed_form)                = -0.68666968773717477467320678793521          
y[1] (numeric)                    = -0.68666968773717477467320678793651          
absolute error                    = 1.30e-30                                     
relative error                    = 1.8931955541593377398502714794914e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.43                                         
y[1] (closed_form)                = -0.67427237030720623675519272663419          
y[1] (numeric)                    = -0.67427237030720623675519272663549          
absolute error                    = 1.30e-30                                     
relative error                    = 1.9280042565109186780251538240919e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.44                                         
y[1] (closed_form)                = -0.66180762620209874716071320241217          
y[1] (numeric)                    = -0.66180762620209874716071320241347          
absolute error                    = 1.30e-30                                     
relative error                    = 1.9643170440030770911372704143518e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1240.6MB, alloc=44.3MB, time=14.72
 
TOP MAIN SOLVE Loop
x[1]                              = 3.45                                         
y[1] (closed_form)                = -0.64927670188587556450869877372786          
y[1] (numeric)                    = -0.64927670188587556450869877372917          
absolute error                    = 1.31e-30                                     
relative error                    = 2.0176297658532969477448673110952e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.46                                         
y[1] (closed_form)                = -0.6366808504405259089952895998071           
y[1] (numeric)                    = -0.63668085044052590899528959980842          
absolute error                    = 1.32e-30                                     
relative error                    = 2.0732522410351727587557553635125e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.47                                         
y[1] (closed_form)                = -0.62402133144069780770332606636942          
y[1] (numeric)                    = -0.62402133144069780770332606637073          
absolute error                    = 1.31e-30                                     
relative error                    = 2.0992872102233452797063764784726e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.48                                         
y[1] (closed_form)                = -0.61129941082774167944168171193953          
y[1] (numeric)                    = -0.61129941082774167944168171194085          
absolute error                    = 1.32e-30                                     
relative error                    = 2.1593346511043233452790173062162e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.49                                         
y[1] (closed_form)                = -0.59851636078311725465099119202927          
y[1] (numeric)                    = -0.59851636078311725465099119203058          
absolute error                    = 1.31e-30                                     
relative error                    = 2.1887455144684025372002083348041e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.5                                          
y[1] (closed_form)                = -0.58567345960117648957828882662812          
y[1] (numeric)                    = -0.58567345960117648957828882662943          
absolute error                    = 1.31e-30                                     
relative error                    = 2.2367412736989396901845963748786e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.51                                         
y[1] (closed_form)                = -0.57277199156133519632312638234021          
y[1] (numeric)                    = -0.57277199156133519632312638234151          
absolute error                    = 1.30e-30                                     
relative error                    = 2.2696640533282600458677777072627e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.52                                         
y[1] (closed_form)                = -0.55981324679964617148564219083928          
y[1] (numeric)                    = -0.55981324679964617148564219084057          
absolute error                    = 1.29e-30                                     
relative error                    = 2.3043398979475798663124207759617e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.53                                         
y[1] (closed_form)                = -0.54679852117978666599669476067737          
y[1] (numeric)                    = -0.54679852117978666599669476067867          
absolute error                    = 1.30e-30                                     
relative error                    = 2.3774753399023214167574586248795e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.54                                         
y[1] (closed_form)                = -0.53372911616347309727556778564526          
y[1] (numeric)                    = -0.53372911616347309727556778564655          
absolute error                    = 1.29e-30                                     
relative error                    = 2.4169563940463249006735086671011e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.55                                         
y[1] (closed_form)                = -0.52060633868031596213604339927352          
y[1] (numeric)                    = -0.52060633868031596213604339927482          
absolute error                    = 1.30e-30                                     
relative error                    = 2.4970883053313710656742449864939e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1280.8MB, alloc=44.3MB, time=15.20
 
TOP MAIN SOLVE Loop
x[1]                              = 3.56                                         
y[1] (closed_form)                = -0.50743150099712796484109919041775          
y[1] (numeric)                    = -0.50743150099712796484109919041905          
absolute error                    = 1.30e-30                                     
relative error                    = 2.5619221460343628340838408145137e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.57                                         
y[1] (closed_form)                = -0.49420592058669842938451397997045          
y[1] (numeric)                    = -0.49420592058669842938451397997176          
absolute error                    = 1.31e-30                                     
relative error                    = 2.6507169287750105080585815815505e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.58                                         
y[1] (closed_form)                = -0.48093091999604711844879990620526          
y[1] (numeric)                    = -0.48093091999604711844879990620657          
absolute error                    = 1.31e-30                                     
relative error                    = 2.7238839208150043471902372337344e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.59                                         
y[1] (closed_form)                = -0.4676078267141706335477769073038           
y[1] (numeric)                    = -0.46760782671417063354777690730512          
absolute error                    = 1.32e-30                                     
relative error                    = 2.8228783279259812818376842363575e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.6                                          
y[1] (closed_form)                = -0.45423797303929462160356437777325          
y[1] (numeric)                    = -0.45423797303929462160356437777456          
absolute error                    = 1.31e-30                                     
relative error                    = 2.8839508754295102528267251816535e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.61                                         
y[1] (closed_form)                = -0.44082269594564506262670950714588          
y[1] (numeric)                    = -0.4408226959456450626267095071472           
absolute error                    = 1.32e-30                                     
relative error                    = 2.9944011779347234165482921798861e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.62                                         
y[1] (closed_form)                = -0.42736333694975196125966073127315          
y[1] (numeric)                    = -0.42736333694975196125966073127446          
absolute error                    = 1.31e-30                                     
relative error                    = 3.0653074017765489440558087440805e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.63                                         
y[1] (closed_form)                = -0.4138612419762988117030187298661           
y[1] (numeric)                    = -0.41386124197629881170301872986741          
absolute error                    = 1.31e-30                                     
relative error                    = 3.1653121073729867612864356004823e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.64                                         
y[1] (closed_form)                = -0.40031776122353125096628060526118          
y[1] (numeric)                    = -0.40031776122353125096628060526249          
absolute error                    = 1.31e-30                                     
relative error                    = 3.2724003951164091518214654790995e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.65                                         
y[1] (closed_form)                = -0.38673424902823835946559308623295          
y[1] (numeric)                    = -0.38673424902823835946559308623425          
absolute error                    = 1.30e-30                                     
relative error                    = 3.3614814391705899282372110306332e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1320.8MB, alloc=44.3MB, time=15.67
 
TOP MAIN SOLVE Loop
x[1]                              = 3.66                                         
y[1] (closed_form)                = -0.37311206373032011072593977374958          
y[1] (numeric)                    = -0.37311206373032011072593977375087          
absolute error                    = 1.29e-30                                     
relative error                    = 3.4574063006775169519636624491576e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.67                                         
y[1] (closed_form)                = -0.3594525675369545133299321275659           
y[1] (numeric)                    = -0.35945256753695451332993212756719          
absolute error                    = 1.29e-30                                     
relative error                    = 3.5887906124564765821950676483978e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.68                                         
y[1] (closed_form)                = -0.34575712638637802828581564349212          
y[1] (numeric)                    = -0.3457571263863780282858156434934           
absolute error                    = 1.28e-30                                     
relative error                    = 3.7020205870453139551603452738580e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.69                                         
y[1] (closed_form)                = -0.3320271098112928836594384802475           
y[1] (numeric)                    = -0.33202710981129288365943848024879          
absolute error                    = 1.29e-30                                     
relative error                    = 3.8852249165231405060013945677559e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.7                                          
y[1] (closed_form)                = -0.31826389080191494562489248065319          
y[1] (numeric)                    = -0.31826389080191494562489248065447          
absolute error                    = 1.28e-30                                     
relative error                    = 4.0218197445360283827589483432076e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.71                                         
y[1] (closed_form)                = -0.30446884566867584103259512935938          
y[1] (numeric)                    = -0.30446884566867584103259512936064          
absolute error                    = 1.26e-30                                     
relative error                    = 4.1383544422510039174511724640461e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.72                                         
y[1] (closed_form)                = -0.29064335390459306116814112243345          
y[1] (numeric)                    = -0.2906433539045930611681411224347           
absolute error                    = 1.25e-30                                     
relative error                    = 4.3008036592170847011446173760205e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.73                                         
y[1] (closed_form)                = -0.2767887980473218095768564657559           
y[1] (numeric)                    = -0.27678879804732180957685646575715          
absolute error                    = 1.25e-30                                     
relative error                    = 4.5160787171245672410273518077004e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.74                                         
y[1] (closed_form)                = -0.26290656354090238865431623652305          
y[1] (numeric)                    = -0.2629065635409023886543162365243           
absolute error                    = 1.25e-30                                     
relative error                    = 4.7545408648785138514501566199288e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.75                                         
y[1] (closed_form)                = -0.24899803859721695014895682894042          
y[1] (numeric)                    = -0.24899803859721695014895682894168          
absolute error                    = 1.26e-30                                     
relative error                    = 5.0602808242927380785973971104806e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.76                                         
y[1] (closed_form)                = -0.23506461405716946378628009980914          
y[1] (numeric)                    = -0.23506461405716946378628009981039          
absolute error                    = 1.25e-30                                     
relative error                    = 5.3176868199140798619827271178959e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1361.0MB, alloc=44.3MB, time=16.15
 
TOP MAIN SOLVE Loop
x[1]                              = 3.77                                         
y[1] (closed_form)                = -0.22110768325160278590210401972181          
y[1] (numeric)                    = -0.22110768325160278590210401972306          
absolute error                    = 1.25e-30                                     
relative error                    = 5.6533539749389911078513553347290e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.78                                         
y[1] (closed_form)                = -0.2071286418619667362620944483375           
y[1] (numeric)                    = -0.20712864186196673626209444833876          
absolute error                    = 1.26e-30                                     
relative error                    = 6.0831760816530658683261029546619e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.79                                         
y[1] (closed_form)                = -0.19312888778075111614378653160748          
y[1] (numeric)                    = -0.19312888778075111614378653160873          
absolute error                    = 1.25e-30                                     
relative error                    = 6.4723616148976017507028701485742e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.8                                          
y[1] (closed_form)                = -0.17910982097169762426298208823185          
y[1] (numeric)                    = -0.17910982097169762426298208823309          
absolute error                    = 1.24e-30                                     
relative error                    = 6.9231267904395981485461725275544e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.81                                         
y[1] (closed_form)                = -0.16507284332980464923644066384715          
y[1] (numeric)                    = -0.16507284332980464923644066384839          
absolute error                    = 1.24e-30                                     
relative error                    = 7.5118352297510367403681395493021e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.82                                         
y[1] (closed_form)                = -0.15101935854113893798495569976629          
y[1] (numeric)                    = -0.15101935854113893798495569976752          
absolute error                    = 1.23e-30                                     
relative error                    = 8.1446512015539895126105670735126e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.83                                         
y[1] (closed_form)                = -0.1369507719424681587931522884012           
y[1] (numeric)                    = -0.13695077194246815879315228840246          
absolute error                    = 1.26e-30                                     
relative error                    = 9.2003862565251925790682759710228e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.84                                         
y[1] (closed_form)                = -0.12286849038072839565272806138494          
y[1] (numeric)                    = -0.12286849038072839565272806138619          
absolute error                    = 1.25e-30                                     
relative error                    = 1.0173478945876747429137762607821e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.85                                         
y[1] (closed_form)                = -0.10877392207234062702259285529079          
y[1] (numeric)                    = -0.10877392207234062702259285529204          
absolute error                    = 1.25e-30                                     
relative error                    = 1.1491725003431258162048939939064e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.86                                         
y[1] (closed_form)                = -0.09466847646239025724079526406914          
y[1] (numeric)                    = -0.094668476462390257240795264070381         
absolute error                    = 1.241e-30                                    
relative error                    = 1.3108904319306570010178076110370e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.87                                         
y[1] (closed_form)                = -0.08055356408368378251774488622377          
y[1] (numeric)                    = -0.080553564083683782517744886225023         
absolute error                    = 1.253e-30                                    
relative error                    = 1.5554867301691454243202338142466e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1401.1MB, alloc=44.3MB, time=16.63
 
TOP MAIN SOLVE Loop
x[1]                              = 3.88                                         
y[1] (closed_form)                = -0.06643059641569668572667855767274          
y[1] (numeric)                    = -0.066430596415696685726678557673991         
absolute error                    = 1.251e-30                                    
relative error                    = 1.8831684005540630287957334972435e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.89                                         
y[1] (closed_form)                = -0.05230098574342666508434849447301          
y[1] (numeric)                    = -0.052300985743426665084348494474246         
absolute error                    = 1.236e-30                                    
relative error                    = 2.3632441768181089294610202575986e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.9                                          
y[1] (closed_form)                = -0.03816614501616631128144235923566          
y[1] (numeric)                    = -0.038166145016166311281442359236905         
absolute error                    = 1.245e-30                                    
relative error                    = 3.2620533183863507995975033092664e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.91                                         
y[1] (closed_form)                = -0.0240274877062093556773331657979           
y[1] (numeric)                    = -0.024027487706209355677333165799145         
absolute error                    = 1.245e-30                                    
relative error                    = 5.1815654438073364280203781218028e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.92                                         
y[1] (closed_form)                = -0.00988642766750461881659514647194          
y[1] (numeric)                    = -0.0098864276675046188165951464731871        
absolute error                    = 1.2471e-30                                   
relative error                    = 1.2614263128622817796196249030421e-26      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.93                                         
y[1] (closed_form)                = 0.0042556210057282062453540533246            
y[1] (numeric)                    = 0.0042556210057282062453540533233507         
absolute error                    = 1.2493e-30                                   
relative error                    = 2.9356467559456093290354085261106e-26      % 
Desired digits                    = 8                                   
Estimated correct digits          = 9                                   
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.94                                         
y[1] (closed_form)                = 0.0183972441204067975036372051052            
y[1] (numeric)                    = 0.018397244120406797503637205103946          
absolute error                    = 1.254e-30                                    
relative error                    = 6.8162383006540857530947201892898e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.95                                         
y[1] (closed_form)                = 0.03253702752600433374581102380259           
y[1] (numeric)                    = 0.032537027526004333745811023801351          
absolute error                    = 1.239e-30                                    
relative error                    = 3.8079692406129077701802779708644e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.96                                         
y[1] (closed_form)                = 0.04667355725596336877914324998018           
y[1] (numeric)                    = 0.04667355725596336877914324997893           
absolute error                    = 1.250e-30                                    
relative error                    = 2.6781759811981986645912085995184e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.97                                         
y[1] (closed_form)                = 0.060805419669091308873695062432             
y[1] (numeric)                    = 0.060805419669091308873695062430747          
absolute error                    = 1.253e-30                                    
relative error                    = 2.0606715763478672488480847062130e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.98                                         
y[1] (closed_form)                = 0.07493120159092335399129368470176           
y[1] (numeric)                    = 0.074931201590923353991293684700506          
absolute error                    = 1.254e-30                                    
relative error                    = 1.6735351540817955624072927996188e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1441.3MB, alloc=44.3MB, time=17.10
 
TOP MAIN SOLVE Loop
x[1]                              = 3.99                                         
y[1] (closed_form)                = 0.08904949045503876662407434660995           
y[1] (numeric)                    = 0.089049490455038766624074346608704          
absolute error                    = 1.246e-30                                    
relative error                    = 1.3992219311227922611182736992500e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4                                            
y[1] (closed_form)                = 0.10315887444431633673347091141408           
y[1] (numeric)                    = 0.10315887444431633673347091141284           
absolute error                    = 1.24e-30                                     
relative error                    = 1.2020294004558318477141817551505e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.01                                         
y[1] (closed_form)                = 0.11725794263211491736087376461267           
y[1] (numeric)                    = 0.11725794263211491736087376461143           
absolute error                    = 1.24e-30                                     
relative error                    = 1.0574976604274698405466860013224e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.02                                         
y[1] (closed_form)                = 0.13134528512336491297404395277914           
y[1] (numeric)                    = 0.13134528512336491297404395277789           
absolute error                    = 1.25e-30                                     
relative error                    = 9.5169004264290751442728633998619e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.03                                         
y[1] (closed_form)                = 0.14541949319555661151802477938005           
y[1] (numeric)                    = 0.14541949319555661151802477937881           
absolute error                    = 1.24e-30                                     
relative error                    = 8.5270548861869435910429482291545e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.04                                         
y[1] (closed_form)                = 0.15947915943961126145483565149381           
y[1] (numeric)                    = 0.15947915943961126145483565149257           
absolute error                    = 1.24e-30                                     
relative error                    = 7.7753106070861954809761293221693e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.05                                         
y[1] (closed_form)                = 0.17352287790062080680163638093701           
y[1] (numeric)                    = 0.17352287790062080680163638093577           
absolute error                    = 1.24e-30                                     
relative error                    = 7.1460317797988970240931620228459e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.06                                         
y[1] (closed_form)                = 0.187549244218442206311140844957             
y[1] (numeric)                    = 0.18754924421844220631114084495576           
absolute error                    = 1.24e-30                                     
relative error                    = 6.6115968910850325148285104293561e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.07                                         
y[1] (closed_form)                = 0.20155685576813227747952350723608           
y[1] (numeric)                    = 0.20155685576813227747952350723484           
absolute error                    = 1.24e-30                                     
relative error                    = 6.1521102582909697414846932195708e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.08                                         
y[1] (closed_form)                = 0.21554431180020902201444665513219           
y[1] (numeric)                    = 0.21554431180020902201444665513095           
absolute error                    = 1.24e-30                                     
relative error                    = 5.7528773997495837511451309228807e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.09                                         
y[1] (closed_form)                = 0.22951021358072540674754559870844           
y[1] (numeric)                    = 0.22951021358072540674754559870718           
absolute error                    = 1.26e-30                                     
relative error                    = 5.4899517557061634274337767914553e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1481.5MB, alloc=44.3MB, time=17.58
 
TOP MAIN SOLVE Loop
x[1]                              = 4.1                                          
y[1] (closed_form)                = 0.24345316453114159273000834469866           
y[1] (numeric)                    = 0.2434531645311415927300083446974            
absolute error                    = 1.26e-30                                     
relative error                    = 5.1755334642151494592582410165243e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.11                                         
y[1] (closed_form)                = 0.25737177036798162540489998982157           
y[1] (numeric)                    = 0.25737177036798162540489998982031           
absolute error                    = 1.26e-30                                     
relative error                    = 4.8956418110599067215724056790656e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.12                                         
y[1] (closed_form)                = 0.27126463924226062030359478821292           
y[1] (numeric)                    = 0.27126463924226062030359478821166           
absolute error                    = 1.26e-30                                     
relative error                    = 4.6449106065561352993043960503871e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.13                                         
y[1] (closed_form)                = 0.28513038187866850166393518388583           
y[1] (numeric)                    = 0.28513038187866850166393518388458           
absolute error                    = 1.25e-30                                     
relative error                    = 4.3839593373529459762916979453142e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.14                                         
y[1] (closed_form)                = 0.29896761171449637571224205454357           
y[1] (numeric)                    = 0.29896761171449637571224205454233           
absolute error                    = 1.24e-30                                     
relative error                    = 4.1476064677673402250238448531736e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.15                                         
y[1] (closed_form)                = 0.3127749450382916460876195575495            
y[1] (numeric)                    = 0.31277494503829164608761955754825           
absolute error                    = 1.25e-30                                     
relative error                    = 3.9964837971499541206685465353854e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.16                                         
y[1] (closed_form)                = 0.32655100112822800601255769193751           
y[1] (numeric)                    = 0.32655100112822800601255769193627           
absolute error                    = 1.24e-30                                     
relative error                    = 3.7972628952776799193859198428434e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.17                                         
y[1] (closed_form)                = 0.34029440239017647032592345865515           
y[1] (numeric)                    = 0.34029440239017647032592345865391           
absolute error                    = 1.24e-30                                     
relative error                    = 3.6439036060846941371958562345616e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.18                                         
y[1] (closed_form)                = 0.35400377449546364039019612975419           
y[1] (numeric)                    = 0.35400377449546364039019612975295           
absolute error                    = 1.24e-30                                     
relative error                    = 3.5027875105774893476021656644744e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.19                                         
y[1] (closed_form)                = 0.36767774651830342616125407443009           
y[1] (numeric)                    = 0.36767774651830342616125407442885           
absolute error                    = 1.24e-30                                     
relative error                    = 3.3725184940945871380493677472389e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.2                                          
y[1] (closed_form)                = 0.38131495107288848236303221653169           
y[1] (numeric)                    = 0.38131495107288848236303221653046           
absolute error                    = 1.23e-30                                     
relative error                    = 3.2256799701643093516831246708362e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1521.6MB, alloc=44.3MB, time=18.06
 
TOP MAIN SOLVE Loop
x[1]                              = 4.21                                         
y[1] (closed_form)                = 0.39491402445012764973767514046535           
y[1] (numeric)                    = 0.39491402445012764973767514046411           
absolute error                    = 1.24e-30                                     
relative error                    = 3.1399239409807168967270995540239e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.22                                         
y[1] (closed_form)                = 0.40847360675401572774100831806602           
y[1] (numeric)                    = 0.40847360675401572774100831806479           
absolute error                    = 1.23e-30                                     
relative error                    = 3.0112104666304925185845861972554e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.23                                         
y[1] (closed_form)                = 0.42199234203762194181969900775442           
y[1] (numeric)                    = 0.42199234203762194181969900775319           
absolute error                    = 1.23e-30                                     
relative error                    = 2.9147448365078189957808161773686e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.24                                         
y[1] (closed_form)                = 0.43546887843868350653670245487627           
y[1] (numeric)                    = 0.43546887843868350653670245487504           
absolute error                    = 1.23e-30                                     
relative error                    = 2.8245416857572084610210401095533e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.25                                         
y[1] (closed_form)                = 0.44890186831479072530167510789344           
y[1] (numeric)                    = 0.4489018683147907253016751078922            
absolute error                    = 1.24e-30                                     
relative error                    = 2.7622963670323927525373784641633e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.26                                         
y[1] (closed_form)                = 0.46228996837815010830903568336714           
y[1] (numeric)                    = 0.46228996837815010830903568336589           
absolute error                    = 1.25e-30                                     
relative error                    = 2.7039306182337669586954636422897e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.27                                         
y[1] (closed_form)                = 0.47563183982991203248418249756704           
y[1] (numeric)                    = 0.4756318398299120324841824975658            
absolute error                    = 1.24e-30                                     
relative error                    = 2.6070584350354452099130849174243e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.28                                         
y[1] (closed_form)                = 0.48892614849404951078381178646338           
y[1] (numeric)                    = 0.48892614849404951078381178646216           
absolute error                    = 1.22e-30                                     
relative error                    = 2.4952643742981319473257824013767e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.29                                         
y[1] (closed_form)                = 0.50217156495077468308497225146877           
y[1] (numeric)                    = 0.50217156495077468308497225146756           
absolute error                    = 1.21e-30                                     
relative error                    = 2.4095350761618892693415337489047e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.3                                          
y[1] (closed_form)                = 0.51536676466947968712494696394861           
y[1] (numeric)                    = 0.51536676466947968712494696394739           
absolute error                    = 1.22e-30                                     
relative error                    = 2.3672461703703826242716485006504e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1561.7MB, alloc=44.3MB, time=18.53
 
TOP MAIN SOLVE Loop
x[1]                              = 4.31                                         
y[1] (closed_form)                = 0.52851042814118861551565233014674           
y[1] (numeric)                    = 0.52851042814118861551565233014554           
absolute error                    = 1.20e-30                                     
relative error                    = 2.2705323038194180863734478237032e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.32                                         
y[1] (closed_form)                = 0.5416012410105073137472289395539            
y[1] (numeric)                    = 0.54160124101050731374722893955271           
absolute error                    = 1.19e-30                                     
relative error                    = 2.1971884661484988204160799012157e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.33                                         
y[1] (closed_form)                = 0.55463789420705782431098173611012           
y[1] (numeric)                    = 0.55463789420705782431098173610892           
absolute error                    = 1.20e-30                                     
relative error                    = 2.1635737704427658928688587771584e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.34                                         
y[1] (closed_form)                = 0.56761908407638433360678555656517           
y[1] (numeric)                    = 0.56761908407638433360678555656398           
absolute error                    = 1.19e-30                                     
relative error                    = 2.0964763754135194812119268543904e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.35                                         
y[1] (closed_form)                = 0.58054351251031753114935322090555           
y[1] (numeric)                    = 0.58054351251031753114935322090436           
absolute error                    = 1.19e-30                                     
relative error                    = 2.0498032866724199088172752557604e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.36                                         
y[1] (closed_form)                = 0.59340988707678434474608215192153           
y[1] (numeric)                    = 0.59340988707678434474608215192036           
absolute error                    = 1.17e-30                                     
relative error                    = 1.9716557231015729726740851036496e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.37                                         
y[1] (closed_form)                = 0.60621692114905007078113615798543           
y[1] (numeric)                    = 0.60621692114905007078113615798427           
absolute error                    = 1.16e-30                                     
relative error                    = 1.9135064686107495264280257349705e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.38                                         
y[1] (closed_form)                = 0.61896333403437997550043538709408           
y[1] (numeric)                    = 0.61896333403437997550043538709292           
absolute error                    = 1.16e-30                                     
relative error                    = 1.8741013178263131861180612030876e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.39                                         
y[1] (closed_form)                = 0.63164785110210750124464359685839           
y[1] (numeric)                    = 0.63164785110210750124464359685723           
absolute error                    = 1.16e-30                                     
relative error                    = 1.8364663126392604693535808051896e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.4                                          
y[1] (closed_form)                = 0.64426920391109627091625259116268           
y[1] (numeric)                    = 0.6442692039110962709162525911615            
absolute error                    = 1.18e-30                                     
relative error                    = 1.8315325221765994439176406607154e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.41                                         
y[1] (closed_form)                = 0.65682613033658314458653509804551           
y[1] (numeric)                    = 0.65682613033658314458653509804434           
absolute error                    = 1.17e-30                                     
relative error                    = 1.7812933224816233971814401799197e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1601.9MB, alloc=44.3MB, time=19.00
 
TOP MAIN SOLVE Loop
x[1]                              = 4.42                                         
y[1] (closed_form)                = 0.66931737469638964404240758834567           
y[1] (numeric)                    = 0.6693173746963896440424075883445            
absolute error                    = 1.17e-30                                     
relative error                    = 1.7480496461498940996401188705916e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.43                                         
y[1] (closed_form)                = 0.68174168787648912423592418536684           
y[1] (numeric)                    = 0.68174168787648912423592418536566           
absolute error                    = 1.18e-30                                     
relative error                    = 1.7308608538748772245945478156946e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.44                                         
y[1] (closed_form)                = 0.69409782745591713502389567691445           
y[1] (numeric)                    = 0.69409782745591713502389567691328           
absolute error                    = 1.17e-30                                     
relative error                    = 1.6856413515777902360596881753582e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.45                                         
y[1] (closed_form)                = 0.70638455783101248226555128894723           
y[1] (numeric)                    = 0.70638455783101248226555128894607           
absolute error                    = 1.16e-30                                     
relative error                    = 1.6421650036657587688657520774256e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.46                                         
y[1] (closed_form)                = 0.71860065033897656427566732713378           
y[1] (numeric)                    = 0.71860065033897656427566732713262           
absolute error                    = 1.16e-30                                     
relative error                    = 1.6142484695119710786757258373799e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.47                                         
y[1] (closed_form)                = 0.73074488338073862780248314394143           
y[1] (numeric)                    = 0.73074488338073862780248314394027           
absolute error                    = 1.16e-30                                     
relative error                    = 1.5874213099287722124402463403750e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.48                                         
y[1] (closed_form)                = 0.74281604254311465710719401168383           
y[1] (numeric)                    = 0.74281604254311465710719401168267           
absolute error                    = 1.16e-30                                     
relative error                    = 1.5616248620972279008643097320963e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.49                                         
y[1] (closed_form)                = 0.75481292072024768035791168714308           
y[1] (numeric)                    = 0.75481292072024768035791168714193           
absolute error                    = 1.15e-30                                     
relative error                    = 1.5235563255894746616149040315895e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.5                                          
y[1] (closed_form)                = 0.7667343182343173494086531897048            
y[1] (numeric)                    = 0.76673431823431734940865318970364           
absolute error                    = 1.16e-30                                     
relative error                    = 1.5129099773065054644177724038708e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.51                                         
y[1] (closed_form)                = 0.77857904295550672210597087530689           
y[1] (numeric)                    = 0.77857904295550672210597087530575           
absolute error                    = 1.14e-30                                     
relative error                    = 1.4642058636365676212849832860716e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.52                                         
y[1] (closed_form)                = 0.79034591042121425054496512854323           
y[1] (numeric)                    = 0.79034591042121425054496512854209           
absolute error                    = 1.14e-30                                     
relative error                    = 1.4424064007523463605016185918182e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1641.9MB, alloc=44.3MB, time=19.48
 
TOP MAIN SOLVE Loop
x[1]                              = 4.53                                         
y[1] (closed_form)                = 0.80203374395449905417519706405556           
y[1] (numeric)                    = 0.80203374395449905417519706405441           
absolute error                    = 1.15e-30                                     
relative error                    = 1.4338548828754039971494552431711e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.54                                         
y[1] (closed_form)                = 0.81364137478174763332789471118474           
y[1] (numeric)                    = 0.8136413747817476333278947111836            
absolute error                    = 1.14e-30                                     
relative error                    = 1.4011086890779064515445812984997e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.55                                         
y[1] (closed_form)                = 0.82516764214955025659115522901715           
y[1] (numeric)                    = 0.825167642149550256591155229016             
absolute error                    = 1.15e-30                                     
relative error                    = 1.3936561993684894854185135502605e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.56                                         
y[1] (closed_form)                = 0.83661139344077533449180229642819           
y[1] (numeric)                    = 0.83661139344077533449180229642702           
absolute error                    = 1.17e-30                                     
relative error                    = 1.3984987643881826019316791734182e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.57                                         
y[1] (closed_form)                = 0.84797148428983017214325881369048           
y[1] (numeric)                    = 0.84797148428983017214325881368931           
absolute error                    = 1.17e-30                                     
relative error                    = 1.3797633784582583233476736000148e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.58                                         
y[1] (closed_form)                = 0.85924677869709657488022043541501           
y[1] (numeric)                    = 0.85924677869709657488022043541385           
absolute error                    = 1.16e-30                                     
relative error                    = 1.3500196087542454010997528292176e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.59                                         
y[1] (closed_form)                = 0.87043614914252986341492915429131           
y[1] (numeric)                    = 0.87043614914252986341492915429015           
absolute error                    = 1.16e-30                                     
relative error                    = 1.3326652404575805425330024141550e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.6                                          
y[1] (closed_form)                = 0.88153847669840993870819683867964           
y[1] (numeric)                    = 0.88153847669840993870819683867849           
absolute error                    = 1.15e-30                                     
relative error                    = 1.3045374993806827837370458298772e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.61                                         
y[1] (closed_form)                = 0.89255265114123312154265052923045           
y[1] (numeric)                    = 0.8925526511412331215426505292293            
absolute error                    = 1.15e-30                                     
relative error                    = 1.2884393974177212790376481243159e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.62                                         
y[1] (closed_form)                = 0.90347757106273357770748505883565           
y[1] (numeric)                    = 0.90347757106273357770748505883449           
absolute error                    = 1.16e-30                                     
relative error                    = 1.2839278330235987823058101842859e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.63                                         
y[1] (closed_form)                = 0.91431214398002322674472206657808           
y[1] (numeric)                    = 0.91431214398002322674472206657694           
absolute error                    = 1.14e-30                                     
relative error                    = 1.2468389570300925797726661124778e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1682.0MB, alloc=44.3MB, time=19.95
 
TOP MAIN SOLVE Loop
x[1]                              = 4.64                                         
y[1] (closed_form)                = 0.92505528644483912035788373112271           
y[1] (numeric)                    = 0.92505528644483912035788373112157           
absolute error                    = 1.14e-30                                     
relative error                    = 1.2323587754211250530342333997200e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.65                                         
y[1] (closed_form)                = 0.93570592415188736583627953471896           
y[1] (numeric)                    = 0.93570592415188736583627953471782           
absolute error                    = 1.14e-30                                     
relative error                    = 1.2183314977227298585485126875495e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.66                                         
y[1] (closed_form)                = 0.94626299204627276019284993103656           
y[1] (numeric)                    = 0.94626299204627276019284993103544           
absolute error                    = 1.12e-30                                     
relative error                    = 1.1836032999431001823838283393798e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.67                                         
y[1] (closed_form)                = 0.9567254344300033921416775291681            
y[1] (numeric)                    = 0.95672543443000339214167752916697           
absolute error                    = 1.13e-30                                     
relative error                    = 1.1811121136057492798397804620726e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.68                                         
y[1] (closed_form)                = 0.9670922050675595615437215818151            
y[1] (numeric)                    = 0.96709220506755956154372158181397           
absolute error                    = 1.13e-30                                     
relative error                    = 1.1684511508611114827076560173870e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.69                                         
y[1] (closed_form)                = 0.97736226729051645951680501050091           
y[1] (numeric)                    = 0.97736226729051645951680501049978           
absolute error                    = 1.13e-30                                     
relative error                    = 1.1561731384746743790773998309494e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.7                                          
y[1] (closed_form)                = 0.98753459410121014702902824524786           
y[1] (numeric)                    = 0.98753459410121014702902824524676           
absolute error                    = 1.10e-30                                     
relative error                    = 1.1138850290112100441924792347875e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.71                                         
y[1] (closed_form)                = 0.99760816827543646546413856486887           
y[1] (numeric)                    = 0.99760816827543646546413856486779           
absolute error                    = 1.08e-30                                     
relative error                    = 1.0825893716036769758449294848726e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.72                                         
y[1] (closed_form)                = 1.0075819824641726093533805411363            
y[1] (numeric)                    = 1.0075819824641726093533805411351            
absolute error                    = 1.2e-30                                      
relative error                    = 1.1909700856949070648041577984046e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.73                                         
y[1] (closed_form)                = 1.0174550392943111892013220965005            
y[1] (numeric)                    = 1.0174550392943111892013220964994            
absolute error                    = 1.1e-30                                      
relative error                    = 1.0811288533820035280018705014458e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1722.1MB, alloc=44.3MB, time=20.42
 
TOP MAIN SOLVE Loop
x[1]                              = 4.74                                         
y[1] (closed_form)                = 1.0272263514683967110833183652918            
y[1] (numeric)                    = 1.0272263514683967110833183652906            
absolute error                    = 1.2e-30                                      
relative error                    = 1.1681943305724461673722069713648e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.75                                         
y[1] (closed_form)                = 1.0368949418633544994497670679704            
y[1] (numeric)                    = 1.0368949418633544994497670679692            
absolute error                    = 1.2e-30                                      
relative error                    = 1.1573014309854161033456975198196e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.76                                         
y[1] (closed_form)                = 1.04645984362820219032714880098              
y[1] (numeric)                    = 1.0464598436282021903271488009787            
absolute error                    = 1.3e-30                                      
relative error                    = 1.2422836938422248301415358050344e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.77                                         
y[1] (closed_form)                = 1.0559201002807340238479581110868            
y[1] (numeric)                    = 1.0559201002807340238479581110856            
absolute error                    = 1.2e-30                                      
relative error                    = 1.1364496231115971032309981517501e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.78                                         
y[1] (closed_form)                = 1.0652747658031682677608423363072            
y[1] (numeric)                    = 1.0652747658031682677608423363062            
absolute error                    = 1.0e-30                                      
relative error                    = 9.3872494881266234534171903830957e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.79                                         
y[1] (closed_form)                = 1.0745229047367482072583031201103            
y[1] (numeric)                    = 1.0745229047367482072583031201094            
absolute error                    = 9e-31                                        
relative error                    = 8.3758102878271795182763955613598e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.8                                          
y[1] (closed_form)                = 1.0836635922752872411018117241531            
y[1] (numeric)                    = 1.0836635922752872411018117241521            
absolute error                    = 1.0e-30                                      
relative error                    = 9.2279560476916543290329402756297e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.81                                         
y[1] (closed_form)                = 1.0926959143576487296126796149424            
y[1] (numeric)                    = 1.0926959143576487296126796149414            
absolute error                    = 1.0e-30                                      
relative error                    = 9.1516769382986036947804007835368e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.82                                         
y[1] (closed_form)                = 1.1016189677591513466209515204681            
y[1] (numeric)                    = 1.101618967759151346620951520467             
absolute error                    = 1.1e-30                                      
relative error                    = 9.9853037410707936899082838219361e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.83                                         
y[1] (closed_form)                = 1.1104318601818907949132969402232            
y[1] (numeric)                    = 1.1104318601818907949132969402222            
absolute error                    = 1.0e-30                                      
relative error                    = 9.0055052980576237093380873742901e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.84                                         
y[1] (closed_form)                = 1.1191337103439688530836231647732            
y[1] (numeric)                    = 1.1191337103439688530836231647722            
absolute error                    = 1.0e-30                                      
relative error                    = 8.9354827824161174052954460449101e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1762.2MB, alloc=44.3MB, time=20.90
 
TOP MAIN SOLVE Loop
x[1]                              = 4.85                                         
y[1] (closed_form)                = 1.1277236480676208309560820347565            
y[1] (numeric)                    = 1.1277236480676208309560820347556            
absolute error                    = 9e-31                                        
relative error                    = 7.9806786134366314898505900434749e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.86                                         
y[1] (closed_form)                = 1.1362008143662326209083674400283            
y[1] (numeric)                    = 1.1362008143662326209083674400273            
absolute error                    = 1.0e-30                                      
relative error                    = 8.8012610742388458537776703143321e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.87                                         
y[1] (closed_form)                = 1.1445643615302386434626851969206            
y[1] (numeric)                    = 1.1445643615302386434626851969194            
absolute error                    = 1.2e-30                                      
relative error                    = 1.0484338324108274999330497183995e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.88                                         
y[1] (closed_form)                = 1.15281345321189209742141758935              
y[1] (numeric)                    = 1.152813453211892097421417589349             
absolute error                    = 1.0e-30                                      
relative error                    = 8.6744303444227387589172036710772e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.89                                         
y[1] (closed_form)                = 1.1609472645088990375931106469627            
y[1] (numeric)                    = 1.1609472645088990375931106469616            
absolute error                    = 1.1e-30                                      
relative error                    = 9.4750212488361321512128728308545e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.9                                          
y[1] (closed_form)                = 1.1689649820469079167707063940402            
y[1] (numeric)                    = 1.1689649820469079167707063940393            
absolute error                    = 9e-31                                        
relative error                    = 7.6991185691812711520121864816362e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.91                                         
y[1] (closed_form)                = 1.1768658040608463430765633017891            
y[1] (numeric)                    = 1.176865804060846343076563301788             
absolute error                    = 1.1e-30                                      
relative error                    = 9.3468600770315846011821950369668e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.92                                         
y[1] (closed_form)                = 1.1846489404750969190663108471529            
y[1] (numeric)                    = 1.1846489404750969190663108471519            
absolute error                    = 1.0e-30                                      
relative error                    = 8.4413193295809264757044439126368e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.93                                         
y[1] (closed_form)                = 1.1923136129825041450744407692349            
y[1] (numeric)                    = 1.1923136129825041450744407692341            
absolute error                    = 8e-31                                        
relative error                    = 6.7096441010922106781270504469836e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.94                                         
y[1] (closed_form)                = 1.1998590551222044861771393308629            
y[1] (numeric)                    = 1.1998590551222044861771393308619            
absolute error                    = 1.0e-30                                      
relative error                    = 8.3343122321825621893783873118936e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.95                                         
y[1] (closed_form)                = 1.2072845123562718198305224750121            
y[1] (numeric)                    = 1.2072845123562718198305224750112            
absolute error                    = 9e-31                                        
relative error                    = 7.4547465058046598182498221838261e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1802.2MB, alloc=44.3MB, time=21.37
 
TOP MAIN SOLVE Loop
x[1]                              = 4.96                                         
y[1] (closed_form)                = 1.214589242145170599703381046032             
y[1] (numeric)                    = 1.2145892421451705997033810460311            
absolute error                    = 9e-31                                        
relative error                    = 7.4099124936299234565014929769323e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.97                                         
y[1] (closed_form)                = 1.2217725140220091904509302280904            
y[1] (numeric)                    = 1.2217725140220091904509302280896            
absolute error                    = 8e-31                                        
relative error                    = 6.5478637865771195593245069639699e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.98                                         
y[1] (closed_form)                = 1.2288336096655859481579633986097            
y[1] (numeric)                    = 1.2288336096655859481579633986088            
absolute error                    = 9e-31                                        
relative error                    = 7.3240184262613509388726718960512e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.99                                         
y[1] (closed_form)                = 1.2357718229722207419042376121081            
y[1] (numeric)                    = 1.2357718229722207419042376121072            
absolute error                    = 9e-31                                        
relative error                    = 7.2828978883444840448716108230282e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
Finished!
diff  (  y  ,  x  ,  1  )   =  neg ( sin ( x )  )   -  cos ( x )  ; 
Iterations                       = 4900                                
Total Elapsed Time               = 21 Seconds
Elapsed Time(since restart)      = 21 Seconds
Time to Timeout                  = 2 Minutes 38 Seconds
Percent Done                     = 100                                        % 
> quit
memory used=1819.6MB, alloc=44.3MB, time=21.56