|\^/|     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(c(1.0) / (c(x) * c(x) + c(0.000001))) ;
> end;
  exact_soln_y := proc(x) return c(1.0)/(c(x)*c(x) + c(0.1*10^(-5))) end proc

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

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

# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local min_size;
>     min_size := glob_estimated_size_answer;
>     if (float_abs(array_y[1]) < min_size) then # if number 3
>         min_size := float_abs(array_y[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     if (min_size < glob__1) then # if number 3
>         min_size := glob__1;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    min_size := glob_estimated_size_answer;
    if float_abs(array_y[1]) < min_size then
        min_size := float_abs(array_y[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if min_size < glob__1 then
        min_size := glob__1;
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    min_size
end proc

# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     max_estimated_step_error  := glob__small;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
>     est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 3
>         max_estimated_step_error := est_tmp;
>     fi;# end if 3;
>     omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
>     max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    max_estimated_step_error := glob__small;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
    est_tmp := float_abs(array_y[no_terms - 3]
         + array_y[no_terms - 2]*hn_div_ho
         + array_y[no_terms - 1]*hn_div_ho_2
         + array_y[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    omniout_float(ALWAYS, "max_estimated_step_error", 32,
        max_estimated_step_error, 32, "");
    max_estimated_step_error
end proc

# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
>         est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
>     fi;# end if 3;
>     if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
>         array_max_est_error[1] := c(est_tmp);
>     fi;# end if 3
>     ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    est_tmp := c(float_abs(array_y[no_terms - 3]))
         + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
    end if;
    if c(array_max_est_error[1]) <= c(est_tmp) then
        array_max_est_error[1] := c(est_tmp)
    end if
end proc

# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local ret;
>     if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 3;
>     return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    if glob_check_sign*glob_next_display - glob_h/glob__10 <=
    glob_check_sign*array_x[1] then ret := true
    else ret := false
    end if;
    return ret
end proc

# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> 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)*35*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_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, 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)*35*ATS_MAX_TERMS/float_abs(numeric_val))
                    ;
                if glob_prec < evalf(est_rel_err) then
                    glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
                else glob_est_digits := Digits
                end if
            else relerr := glob__m1; glob_est_digits := -16
            end if;
            array_est_digits[1] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[1] := relerr
            else array_last_rel_error[1] := relerr
            end if;
            array_est_rel_error[1] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ")
        end if
    end if
end proc

# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>     #TOP PROGRESS REPORT
>     clock_sec1   := elapsed_time_seconds();
>     total_clock_sec   :=  (clock_sec1) - (glob_orig_start_sec);
>     glob_clock_sec   :=  (clock_sec1) - (glob_clock_start_sec);
>     left_sec   :=  (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
>     expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h)  ,( clock_sec1) - (glob_orig_start_sec));
>     opt_clock_sec   := ( clock_sec1) - (glob_optimal_clock_start_sec);
>     glob_optimal_expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
>     glob_total_exp_sec   := glob_optimal_expect_sec + c(total_clock_sec);
>     percent_done   :=  comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
>     glob_percent_done := percent_done;
>     omniout_str_noeol(INFO,"Total Elapsed Time              ");
>     omniout_timestr((total_clock_sec));
>     omniout_str_noeol(INFO,"Elapsed Time(since restart)     ");
>     omniout_timestr((glob_clock_sec));
>     if (c(percent_done) < glob__100)  then # if number 3
>         omniout_str_noeol(INFO,"Expected Time Remaining         ");
>         omniout_timestr((expect_sec));
>         omniout_str_noeol(INFO,"Optimized Time Remaining        ");
>         omniout_timestr((glob_optimal_expect_sec));
>         omniout_str_noeol(INFO,"Expected Total Time             ");
>         omniout_timestr((glob_total_exp_sec));
>     fi;# end if 3;
>     omniout_str_noeol(INFO,"Time to Timeout                 ");
>     omniout_timestr((left_sec));
>     omniout_float(INFO,    "Percent Done                    ",33,percent_done,4,"%");
>     #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    clock_sec1 := elapsed_time_seconds();
    total_clock_sec := clock_sec1 - glob_orig_start_sec;
    glob_clock_sec := clock_sec1 - glob_clock_start_sec;
    left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
    expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
        clock_sec1 - glob_orig_start_sec);
    opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
    glob_optimal_expect_sec :=
        comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
        ;
    glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
    percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
    glob_percent_done := percent_done;
    omniout_str_noeol(INFO, "Total Elapsed Time              ");
    omniout_timestr(total_clock_sec);
    omniout_str_noeol(INFO, "Elapsed Time(since restart)     ");
    omniout_timestr(glob_clock_sec);
    if c(percent_done) < glob__100 then
        omniout_str_noeol(INFO, "Expected Time Remaining         ");
        omniout_timestr(expect_sec);
        omniout_str_noeol(INFO, "Optimized Time Remaining        ");
        omniout_timestr(glob_optimal_expect_sec);
        omniout_str_noeol(INFO, "Expected Total Time             ");
        omniout_timestr(glob_total_exp_sec)
    end if;
    omniout_str_noeol(INFO, "Time to Timeout                 ");
    omniout_timestr(left_sec);
    omniout_float(INFO, "Percent Done                    ", 33,
        percent_done, 4, "%")
end proc

# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14,  rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
>     #TOP CHECK FOR POLE
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,1] :=  glob_larger_float;
>     array_ord_test_poles[1,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 3;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 4
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 5
>             found_sing := 0;
>         fi;# end if 5;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 5
>         if (rad_c  < array_rad_test_poles[1,1]) then # if number 6
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,1] := rad_c;
>             array_ord_test_poles[1,1] := tmp_ord;
>         fi;# end if 6;
>     fi;# end if 5;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,2] :=  glob_larger_float;
>     array_ord_test_poles[1,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 5;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 6
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 7
>             found_sing := 0;
>         fi;# end if 7;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 7
>         if (rad_c  < array_rad_test_poles[1,2]) then # if number 8
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 9
>                 glob_min_pole_est := rad_c;
>             fi;# end if 9;
>             array_ord_test_poles[1,2] := tmp_ord;
>         fi;# end if 8;
>     fi;# end if 7;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,3] :=  glob_larger_float;
>     array_ord_test_poles[1,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 7;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 8
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 9
>             found_sing := 0;
>         fi;# end if 9;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 9
>         if (rad_c  < array_rad_test_poles[1,3]) then # if number 10
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 11
>                 glob_min_pole_est := rad_c;
>             fi;# end if 11;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test1
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
>         h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
>         omniout_str(ALWAYS,"SETTING H FOR POLE");
>         glob_h_reason := 6;
>         if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 10;
>         term := 1;
>         ratio := c(1.0);
>         while (term <= ATS_MAX_TERMS)  do # do number 1
>             array_y[term] := array_y[term]* ratio;
>             array_y_higher[1,term] := array_y_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             ratio := ratio * h_new / float_abs(glob_h);
>             term := term + 1;
>         od;# end do number 1;
>         glob_h := h_new;
>     fi;# end if 9;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 9
>         display_poles();
>     fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 1] := glob_larger_float;
    array_ord_test_poles[1, 1] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 1] then
            array_rad_test_poles[1, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
                array_y_higher[1, last_no], last_no);
            array_rad_test_poles[1, 1] := rad_c;
            array_ord_test_poles[1, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 2] := glob_larger_float;
    array_ord_test_poles[1, 2] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 2] then
            array_rad_test_poles[1, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
                last_no);
            array_rad_test_poles[1, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 3] := glob_larger_float;
    array_ord_test_poles[1, 3] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
            array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
            array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 3] then
            array_rad_test_poles[1, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y_higher[1, last_no - 5],
                array_y_higher[1, last_no - 4],
                array_y_higher[1, last_no - 3],
                array_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
                last_no);
            array_rad_test_poles[1, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 3] := tmp_ord
        end if
    end if;
    if
    float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
    then
        h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
        omniout_str(ALWAYS, "SETTING H FOR POLE");
        glob_h_reason := 6;
        if glob_check_sign*h_new < glob_check_sign*glob_min_h then
            omniout_str(ALWAYS, "SETTING H FOR MIN H");
            h_new := glob_min_h;
            glob_h_reason := 5
        end if;
        term := 1;
        ratio := c(1.0);
        while term <= ATS_MAX_TERMS do
            array_y[term] := array_y[term]*ratio;
            array_y_higher[1, term] := array_y_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            ratio := ratio*h_new/float_abs(glob_h);
            term := term + 1
        end do;
        glob_h := h_new
    end if;
    if reached_interval() then display_poles() end if
end proc

# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_0D000001,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> 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 neg ID_CONST $eq_no = 1
>     array_tmp1[1] := neg(array_const_2D0[1]);
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
>     array_tmp2[1] := array_tmp1[1] * array_x[1];
>     #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
>     array_tmp3[1] := array_x[1] * array_x[1];
>     #emit pre add FULL - CONST $eq_no = 1 i = 1
>     array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1];
>     #emit pre div LINEAR - FULL $eq_no = 1 i = 1
>     array_tmp5[1] := array_tmp2[1] / array_tmp4[1];
>     #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
>     array_tmp6[1] := array_x[1] * array_x[1];
>     #emit pre add FULL - CONST $eq_no = 1 i = 1
>     array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1];
>     #emit pre div FULL - FULL $eq_no = 1 i = 1
>     array_tmp8[1] :=  (array_tmp5[1] / (array_tmp7[1]));
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp9[1] := array_const_0D0[1] + array_tmp8[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_tmp9[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[2] := temporary;
>                 array_y_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[1] * array_x[2];
>     #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
>     array_tmp3[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
>     #emit pre add FULL CONST $eq_no = 1 i = 2
>     array_tmp4[2] := array_tmp3[2];
>     #emit pre div LINEAR - FULL $eq_no = 1 i = 2
>     array_tmp5[2] := (array_tmp2[2] -  array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
>     #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
>     array_tmp6[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
>     #emit pre add FULL CONST $eq_no = 1 i = 2
>     array_tmp7[2] := array_tmp6[2];
>     #emit pre div FULL - FULL $eq_no = 1 i = 2
>     array_tmp8[2] :=  ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp9[2] := array_tmp8[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_tmp9[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 mult LINEAR - LINEAR $eq_no = 1 i = 3
>     array_tmp3[3] := array_x[2] * array_x[2];
>     #emit pre add FULL CONST $eq_no = 1 i = 3
>     array_tmp4[3] := array_tmp3[3];
>     #emit pre div LINEAR FULL $eq_no = 1 i = 3
>     array_tmp5[3] :=  neg( ats(3,array_tmp4,array_tmp5,2)) / array_tmp4[1];
>     #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
>     array_tmp6[3] := array_x[2] * array_x[2];
>     #emit pre add FULL CONST $eq_no = 1 i = 3
>     array_tmp7[3] := array_tmp6[3];
>     #emit pre div FULL - FULL $eq_no = 1 i = 3
>     array_tmp8[3] :=  ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp9[3] := array_tmp8[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_tmp9[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 add FULL CONST $eq_no = 1 i = 4
>     array_tmp4[4] := array_tmp3[4];
>     #emit pre div LINEAR FULL $eq_no = 1 i = 4
>     array_tmp5[4] :=  neg( ats(4,array_tmp4,array_tmp5,2)) / array_tmp4[1];
>     #emit pre add FULL CONST $eq_no = 1 i = 4
>     array_tmp7[4] := array_tmp6[4];
>     #emit pre div FULL - FULL $eq_no = 1 i = 4
>     array_tmp8[4] :=  ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp9[4] := array_tmp8[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_tmp9[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 add FULL CONST $eq_no = 1 i = 5
>     array_tmp4[5] := array_tmp3[5];
>     #emit pre div LINEAR FULL $eq_no = 1 i = 5
>     array_tmp5[5] :=  neg( ats(5,array_tmp4,array_tmp5,2)) / array_tmp4[1];
>     #emit pre add FULL CONST $eq_no = 1 i = 5
>     array_tmp7[5] := array_tmp6[5];
>     #emit pre div FULL - FULL $eq_no = 1 i = 5
>     array_tmp8[5] :=  ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp9[5] := array_tmp8[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_tmp9[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 mult LINEAR - LINEAR $eq_no = 1 i = 1
>         #emit FULL - NOT FULL add $eq_no = 1
>         array_tmp4[kkk] := array_tmp3[kkk];
>         #emit div LINEAR FULL $eq_no = 1 i = 1
>         array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
>         #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
>         #emit FULL - NOT FULL add $eq_no = 1
>         array_tmp7[kkk] := array_tmp6[kkk];
>         #emit div FULL FULL $eq_no = 1
>         array_tmp8[kkk] :=  ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2)) /array_tmp7[1]);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp9[kkk] := array_tmp8[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_tmp9[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y[kkk + order_d] := c(temporary);
>                 array_y_higher[1,kkk + order_d] := c(temporary);
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
>                     if (adj3 <= order_d + 1) then # if number 3
>                         if (adj2 > 0) then # if number 4
>                             temporary := c(temporary) / c(glob_h) * c(adj2);
>                         else
>                             temporary := c(temporary);
>                         fi;# end if 4;
>                         array_y_higher[adj3,term] := c(temporary);
>                     fi;# end if 3;
>                     term  := term - 1;
>                     adj2 := adj2 - 1;
>                     adj3 := adj3 + 1;
>                 od;# end do number 1
>             fi;# end if 2
>         fi;# end if 1;
>         kkk   :=  kkk + 1;
>     od;# end do number 1;
>     #BOTTOM ATOMALL
>     #END OUTFILE4
>     #BEGIN OUTFILE5
>     #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, 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] := neg(array_const_2D0[1]);
    array_tmp2[1] := array_tmp1[1]*array_x[1];
    array_tmp3[1] := array_x[1]*array_x[1];
    array_tmp4[1] := array_tmp3[1] + array_const_0D000001[1];
    array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
    array_tmp6[1] := array_x[1]*array_x[1];
    array_tmp7[1] := array_tmp6[1] + array_const_0D000001[1];
    array_tmp8[1] := array_tmp5[1]/array_tmp7[1];
    array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
    if not array_y_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp9[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_tmp2[2] := array_tmp1[1]*array_x[2];
    array_tmp3[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
    array_tmp4[2] := array_tmp3[2];
    array_tmp5[2] :=
        (-array_tmp4[2]*array_tmp5[1] + array_tmp2[2])/array_tmp4[1];
    array_tmp6[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
    array_tmp7[2] := array_tmp6[2];
    array_tmp8[2] :=
        (array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1];
    array_tmp9[2] := array_tmp8[2];
    if not array_y_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp9[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y[3] := temporary; array_y_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp3[3] := array_x[2]*array_x[2];
    array_tmp4[3] := array_tmp3[3];
    array_tmp5[3] := neg(ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1];
    array_tmp6[3] := array_x[2]*array_x[2];
    array_tmp7[3] := array_tmp6[3];
    array_tmp8[3] :=
        (array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1];
    array_tmp9[3] := array_tmp8[3];
    if not array_y_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp9[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_tmp4[4] := array_tmp3[4];
    array_tmp5[4] := neg(ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1];
    array_tmp7[4] := array_tmp6[4];
    array_tmp8[4] :=
        (array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1];
    array_tmp9[4] := array_tmp8[4];
    if not array_y_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp9[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_tmp4[5] := array_tmp3[5];
    array_tmp5[5] := neg(ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1];
    array_tmp7[5] := array_tmp6[5];
    array_tmp8[5] :=
        (array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1];
    array_tmp9[5] := array_tmp8[5];
    if not array_y_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp9[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_tmp4[kkk] := array_tmp3[kkk];
        array_tmp5[kkk] :=
            neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
        array_tmp7[kkk] := array_tmp6[kkk];
        array_tmp8[kkk] := (
            array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/
            array_tmp7[1];
        array_tmp9[kkk] := array_tmp8[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_tmp9[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y[kkk + order_d] := c(temporary);
                array_y_higher[1, kkk + order_d] := c(temporary);
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
                do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then
                            temporary := c(temporary)*c(adj2)/c(glob_h)
                        else temporary := c(temporary)
                        end if;
                        array_y_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        kkk := kkk + 1
    end do
end proc

# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
>     #BEGIN OUTFIEMAIN
>     local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
>     term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
>     rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
>     x_start,x_end
>     ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
>     global
>     ALWAYS,
>     INFO,
>     DEBUGL,
>     DEBUGMASSIVE,
>     glob_iolevel,
>     glob_yes_pole,
>     glob_no_pole,
>     glob_not_given,
>     glob_no_sing_tests,
>     glob_ratio_test,
>     glob_three_term_test,
>     glob_six_term_test,
>     glob_log_10,
>     #Top Generate Globals Decl
>     MAX_UNCHANGED,
>     glob__small,
>     glob_small_float,
>     glob_smallish_float,
>     glob_large_float,
>     glob_larger_float,
>     glob__m2,
>     glob__m1,
>     glob__0,
>     glob__1,
>     glob__2,
>     glob__3,
>     glob__4,
>     glob__5,
>     glob__8,
>     glob__10,
>     glob__100,
>     glob__pi,
>     glob__0_5,
>     glob__0_8,
>     glob__m0_8,
>     glob__0_25,
>     glob__0_125,
>     glob_prec,
>     glob_check_sign,
>     glob_desired_digits_correct,
>     glob_max_estimated_step_error,
>     glob_ratio_of_radius,
>     glob_percent_done,
>     glob_total_exp_sec,
>     glob_optimal_expect_sec,
>     glob_estimated_size_answer,
>     glob_almost_1,
>     glob_clock_sec,
>     glob_clock_start_sec,
>     glob_disp_incr,
>     glob_h,
>     glob_diff_rc_fm,
>     glob_diff_rc_fmm1,
>     glob_diff_rc_fmm2,
>     glob_diff_ord_fm,
>     glob_diff_ord_fmm1,
>     glob_diff_ord_fmm2,
>     glob_six_term_ord_save,
>     glob_guess_error_rc,
>     glob_guess_error_ord,
>     glob_least_given_sing,
>     glob_least_ratio_sing,
>     glob_least_3_sing,
>     glob_least_6_sing,
>     glob_last_good_h,
>     glob_max_h,
>     glob_min_h,
>     glob_display_interval,
>     glob_abserr,
>     glob_relerr,
>     glob_min_pole_est,
>     glob_max_rel_trunc_err,
>     glob_max_trunc_err,
>     glob_max_hours,
>     glob_optimal_clock_start_sec,
>     glob_optimal_start,
>     glob_upper_ratio_limit,
>     glob_lower_ratio_limit,
>     glob_max_sec,
>     glob_orig_start_sec,
>     glob_normmax,
>     glob_max_minutes,
>     glob_next_display,
>     glob_est_digits,
>     glob_subiter_method,
>     glob_html_log,
>     glob_min_good_digits,
>     glob_good_digits,
>     glob_min_apfp_est_good_digits,
>     glob_apfp_est_good_digits,
>     glob_max_opt_iter,
>     glob_dump,
>     glob_djd_debug,
>     glob_display_flag,
>     glob_djd_debug2,
>     glob_h_reason,
>     glob_sec_in_minute,
>     glob_min_in_hour,
>     glob_hours_in_day,
>     glob_days_in_year,
>     glob_sec_in_hour,
>     glob_sec_in_day,
>     glob_sec_in_year,
>     glob_not_yet_finished,
>     glob_initial_pass,
>     glob_not_yet_start_msg,
>     glob_reached_optimal_h,
>     glob_optimal_done,
>     glob_type_given_pole,
>     glob_optimize,
>     glob_look_poles,
>     glob_dump_closed_form,
>     glob_max_iter,
>     glob_no_eqs,
>     glob_unchanged_h_cnt,
>     glob_warned,
>     glob_warned2,
>     glob_start,
>     glob_iter,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_1,
>     array_const_0D0,
>     array_const_2D0,
>     array_const_0D000001,
>     #END CONST
>     array_y_init,
>     array_norms,
>     array_fact_1,
>     array_1st_rel_error,
>     array_last_rel_error,
>     array_est_rel_error,
>     array_max_est_error,
>     array_type_pole,
>     array_type_real_pole,
>     array_type_complex_pole,
>     array_est_digits,
>     array_y,
>     array_x,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_tmp6,
>     array_tmp7,
>     array_tmp8,
>     array_tmp9,
>     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 := 20;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=20;
>     #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..(20),[]);
>     array_norms:= Array(0..(20),[]);
>     array_fact_1:= Array(0..(20),[]);
>     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..(20),[]);
>     array_x:= Array(0..(20),[]);
>     array_tmp0:= Array(0..(20),[]);
>     array_tmp1:= Array(0..(20),[]);
>     array_tmp2:= Array(0..(20),[]);
>     array_tmp3:= Array(0..(20),[]);
>     array_tmp4:= Array(0..(20),[]);
>     array_tmp5:= Array(0..(20),[]);
>     array_tmp6:= Array(0..(20),[]);
>     array_tmp7:= Array(0..(20),[]);
>     array_tmp8:= Array(0..(20),[]);
>     array_tmp9:= Array(0..(20),[]);
>     array_m1:= Array(0..(20),[]);
>     array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
>     array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
>     array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
>     array_y_set_initial := Array(0..(2) ,(0..20+ 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..(20) ,(0..20+ 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 <= 20) do # do number 1
>         array_y_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) 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 <= 20) do # do number 1
>         array_y[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp4[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp5[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp6[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp7[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp8[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) do # do number 1
>         array_tmp9[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <=20) do # do number 1
>         term := 1;
>         while (term <= 20) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5);
>     zero_ats_ar(array_tmp6);
>     zero_ats_ar(array_tmp7);
>     zero_ats_ar(array_tmp8);
>     zero_ats_ar(array_tmp9);
>     zero_ats_ar(array_m1);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := c(1);
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := c(0.0);
>     zero_ats_ar(array_const_2D0);
>     array_const_2D0[1]   := c(2.0);
>     zero_ats_ar(array_const_0D000001);
>     array_const_0D000001[1]   := c(0.000001);
>     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;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 20;
>     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/sing1_backpostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =  neg ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 )  ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=20;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(-1.5);");
>     omniout_str(ALWAYS,"x_end := c(-2.0);");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"glob_max_h := c(0.1);");
>     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 := 2;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.001);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=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,"");
>     omniout_str(ALWAYS,"return(c(1.0) / (c(x) * c(x) + c(0.000001))) ;");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(-1.5);
>     x_end := c(-2.0);
>     array_y_init[0 + 1] := exact_soln_y(x_start);
>     glob_look_poles := true;
>     glob_max_h := c(0.1);
>     glob_type_given_pole := 2;
>     array_given_rad_poles[1,1] := c(0.0);
>     array_given_rad_poles[1,2] := c(0.001);
>     array_given_ord_poles[1,1] := c(1.0);
>     array_given_ord_poles[1,2] := c(0.0);
>     #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 ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 )  ; ");
>         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,"2016-08-26T17:08:37-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"sing1_back.ode.txt\">sing1_back</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =  neg ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 )  ; ")
>             ;
>             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.sing1_back.mxt.txt\">sing1_back diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.sing1_back.mxt.txt\">sing1_back maple results</a>")
>             ;
>             logitem_str(html_log_file,"OK")
>             ;
>             logend(html_log_file)
>             ;
>             ;
>         fi;# end if 15;
>         if (glob_html_log)  then # if number 15
>             fclose(html_log_file);
>         fi;# end if 15
>         ;
>         ;;
>     fi;# end if 14
>     #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_0D000001, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, 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 := 20;
    Digits := 32;
    max_terms := 20;
    glob_html_log := true;
    array_y_init := Array(0 .. 20, []);
    array_norms := Array(0 .. 20, []);
    array_fact_1 := Array(0 .. 20, []);
    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 .. 20, []);
    array_x := Array(0 .. 20, []);
    array_tmp0 := Array(0 .. 20, []);
    array_tmp1 := Array(0 .. 20, []);
    array_tmp2 := Array(0 .. 20, []);
    array_tmp3 := Array(0 .. 20, []);
    array_tmp4 := Array(0 .. 20, []);
    array_tmp5 := Array(0 .. 20, []);
    array_tmp6 := Array(0 .. 20, []);
    array_tmp7 := Array(0 .. 20, []);
    array_tmp8 := Array(0 .. 20, []);
    array_tmp9 := Array(0 .. 20, []);
    array_m1 := Array(0 .. 20, []);
    array_y_higher := Array(0 .. 2, 0 .. 21, []);
    array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
    array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
    array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
    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 .. 20, 0 .. 21, []);
    term := 1;
    while term <= 20 do array_y_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 20 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 <= 20 do array_y[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp5[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp6[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp7[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp8[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_tmp9[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 20 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 <= 20 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 <= 20 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 <= 20 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 <= 20 do
        term := 1;
        while term <= 20 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y);
    zero_ats_ar(array_x);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5);
    zero_ats_ar(array_tmp6);
    zero_ats_ar(array_tmp7);
    zero_ats_ar(array_tmp8);
    zero_ats_ar(array_tmp9);
    zero_ats_ar(array_m1);
    zero_ats_ar(array_const_1);
    array_const_1[1] := c(1);
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := c(0.);
    zero_ats_ar(array_const_2D0);
    array_const_2D0[1] := c(2.0);
    zero_ats_ar(array_const_0D000001);
    array_const_0D000001[1] := c(0.1*10^(-5));
    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;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 20;
    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/sing1_backpostode.ode#################");
    omniout_str(ALWAYS, "diff  (  y  ,  x  ,  1  )   =  neg ( 2.0 )   *  \
        x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 ) \
         ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=20;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(-1.5);");
    omniout_str(ALWAYS, "x_end := c(-2.0);");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_h := c(0.1);");
    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 := 2;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.001);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=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, "");
    omniout_str(ALWAYS, "return(c(1.0) / (c(x) * c(x) + c(0.000001))) ;");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(-1.5);
    x_end := c(-2.0);
    array_y_init[1] := exact_soln_y(x_start);
    glob_look_poles := true;
    glob_max_h := c(0.1);
    glob_type_given_pole := 2;
    array_given_rad_poles[1, 1] := c(0.);
    array_given_rad_poles[1, 2] := c(0.001);
    array_given_ord_poles[1, 1] := c(1.0);
    array_given_ord_poles[1, 2] := c(0.);
    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 ( 2.0 )   *\
              x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000\
            001 )  ; ");
        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, "2016-08-26T17:08:37-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"sing1_back.ode.txt\">sing1_back</a>");
            logitem_str(html_log_file, "diff  (  y  ,  x  ,  1  )   =  ne\
                g ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  \
                x  *  x  +  0.000001 )  ; ");
            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.sing1_back.mxt.t\
                xt\">sing1_back diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.sing1_back.mxt.\
                txt\">sing1_back 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/sing1_backpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  neg ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-1.5);
x_end := c(-2.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.1);







glob_type_given_pole := 2;

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

array_given_rad_poles[1,2] := c(0.001);

array_given_ord_poles[1,1] := c(1.0);

array_given_ord_poles[1,2] := c(0.0);
#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(c(1.0) / (c(x) * c(x) + c(0.000001))) ;
end;


#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = -1.501                                       
y[1] (closed_form)                = 0.44385224691322954884194510257869           
y[1] (numeric)                    = 0.44385224691322954884194510257869           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.502                                       
y[1] (closed_form)                = 0.44326142894186847990141865820333           
y[1] (numeric)                    = 0.44326142894186847990141865820333           
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]                              = -1.503                                       
y[1] (closed_form)                = 0.44267178985484792010659536699705           
y[1] (numeric)                    = 0.44267178985484792010659536699705           
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]                              = -1.504                                       
y[1] (closed_form)                = 0.4420833265178820495159850699619            
y[1] (numeric)                    = 0.4420833265178820495159850699619            
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]                              = -1.505                                       
y[1] (closed_form)                = 0.44149603580709448809859136274815           
y[1] (numeric)                    = 0.44149603580709448809859136274816           
absolute error                    = 1e-32                                        
relative error                    = 2.2650260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
memory used=4.5MB, alloc=40.3MB, time=0.10
 
TOP MAIN SOLVE Loop
x[1]                              = -1.506                                       
y[1] (closed_form)                = 0.44090991460897683767945584661979           
y[1] (numeric)                    = 0.44090991460897683767945584661979           
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]                              = -1.507                                       
y[1] (closed_form)                = 0.44032495982034741639329825411153           
y[1] (numeric)                    = 0.44032495982034741639329825411154           
absolute error                    = 1e-32                                        
relative error                    = 2.2710500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.508                                       
y[1] (closed_form)                = 0.43974116834831018462532953103803           
y[1] (numeric)                    = 0.43974116834831018462532953103804           
absolute error                    = 1e-32                                        
relative error                    = 2.2740650000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.509                                       
y[1] (closed_form)                = 0.43915853711021386142440193194624           
y[1] (numeric)                    = 0.43915853711021386142440193194625           
absolute error                    = 1e-32                                        
relative error                    = 2.2770820000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.51                                        
y[1] (closed_form)                = 0.43857706303361123037970686386261           
y[1] (numeric)                    = 0.43857706303361123037970686386262           
absolute error                    = 1e-32                                        
relative error                    = 2.2801010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.511                                       
y[1] (closed_form)                = 0.43799674305621863395823788654308           
y[1] (numeric)                    = 0.43799674305621863395823788654309           
absolute error                    = 1e-32                                        
relative error                    = 2.2831220000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.512                                       
y[1] (closed_form)                = 0.43741757412587565530620323732747           
y[1] (numeric)                    = 0.43741757412587565530620323732748           
absolute error                    = 1e-32                                        
relative error                    = 2.2861450000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.513                                       
y[1] (closed_form)                = 0.43683955320050498652349978376442           
y[1] (numeric)                    = 0.43683955320050498652349978376444           
absolute error                    = 2e-32                                        
relative error                    = 4.5783400000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.514                                       
y[1] (closed_form)                = 0.43626267724807248242624870375452           
y[1] (numeric)                    = 0.43626267724807248242624870375454           
absolute error                    = 2e-32                                        
relative error                    = 4.5843940000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.515                                       
y[1] (closed_form)                = 0.43568694324654739881824273513806           
y[1] (numeric)                    = 0.43568694324654739881824273513808           
absolute error                    = 2e-32                                        
relative error                    = 4.5904520000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.516                                       
y[1] (closed_form)                = 0.43511234818386281429796580626101           
y[1] (numeric)                    = 0.43511234818386281429796580626102           
absolute error                    = 1e-32                                        
relative error                    = 2.2982570000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.517                                       
y[1] (closed_form)                = 0.43453888905787623463361853569085           
y[1] (numeric)                    = 0.43453888905787623463361853569087           
absolute error                    = 2e-32                                        
relative error                    = 4.6025800000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.518                                       
y[1] (closed_form)                = 0.43396656287633037874431775031734           
y[1] (numeric)                    = 0.43396656287633037874431775031736           
absolute error                    = 2e-32                                        
relative error                    = 4.6086500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.519                                       
y[1] (closed_form)                = 0.4333953666568141453313350917628            
y[1] (numeric)                    = 0.43339536665681414533133509176282           
absolute error                    = 2e-32                                        
relative error                    = 4.6147240000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.52                                        
y[1] (closed_form)                = 0.43282529742672375920889923437533           
y[1] (numeric)                    = 0.43282529742672375920889923437535           
absolute error                    = 2e-32                                        
relative error                    = 4.6208020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.521                                       
y[1] (closed_form)                = 0.43225635222322409638970849496119           
y[1] (numeric)                    = 0.43225635222322409638970849496121           
absolute error                    = 2e-32                                        
relative error                    = 4.6268840000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.522                                       
y[1] (closed_form)                = 0.43168852809321018698588594357399           
y[1] (numeric)                    = 0.43168852809321018698588594357401           
absolute error                    = 2e-32                                        
relative error                    = 4.6329700000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.523                                       
y[1] (closed_form)                = 0.4311218220932688949916577927425            
y[1] (numeric)                    = 0.43112182209326889499165779274251           
absolute error                    = 1e-32                                        
relative error                    = 2.3195300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.524                                       
y[1] (closed_form)                = 0.43055623128964077401954811401301           
y[1] (numeric)                    = 0.43055623128964077401954811401303           
absolute error                    = 2e-32                                        
relative error                    = 4.6451540000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.525                                       
y[1] (closed_form)                = 0.42999175275818209806735906805307           
y[1] (numeric)                    = 0.42999175275818209806735906805309           
absolute error                    = 2e-32                                        
relative error                    = 4.6512520000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.526                                       
y[1] (closed_form)                = 0.42942838358432706639864609819224           
y[1] (numeric)                    = 0.42942838358432706639864609819225           
absolute error                    = 1e-32                                        
relative error                    = 2.3286770000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.527                                       
y[1] (closed_form)                = 0.42886612086305018162480218550175           
y[1] (numeric)                    = 0.42886612086305018162480218550177           
absolute error                    = 2e-32                                        
relative error                    = 4.6634600000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.528                                       
y[1] (closed_form)                = 0.42830496169882880008223455264618           
y[1] (numeric)                    = 0.42830496169882880008223455264619           
absolute error                    = 1e-32                                        
relative error                    = 2.3347850000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.529                                       
y[1] (closed_form)                = 0.42774490320560585360345138807499           
y[1] (numeric)                    = 0.427744903205605853603451388075             
absolute error                    = 1e-32                                        
relative error                    = 2.3378420000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.53                                        
y[1] (closed_form)                = 0.42718594250675274178617549396578           
y[1] (numeric)                    = 0.4271859425067527417861754939658            
absolute error                    = 2e-32                                        
relative error                    = 4.6818020000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.531                                       
y[1] (closed_form)                = 0.42662807673503239386986649100967           
y[1] (numeric)                    = 0.42662807673503239386986649100968           
absolute error                    = 1e-32                                        
relative error                    = 2.3439620000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.532                                       
y[1] (closed_form)                = 0.42607130303256249933426358901162           
y[1] (numeric)                    = 0.42607130303256249933426358901163           
absolute error                    = 1e-32                                        
relative error                    = 2.3470250000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.533                                       
y[1] (closed_form)                = 0.42551561855077890633975720078805           
y[1] (numeric)                    = 0.42551561855077890633975720078806           
absolute error                    = 1e-32                                        
relative error                    = 2.3500900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.534                                       
y[1] (closed_form)                = 0.42496102045039918713456008247643           
y[1] (numeric)                    = 0.42496102045039918713456008247644           
absolute error                    = 1e-32                                        
relative error                    = 2.3531570000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.535                                       
y[1] (closed_form)                = 0.4244075059013863695587774687148            
y[1] (numeric)                    = 0.42440750590138636955877746871481           
absolute error                    = 1e-32                                        
relative error                    = 2.3562260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.536                                       
y[1] (closed_form)                = 0.42385507208291283378057107689282           
y[1] (numeric)                    = 0.42385507208291283378057107689283           
absolute error                    = 1e-32                                        
relative error                    = 2.3592970000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.537                                       
y[1] (closed_form)                = 0.4233037161833243734046741196341            
y[1] (numeric)                    = 0.42330371618332437340467411963411           
absolute error                    = 1e-32                                        
relative error                    = 2.3623700000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.538                                       
y[1] (closed_form)                = 0.42275343540010442009854382579176           
y[1] (numeric)                    = 0.42275343540010442009854382579178           
absolute error                    = 2e-32                                        
relative error                    = 4.7308900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.539                                       
y[1] (closed_form)                = 0.42220422693983843088643466262927           
y[1] (numeric)                    = 0.42220422693983843088643466262928           
absolute error                    = 1e-32                                        
relative error                    = 2.3685220000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.54                                        
y[1] (closed_form)                = 0.42165608801817843726663970878744           
y[1] (numeric)                    = 0.42165608801817843726663970878745           
absolute error                    = 1e-32                                        
relative error                    = 2.3716010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.541                                       
y[1] (closed_form)                = 0.42110901585980775531207968056354           
y[1] (numeric)                    = 0.42110901585980775531207968056356           
absolute error                    = 2e-32                                        
relative error                    = 4.7493640000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.542                                       
y[1] (closed_form)                = 0.42056300769840585591931919260314           
y[1] (numeric)                    = 0.42056300769840585591931919260315           
absolute error                    = 1e-32                                        
relative error                    = 2.3777650000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.543                                       
y[1] (closed_form)                = 0.42001806077661339437595816620115           
y[1] (numeric)                    = 0.42001806077661339437595816620116           
absolute error                    = 1e-32                                        
relative error                    = 2.3808500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.544                                       
y[1] (closed_form)                = 0.41947417234599739842118311012413           
y[1] (numeric)                    = 0.41947417234599739842118311012415           
absolute error                    = 2e-32                                        
relative error                    = 4.7678740000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.545                                       
y[1] (closed_form)                = 0.41893133966701661397906851454488           
y[1] (numeric)                    = 0.41893133966701661397906851454489           
absolute error                    = 1e-32                                        
relative error                    = 2.3870260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.546                                       
y[1] (closed_form)                = 0.41838956000898700774899304092645           
y[1] (numeric)                    = 0.41838956000898700774899304092646           
absolute error                    = 1e-32                                        
relative error                    = 2.3901170000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.547                                       
y[1] (closed_form)                = 0.41784883065004742584227878038283           
y[1] (numeric)                    = 0.41784883065004742584227878038284           
absolute error                    = 1e-32                                        
relative error                    = 2.3932100000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.548                                       
y[1] (closed_form)                = 0.41730914887712540765887480934188           
y[1] (numeric)                    = 0.41730914887712540765887480934189           
absolute error                    = 1e-32                                        
relative error                    = 2.3963050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.549                                       
y[1] (closed_form)                = 0.41677051198590315420258881171225           
y[1] (numeric)                    = 0.41677051198590315420258881171226           
absolute error                    = 1e-32                                        
relative error                    = 2.3994020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.55                                        
y[1] (closed_form)                = 0.4162329172807836500380228769936            
y[1] (numeric)                    = 0.41623291728078365003802287699361           
absolute error                    = 1e-32                                        
relative error                    = 2.4025010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.551                                       
y[1] (closed_form)                = 0.41569636207485693809699193798475           
y[1] (numeric)                    = 0.41569636207485693809699193798476           
absolute error                    = 1e-32                                        
relative error                    = 2.4056020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.552                                       
y[1] (closed_form)                = 0.41516084368986654654679589239861           
y[1] (numeric)                    = 0.41516084368986654654679589239862           
absolute error                    = 1e-32                                        
relative error                    = 2.4087050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.553                                       
y[1] (closed_form)                = 0.41462635945617606693727947060506           
y[1] (numeric)                    = 0.41462635945617606693727947060507           
absolute error                    = 1e-32                                        
relative error                    = 2.4118100000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.554                                       
y[1] (closed_form)                = 0.41409290671273588284814757608647           
y[1] (numeric)                    = 0.41409290671273588284814757608647           
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]                              = -1.555                                       
y[1] (closed_form)                = 0.41356048280705004826250834358274           
y[1] (numeric)                    = 0.41356048280705004826250834358274           
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]                              = -1.556                                       
y[1] (closed_form)                = 0.41302908509514331489709173830312           
y[1] (numeric)                    = 0.41302908509514331489709173830312           
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]                              = -1.557                                       
y[1] (closed_form)                = 0.41249871094152830772403836238012           
y[1] (numeric)                    = 0.41249871094152830772403836238012           
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]                              = -1.558                                       
y[1] (closed_form)                = 0.41196935771917284792357144475594           
y[1] (numeric)                    = 0.41196935771917284792357144475594           
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]                              = -1.559                                       
y[1] (closed_form)                = 0.41144102280946742251125496917895           
y[1] (numeric)                    = 0.41144102280946742251125496917895           
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]                              = -1.56                                        
y[1] (closed_form)                = 0.41091370360219279988790274165732           
y[1] (numeric)                    = 0.41091370360219279988790274165732           
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]                              = -1.561                                       
y[1] (closed_form)                = 0.41038739749548779056453711174274           
y[1] (numeric)                    = 0.41038739749548779056453711174274           
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]                              = -1.562                                       
y[1] (closed_form)                = 0.40986210189581715231910223805201           
y[1] (numeric)                    = 0.409862101895817152319102238052             
absolute error                    = 1e-32                                        
relative error                    = 2.4398450000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.563                                       
y[1] (closed_form)                = 0.40933781421793963904591542262083           
y[1] (numeric)                    = 0.40933781421793963904591542262082           
absolute error                    = 1e-32                                        
relative error                    = 2.4429700000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.564                                       
y[1] (closed_form)                = 0.40881453188487619256309132466946           
y[1] (numeric)                    = 0.40881453188487619256309132466946           
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]                              = -1.565                                       
y[1] (closed_form)                = 0.40829225232787827664739799430514           
y[1] (numeric)                    = 0.40829225232787827664739799430514           
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]                              = -1.566                                       
y[1] (closed_form)                = 0.40777097298639635257020083128191           
y[1] (numeric)                    = 0.40777097298639635257020083128191           
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]                              = -1.567                                       
y[1] (closed_form)                = 0.40725069130804849541232096241483           
y[1] (numeric)                    = 0.40725069130804849541232096241484           
absolute error                    = 1e-32                                        
relative error                    = 2.4554900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.568                                       
y[1] (closed_form)                = 0.40673140474858915043977833138441           
y[1] (numeric)                    = 0.40673140474858915043977833138442           
absolute error                    = 1e-32                                        
relative error                    = 2.4586250000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.569                                       
y[1] (closed_form)                = 0.40621311077187802882650719281555           
y[1] (numeric)                    = 0.40621311077187802882650719281556           
absolute error                    = 1e-32                                        
relative error                    = 2.4617620000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.57                                        
y[1] (closed_form)                = 0.40569580684984914201422288359654           
y[1] (numeric)                    = 0.40569580684984914201422288359655           
absolute error                    = 1e-32                                        
relative error                    = 2.4649010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.571                                       
y[1] (closed_form)                = 0.40517949046247997400368389192728           
y[1] (numeric)                    = 0.40517949046247997400368389192729           
absolute error                    = 1e-32                                        
relative error                    = 2.4680420000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.572                                       
y[1] (closed_form)                = 0.40466415909776079087563254066369           
y[1] (numeric)                    = 0.40466415909776079087563254066369           
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]                              = -1.573                                       
y[1] (closed_form)                = 0.40414981025166408684371122687758           
y[1] (numeric)                    = 0.40414981025166408684371122687758           
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]                              = -1.574                                       
y[1] (closed_form)                = 0.40363644142811416614563929352321           
y[1] (numeric)                    = 0.40363644142811416614563929352321           
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]                              = -1.575                                       
y[1] (closed_form)                = 0.40312405013895686008289842967058           
y[1] (numeric)                    = 0.40312405013895686008289842967058           
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]                              = -1.576                                       
y[1] (closed_form)                = 0.40261263390392937852311217955557           
y[1] (numeric)                    = 0.40261263390392937852311217955558           
absolute error                    = 1e-32                                        
relative error                    = 2.4837770000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.577                                       
y[1] (closed_form)                = 0.4021021902506302951832178629877            
y[1] (numeric)                    = 0.40210219025063029518321786298771           
absolute error                    = 1e-32                                        
relative error                    = 2.4869300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.578                                       
y[1] (closed_form)                = 0.40159271671448966601541714439467           
y[1] (numeric)                    = 0.40159271671448966601541714439468           
absolute error                    = 1e-32                                        
relative error                    = 2.4900850000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.579                                       
y[1] (closed_form)                = 0.40108421083873928002175480759589           
y[1] (numeric)                    = 0.4010842108387392800217548075959            
absolute error                    = 1e-32                                        
relative error                    = 2.4932420000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.58                                        
y[1] (closed_form)                = 0.40057667017438304182701416959855           
y[1] (numeric)                    = 0.40057667017438304182701416959856           
absolute error                    = 1e-32                                        
relative error                    = 2.4964010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.581                                       
y[1] (closed_form)                = 0.40007009228016748534343216931606           
y[1] (numeric)                    = 0.40007009228016748534343216931607           
absolute error                    = 1e-32                                        
relative error                    = 2.4995620000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.582                                       
y[1] (closed_form)                = 0.39956447472255241786452766484532           
y[1] (numeric)                    = 0.39956447472255241786452766484532           
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]                              = -1.583                                       
y[1] (closed_form)                = 0.39905981507568169392910303325365           
y[1] (numeric)                    = 0.39905981507568169392910303325366           
absolute error                    = 1e-32                                        
relative error                    = 2.5058900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.584                                       
y[1] (closed_form)                = 0.39855611092135411830022195589817           
y[1] (numeric)                    = 0.39855611092135411830022195589818           
absolute error                    = 1e-32                                        
relative error                    = 2.5090570000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.585                                       
y[1] (closed_form)                = 0.39805335984899447740768545505062           
y[1] (numeric)                    = 0.39805335984899447740768545505063           
absolute error                    = 1e-32                                        
relative error                    = 2.5122260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.586                                       
y[1] (closed_form)                = 0.39755155945562469860622398770453           
y[1] (numeric)                    = 0.39755155945562469860622398770453           
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]                              = -1.587                                       
y[1] (closed_form)                = 0.39705070734583513660529586233458           
y[1] (numeric)                    = 0.39705070734583513660529586233458           
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]                              = -1.588                                       
y[1] (closed_form)                = 0.39655080113175598643003158527131           
y[1] (numeric)                    = 0.39655080113175598643003158527131           
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]                              = -1.589                                       
y[1] (closed_form)                = 0.39605183843302882227649012523951           
y[1] (numeric)                    = 0.39605183843302882227649012523951           
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]                              = -1.59                                        
y[1] (closed_form)                = 0.39555381687677826162799666627243           
y[1] (numeric)                    = 0.39555381687677826162799666627243           
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]                              = -1.591                                       
y[1] (closed_form)                = 0.39505673409758375400291235824377           
y[1] (numeric)                    = 0.39505673409758375400291235824377           
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]                              = -1.592                                       
y[1] (closed_form)                = 0.39456058773745149370774502705699           
y[1] (numeric)                    = 0.39456058773745149370774502705699           
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]                              = -1.593                                       
y[1] (closed_form)                = 0.39406537544578645597304592831951           
y[1] (numeric)                    = 0.39406537544578645597304592831951           
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]                              = -1.594                                       
y[1] (closed_form)                = 0.3935710948793645558530515731627            
y[1] (numeric)                    = 0.3935710948793645558530515731627            
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]                              = -1.595                                       
y[1] (closed_form)                = 0.39307774370230492927352157564427           
y[1] (numeric)                    = 0.39307774370230492927352157564427           
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]                              = -1.596                                       
y[1] (closed_form)                = 0.39258531958604233561569351963339           
y[1] (numeric)                    = 0.39258531958604233561569351963338           
absolute error                    = 1e-32                                        
relative error                    = 2.5472170000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.597                                       
y[1] (closed_form)                = 0.39209382020929968122772416983936           
y[1] (numeric)                    = 0.39209382020929968122772416983935           
absolute error                    = 1e-32                                        
relative error                    = 2.5504100000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.598                                       
y[1] (closed_form)                = 0.39160324325806066325841310617735           
y[1] (numeric)                    = 0.39160324325806066325841310617734           
absolute error                    = 1e-32                                        
relative error                    = 2.5536050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.599                                       
y[1] (closed_form)                = 0.39111358642554253321141019132494           
y[1] (numeric)                    = 0.39111358642554253321141019132494           
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]                              = -1.6                                         
y[1] (closed_form)                = 0.39062484741216897962149233535456           
y[1] (numeric)                    = 0.39062484741216897962149233535455           
absolute error                    = 1e-32                                        
relative error                    = 2.5600010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.601                                       
y[1] (closed_form)                = 0.3901370239255431292578579448674            
y[1] (numeric)                    = 0.39013702392554312925785794486739           
absolute error                    = 1e-32                                        
relative error                    = 2.5632020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.602                                       
y[1] (closed_form)                = 0.3896501136804206662627293821513            
y[1] (numeric)                    = 0.38965011368042066626272938215129           
absolute error                    = 1e-32                                        
relative error                    = 2.5664050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.603                                       
y[1] (closed_form)                = 0.38916411439868306863687485649573           
y[1] (numeric)                    = 0.38916411439868306863687485649573           
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]                              = -1.604                                       
y[1] (closed_form)                = 0.3886790238093109614869615678068            
y[1] (numeric)                    = 0.3886790238093109614869615678068            
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]                              = -1.605                                       
y[1] (closed_form)                = 0.38819483964835758645293176388748           
y[1] (numeric)                    = 0.38819483964835758645293176388747           
absolute error                    = 1e-32                                        
relative error                    = 2.5760260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.606                                       
y[1] (closed_form)                = 0.38771155965892238673685279793986           
y[1] (numeric)                    = 0.38771155965892238673685279793985           
absolute error                    = 1e-32                                        
relative error                    = 2.5792370000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.607                                       
y[1] (closed_form)                = 0.38722918159112470715793142171194           
y[1] (numeric)                    = 0.38722918159112470715793142171193           
absolute error                    = 1e-32                                        
relative error                    = 2.5824500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.608                                       
y[1] (closed_form)                = 0.38674770320207760866160156091373           
y[1] (numeric)                    = 0.38674770320207760866160156091372           
absolute error                    = 1e-32                                        
relative error                    = 2.5856650000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.609                                       
y[1] (closed_form)                = 0.38626712225586179671379383069603           
y[1] (numeric)                    = 0.38626712225586179671379383069602           
absolute error                    = 1e-32                                        
relative error                    = 2.5888820000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.61                                        
y[1] (closed_form)                = 0.38578743652349966301467419672304           
y[1] (numeric)                    = 0.38578743652349966301467419672303           
absolute error                    = 1e-32                                        
relative error                    = 2.5921010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.611                                       
y[1] (closed_form)                = 0.38530864378292943996929860726338           
y[1] (numeric)                    = 0.38530864378292943996929860726336           
absolute error                    = 2e-32                                        
relative error                    = 5.1906439999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.612                                       
y[1] (closed_form)                = 0.38483074181897946735577024835052           
y[1] (numeric)                    = 0.3848307418189794673557702483505            
absolute error                    = 2e-32                                        
relative error                    = 5.1970900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.613                                       
y[1] (closed_form)                = 0.38435372842334257063460644099978           
y[1] (numeric)                    = 0.38435372842334257063460644099976           
absolute error                    = 2e-32                                        
relative error                    = 5.2035400000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.614                                       
y[1] (closed_form)                = 0.3838776013945505503461232392974            
y[1] (numeric)                    = 0.38387760139455055034612323929738           
absolute error                    = 2e-32                                        
relative error                    = 5.2099940000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.615                                       
y[1] (closed_form)                = 0.3834023585379487820457276324981            
y[1] (numeric)                    = 0.38340235853794878204572763249809           
absolute error                    = 1e-32                                        
relative error                    = 2.6082260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.616                                       
y[1] (closed_form)                = 0.38292799766567092623007003370149           
y[1] (numeric)                    = 0.38292799766567092623007003370148           
absolute error                    = 1e-32                                        
relative error                    = 2.6114570000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.617                                       
y[1] (closed_form)                = 0.38245451659661374771005358187778           
y[1] (numeric)                    = 0.38245451659661374771005358187776           
absolute error                    = 2e-32                                        
relative error                    = 5.2293799999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
memory used=39.0MB, alloc=40.3MB, time=0.56
 
TOP MAIN SOLVE Loop
x[1]                              = -1.618                                       
y[1] (closed_form)                = 0.38198191315641204388972182167174           
y[1] (numeric)                    = 0.38198191315641204388972182167173           
absolute error                    = 1e-32                                        
relative error                    = 2.6179250000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.619                                       
y[1] (closed_form)                = 0.38151018517741368141305268426751           
y[1] (numeric)                    = 0.3815101851774136814130526842675            
absolute error                    = 1e-32                                        
relative error                    = 2.6211620000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.62                                        
y[1] (closed_form)                = 0.38103933049865474064367449943816           
y[1] (numeric)                    = 0.38103933049865474064367449943815           
absolute error                    = 1e-32                                        
relative error                    = 2.6244010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.621                                       
y[1] (closed_form)                = 0.38056934696583476744548914958735           
y[1] (numeric)                    = 0.38056934696583476744548914958734           
absolute error                    = 1e-32                                        
relative error                    = 2.6276420000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.622                                       
y[1] (closed_form)                = 0.38010023243129213173513855603723           
y[1] (numeric)                    = 0.38010023243129213173513855603722           
absolute error                    = 1e-32                                        
relative error                    = 2.6308850000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.623                                       
y[1] (closed_form)                = 0.37963198475397949228018359002783           
y[1] (numeric)                    = 0.37963198475397949228018359002782           
absolute error                    = 1e-32                                        
relative error                    = 2.6341300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.624                                       
y[1] (closed_form)                = 0.37916460179943936721977934895163           
y[1] (numeric)                    = 0.37916460179943936721977934895162           
absolute error                    = 1e-32                                        
relative error                    = 2.6373770000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.625                                       
y[1] (closed_form)                = 0.3786980814397798097875276544274            
y[1] (numeric)                    = 0.37869808143977980978752765442739           
absolute error                    = 1e-32                                        
relative error                    = 2.6406260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.626                                       
y[1] (closed_form)                = 0.37823242155365018871906673419376           
y[1] (numeric)                    = 0.37823242155365018871906673419375           
absolute error                    = 1e-32                                        
relative error                    = 2.6438770000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.627                                       
y[1] (closed_form)                = 0.37776762002621707282981946485439           
y[1] (numeric)                    = 0.37776762002621707282981946485438           
absolute error                    = 1e-32                                        
relative error                    = 2.6471300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.628                                       
y[1] (closed_form)                = 0.37730367474914021925116539672538           
y[1] (numeric)                    = 0.37730367474914021925116539672537           
absolute error                    = 1e-32                                        
relative error                    = 2.6503850000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.629                                       
y[1] (closed_form)                = 0.37684058362054866481612817403403           
y[1] (numeric)                    = 0.37684058362054866481612817403401           
absolute error                    = 2e-32                                        
relative error                    = 5.3072839999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.63                                        
y[1] (closed_form)                = 0.37637834454501692008847902123564           
y[1] (numeric)                    = 0.37637834454501692008847902123563           
absolute error                    = 1e-32                                        
relative error                    = 2.6569010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.631                                       
y[1] (closed_form)                = 0.37591695543354126553194880612534           
y[1] (numeric)                    = 0.37591695543354126553194880612533           
absolute error                    = 1e-32                                        
relative error                    = 2.6601620000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.632                                       
y[1] (closed_form)                = 0.37545641420351614931901592873837           
y[1] (numeric)                    = 0.37545641420351614931901592873836           
absolute error                    = 1e-32                                        
relative error                    = 2.6634250000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.633                                       
y[1] (closed_form)                = 0.37499671877871068628149503691843           
y[1] (numeric)                    = 0.37499671877871068628149503691841           
absolute error                    = 2e-32                                        
relative error                    = 5.3333800000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.634                                       
y[1] (closed_form)                = 0.37453786708924525750789244920424           
y[1] (numeric)                    = 0.37453786708924525750789244920422           
absolute error                    = 2e-32                                        
relative error                    = 5.3399140000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.635                                       
y[1] (closed_form)                = 0.374079857071568210095218286819             
y[1] (numeric)                    = 0.37407985707156821009521828681898           
absolute error                    = 2e-32                                        
relative error                    = 5.3464520000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.636                                       
y[1] (closed_form)                = 0.37362268666843265656565279169003           
y[1] (numeric)                    = 0.37362268666843265656565279169002           
absolute error                    = 1e-32                                        
relative error                    = 2.6764970000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.637                                       
y[1] (closed_form)                = 0.37316635382887337346115524839818           
y[1] (numeric)                    = 0.37316635382887337346115524839817           
absolute error                    = 1e-32                                        
relative error                    = 2.6797700000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.638                                       
y[1] (closed_form)                = 0.37271085650818379863177844575846           
y[1] (numeric)                    = 0.37271085650818379863177844575844           
absolute error                    = 2e-32                                        
relative error                    = 5.3660900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.639                                       
y[1] (closed_form)                = 0.37225619266789312673610981855489           
y[1] (numeric)                    = 0.37225619266789312673610981855487           
absolute error                    = 2e-32                                        
relative error                    = 5.3726440000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.64                                        
y[1] (closed_form)                = 0.37180236027574350247490241117549           
y[1] (numeric)                    = 0.37180236027574350247490241117547           
absolute error                    = 2e-32                                        
relative error                    = 5.3792020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.641                                       
y[1] (closed_form)                = 0.37134935730566731108158471110134           
y[1] (numeric)                    = 0.37134935730566731108158471110132           
absolute error                    = 2e-32                                        
relative error                    = 5.3857640000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.642                                       
y[1] (closed_form)                = 0.3708971817377645655959483191867            
y[1] (numeric)                    = 0.37089718173776456559594831918668           
absolute error                    = 2e-32                                        
relative error                    = 5.3923300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.643                                       
y[1] (closed_form)                = 0.37044583155828039044990646242753           
y[1] (numeric)                    = 0.37044583155828039044990646242751           
absolute error                    = 2e-32                                        
relative error                    = 5.3989000000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.644                                       
y[1] (closed_form)                = 0.36999530475958260089679461967628           
y[1] (numeric)                    = 0.36999530475958260089679461967625           
absolute error                    = 3e-32                                        
relative error                    = 8.1082109999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.645                                       
y[1] (closed_form)                = 0.36954559934013937781824712696774           
y[1] (numeric)                    = 0.36954559934013937781824712696771           
absolute error                    = 3e-32                                        
relative error                    = 8.1180780000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.646                                       
y[1] (closed_form)                = 0.36909671330449703744523066145453           
y[1] (numeric)                    = 0.3690967133044970374452306614545            
absolute error                    = 3e-32                                        
relative error                    = 8.1279510000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.647                                       
y[1] (closed_form)                = 0.36864864466325789553234707532598           
y[1] (numeric)                    = 0.36864864466325789553234707532595           
absolute error                    = 3e-32                                        
relative error                    = 8.1378299999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.648                                       
y[1] (closed_form)                = 0.36820139143305822552703426666249           
y[1] (numeric)                    = 0.36820139143305822552703426666247           
absolute error                    = 2e-32                                        
relative error                    = 5.4318100000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.649                                       
y[1] (closed_form)                = 0.36775495163654631027779473536721           
y[1] (numeric)                    = 0.36775495163654631027779473536719           
absolute error                    = 2e-32                                        
relative error                    = 5.4384040000000000000000000000001e-30      % 
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)                = 0.36730932330236058682806728078337           
y[1] (numeric)                    = 0.36730932330236058682806728078334           
absolute error                    = 3e-32                                        
relative error                    = 8.1675030000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.651                                       
y[1] (closed_form)                = 0.3668645044651078838448280542754            
y[1] (numeric)                    = 0.36686450446510788384482805427537           
absolute error                    = 3e-32                                        
relative error                    = 8.1774060000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.652                                       
y[1] (closed_form)                = 0.36642049316534175123346298511783           
y[1] (numeric)                    = 0.3664204931653417512334629851178            
absolute error                    = 3e-32                                        
relative error                    = 8.1873150000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.653                                       
y[1] (closed_form)                = 0.36597728744954088149289455096417           
y[1] (numeric)                    = 0.36597728744954088149289455096414           
absolute error                    = 3e-32                                        
relative error                    = 8.1972299999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.654                                       
y[1] (closed_form)                = 0.36553488537008762236737206370396           
y[1] (numeric)                    = 0.36553488537008762236737206370393           
absolute error                    = 3e-32                                        
relative error                    = 8.2071509999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.655                                       
y[1] (closed_form)                = 0.36509328498524658035374618568791           
y[1] (numeric)                    = 0.36509328498524658035374618568788           
absolute error                    = 3e-32                                        
relative error                    = 8.2170779999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.656                                       
y[1] (closed_form)                = 0.36465248435914331462544537742808           
y[1] (numeric)                    = 0.36465248435914331462544537742806           
absolute error                    = 2e-32                                        
relative error                    = 5.4846740000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.657                                       
y[1] (closed_form)                = 0.3642124815617431209367545025768            
y[1] (numeric)                    = 0.36421248156174312093675450257678           
absolute error                    = 2e-32                                        
relative error                    = 5.4913000000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.658                                       
y[1] (closed_form)                = 0.36377327466882990507336397516884           
y[1] (numeric)                    = 0.36377327466882990507336397516881           
absolute error                    = 3e-32                                        
relative error                    = 8.2468949999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.659                                       
y[1] (closed_form)                = 0.36333486176198514541751172299931           
y[1] (numeric)                    = 0.36333486176198514541751172299929           
absolute error                    = 2e-32                                        
relative error                    = 5.5045640000000000000000000000001e-30      % 
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)                = 0.36289724092856694419837995413705           
y[1] (numeric)                    = 0.36289724092856694419837995413702           
absolute error                    = 3e-32                                        
relative error                    = 8.2668029999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.661                                       
y[1] (closed_form)                = 0.36246041026168916700073434479119           
y[1] (numeric)                    = 0.36246041026168916700073434479116           
absolute error                    = 3e-32                                        
relative error                    = 8.2767660000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.662                                       
y[1] (closed_form)                = 0.36202436786020067010710490923144           
y[1] (numeric)                    = 0.36202436786020067010710490923141           
absolute error                    = 3e-32                                        
relative error                    = 8.2867350000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.663                                       
y[1] (closed_form)                = 0.36158911182866461525110555870942           
y[1] (numeric)                    = 0.36158911182866461525110555870939           
absolute error                    = 3e-32                                        
relative error                    = 8.2967099999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.664                                       
y[1] (closed_form)                = 0.36115464027733787136177329817613           
y[1] (numeric)                    = 0.36115464027733787136177329817611           
absolute error                    = 2e-32                                        
relative error                    = 5.5377940000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.665                                       
y[1] (closed_form)                = 0.36072095132215050288107823821002           
y[1] (numeric)                    = 0.36072095132215050288107823820999           
absolute error                    = 3e-32                                        
relative error                    = 8.3166779999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.666                                       
y[1] (closed_form)                = 0.36028804308468534423901220547804           
y[1] (numeric)                    = 0.36028804308468534423901220547801           
absolute error                    = 3e-32                                        
relative error                    = 8.3266709999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.667                                       
y[1] (closed_form)                = 0.35985591369215766007290680811403           
y[1] (numeric)                    = 0.35985591369215766007290680811401           
absolute error                    = 2e-32                                        
relative error                    = 5.5577800000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.668                                       
y[1] (closed_form)                = 0.35942456127739489077986144183163           
y[1] (numeric)                    = 0.35942456127739489077986144183161           
absolute error                    = 2e-32                                        
relative error                    = 5.5644500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.669                                       
y[1] (closed_form)                = 0.35899398397881648299337799697153           
y[1] (numeric)                    = 0.35899398397881648299337799697151           
absolute error                    = 2e-32                                        
relative error                    = 5.5711239999999999999999999999999e-30      % 
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)                = 0.35856417994041380457750203395531           
y[1] (numeric)                    = 0.35856417994041380457750203395529           
absolute error                    = 2e-32                                        
relative error                    = 5.5778020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.671                                       
y[1] (closed_form)                = 0.35813514731173014373396002208978           
y[1] (numeric)                    = 0.35813514731173014373396002208976           
absolute error                    = 2e-32                                        
relative error                    = 5.5844839999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.672                                       
y[1] (closed_form)                = 0.35770688424784079181995897102038           
y[1] (numeric)                    = 0.35770688424784079181995897102036           
absolute error                    = 2e-32                                        
relative error                    = 5.5911699999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.673                                       
y[1] (closed_form)                = 0.35727938890933320947647851143115           
y[1] (numeric)                    = 0.35727938890933320947647851143114           
absolute error                    = 1e-32                                        
relative error                    = 2.7989300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.674                                       
y[1] (closed_form)                = 0.35685265946228727566903628727638           
y[1] (numeric)                    = 0.35685265946228727566903628727637           
absolute error                    = 1e-32                                        
relative error                    = 2.8022770000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.675                                       
y[1] (closed_form)                = 0.35642669407825561924504549073897           
y[1] (numeric)                    = 0.35642669407825561924504549073895           
absolute error                    = 2e-32                                        
relative error                    = 5.6112519999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.676                                       
y[1] (closed_form)                = 0.35600149093424403261400858746796           
y[1] (numeric)                    = 0.35600149093424403261400858746795           
absolute error                    = 1e-32                                        
relative error                    = 2.8089770000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.677                                       
y[1] (closed_form)                = 0.35557704821269196715890382707577           
y[1] (numeric)                    = 0.35557704821269196715890382707576           
absolute error                    = 1e-32                                        
relative error                    = 2.8123300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.678                                       
y[1] (closed_form)                = 0.35515336410145310998922109539952           
y[1] (numeric)                    = 0.35515336410145310998922109539951           
absolute error                    = 1e-32                                        
relative error                    = 2.8156850000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.679                                       
y[1] (closed_form)                = 0.35473043679377604164819112308366           
y[1] (numeric)                    = 0.35473043679377604164819112308365           
absolute error                    = 1e-32                                        
relative error                    = 2.8190420000000000000000000000000e-30      % 
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)                = 0.35430826448828497438882710146432           
y[1] (numeric)                    = 0.35430826448828497438882710146431           
absolute error                    = 1e-32                                        
relative error                    = 2.8224010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.681                                       
y[1] (closed_form)                = 0.35388684538896057063546045279114           
y[1] (numeric)                    = 0.35388684538896057063546045279113           
absolute error                    = 1e-32                                        
relative error                    = 2.8257620000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.682                                       
y[1] (closed_form)                = 0.3534661777051208412495029381876            
y[1] (numeric)                    = 0.35346617770512084124950293818759           
absolute error                    = 1e-32                                        
relative error                    = 2.8291250000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.683                                       
y[1] (closed_form)                = 0.35304625965140212322020554353237           
y[1] (numeric)                    = 0.35304625965140212322020554353236           
absolute error                    = 1e-32                                        
relative error                    = 2.8324900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.684                                       
y[1] (closed_form)                = 0.35262708944774013640321074017484           
y[1] (numeric)                    = 0.35262708944774013640321074017483           
absolute error                    = 1e-32                                        
relative error                    = 2.8358570000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.685                                       
y[1] (closed_form)                = 0.35220866531935111893170885304657           
y[1] (numeric)                    = 0.35220866531935111893170885304656           
absolute error                    = 1e-32                                        
relative error                    = 2.8392260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.686                                       
y[1] (closed_form)                = 0.3517909854967130409270114617021            
y[1] (numeric)                    = 0.35179098549671304092701146170209           
absolute error                    = 1e-32                                        
relative error                    = 2.8425970000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.687                                       
y[1] (closed_form)                = 0.35137404821554689613734508796649           
y[1] (numeric)                    = 0.35137404821554689613734508796648           
absolute error                    = 1e-32                                        
relative error                    = 2.8459700000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.688                                       
y[1] (closed_form)                = 0.3509578517167980711356469644778            
y[1] (numeric)                    = 0.35095785171679807113564696447779           
absolute error                    = 1e-32                                        
relative error                    = 2.8493450000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.689                                       
y[1] (closed_form)                = 0.35054239424661779170911150823669           
y[1] (numeric)                    = 0.35054239424661779170911150823668           
absolute error                    = 1e-32                                        
relative error                    = 2.8527220000000000000000000000000e-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)                = 0.3501276740563446460751913185143            
y[1] (numeric)                    = 0.35012767405634464607519131851428           
absolute error                    = 2e-32                                        
relative error                    = 5.7122019999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.691                                       
y[1] (closed_form)                = 0.34971368940248618456070015478328           
y[1] (numeric)                    = 0.34971368940248618456070015478326           
absolute error                    = 2e-32                                        
relative error                    = 5.7189640000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.692                                       
y[1] (closed_form)                = 0.34930043854670059538259750285116           
y[1] (numeric)                    = 0.34930043854670059538259750285115           
absolute error                    = 1e-32                                        
relative error                    = 2.8628650000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.693                                       
y[1] (closed_form)                = 0.34888791975577845617095508068033           
y[1] (numeric)                    = 0.34888791975577845617095508068032           
absolute error                    = 1e-32                                        
relative error                    = 2.8662500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.694                                       
y[1] (closed_form)                = 0.34847613130162456087651504354035           
y[1] (numeric)                    = 0.34847613130162456087651504354034           
absolute error                    = 1e-32                                        
relative error                    = 2.8696370000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.695                                       
y[1] (closed_form)                = 0.34806507146123982170714779469451           
y[1] (numeric)                    = 0.3480650714612398217071477946945            
absolute error                    = 1e-32                                        
relative error                    = 2.8730260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.696                                       
y[1] (closed_form)                = 0.34765473851670324573940426579317           
y[1] (numeric)                    = 0.34765473851670324573940426579316           
absolute error                    = 1e-32                                        
relative error                    = 2.8764170000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.697                                       
y[1] (closed_form)                = 0.34724513075515398585323337303503           
y[1] (numeric)                    = 0.34724513075515398585323337303501           
absolute error                    = 2e-32                                        
relative error                    = 5.7596199999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.698                                       
y[1] (closed_form)                = 0.34683624646877346563980015295478           
y[1] (numeric)                    = 0.34683624646877346563980015295477           
absolute error                    = 1e-32                                        
relative error                    = 2.8832050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.699                                       
y[1] (closed_form)                = 0.34642808395476757793419390688429           
y[1] (numeric)                    = 0.34642808395476757793419390688427           
absolute error                    = 2e-32                                        
relative error                    = 5.7732040000000000000000000000000e-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)                = 0.34602064151534895662665860669252           
y[1] (numeric)                    = 0.34602064151534895662665860669251           
absolute error                    = 1e-32                                        
relative error                    = 2.8900010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.701                                       
y[1] (closed_form)                = 0.34561391745771932140780990681558           
y[1] (numeric)                    = 0.34561391745771932140780990681556           
absolute error                    = 2e-32                                        
relative error                    = 5.7868039999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.702                                       
y[1] (closed_form)                = 0.34520791009405189510512443882139           
y[1] (numeric)                    = 0.34520791009405189510512443882138           
absolute error                    = 1e-32                                        
relative error                    = 2.8968050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.703                                       
y[1] (closed_form)                = 0.34480261774147389326979770430417           
y[1] (numeric)                    = 0.34480261774147389326979770430416           
absolute error                    = 1e-32                                        
relative error                    = 2.9002100000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.704                                       
y[1] (closed_form)                = 0.34439803872204908567486689876798           
y[1] (numeric)                    = 0.34439803872204908567486689876797           
absolute error                    = 1e-32                                        
relative error                    = 2.9036170000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.705                                       
y[1] (closed_form)                = 0.34399417136276042938728446185208           
y[1] (numeric)                    = 0.34399417136276042938728446185206           
absolute error                    = 2e-32                                        
relative error                    = 5.8140520000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.706                                       
y[1] (closed_form)                = 0.34359101399549277307840712580276           
y[1] (numeric)                    = 0.34359101399549277307840712580274           
absolute error                    = 2e-32                                        
relative error                    = 5.8208740000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.707                                       
y[1] (closed_form)                = 0.34318856495701563223913379206205           
y[1] (numeric)                    = 0.34318856495701563223913379206203           
absolute error                    = 2e-32                                        
relative error                    = 5.8277000000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.708                                       
y[1] (closed_form)                = 0.34278682258896603496768377230043           
y[1] (numeric)                    = 0.34278682258896603496768377230041           
absolute error                    = 2e-32                                        
relative error                    = 5.8345299999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.709                                       
y[1] (closed_form)                = 0.34238578523783143799975485177777           
y[1] (numeric)                    = 0.34238578523783143799975485177775           
absolute error                    = 2e-32                                        
relative error                    = 5.8413640000000000000000000000000e-30      % 
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)                = 0.34198545125493271265253833571412           
y[1] (numeric)                    = 0.3419854512549327126525383357141            
absolute error                    = 2e-32                                        
relative error                    = 5.8482020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.711                                       
y[1] (closed_form)                = 0.34158581899640720035579578906666           
y[1] (numeric)                    = 0.34158581899640720035579578906664           
absolute error                    = 2e-32                                        
relative error                    = 5.8550440000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.712                                       
y[1] (closed_form)                = 0.34118688682319183744491964195848           
y[1] (numeric)                    = 0.34118688682319183744491964195846           
absolute error                    = 2e-32                                        
relative error                    = 5.8618900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.713                                       
y[1] (closed_form)                = 0.34078865310100634889260727174828           
y[1] (numeric)                    = 0.34078865310100634889260727174826           
absolute error                    = 2e-32                                        
relative error                    = 5.8687400000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.714                                       
y[1] (closed_form)                = 0.34039111620033651065747565267444           
y[1] (numeric)                    = 0.34039111620033651065747565267442           
absolute error                    = 2e-32                                        
relative error                    = 5.8755939999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.715                                       
y[1] (closed_form)                = 0.33999427449641748032963124900977           
y[1] (numeric)                    = 0.33999427449641748032963124900975           
absolute error                    = 2e-32                                        
relative error                    = 5.8824519999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.716                                       
y[1] (closed_form)                = 0.33959812636921719575488758113424           
y[1] (numeric)                    = 0.33959812636921719575488758113422           
absolute error                    = 2e-32                                        
relative error                    = 5.8893140000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.717                                       
y[1] (closed_form)                = 0.3392026702034198413209908788402            
y[1] (numeric)                    = 0.33920267020341984132099087884018           
absolute error                    = 2e-32                                        
relative error                    = 5.8961800000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.718                                       
y[1] (closed_form)                = 0.33880790438840938159087251505578           
y[1] (numeric)                    = 0.33880790438840938159087251505576           
absolute error                    = 2e-32                                        
relative error                    = 5.9030499999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.719                                       
y[1] (closed_form)                = 0.33841382731825316196959554809842           
y[1] (numeric)                    = 0.3384138273182531619695955480984            
absolute error                    = 2e-32                                        
relative error                    = 5.9099240000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.72                                        
y[1] (closed_form)                = 0.3380204373916855760933017532106            
y[1] (numeric)                    = 0.33802043739168557609330175321058           
absolute error                    = 2e-32                                        
relative error                    = 5.9168020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.721                                       
y[1] (closed_form)                = 0.33762773301209179963009505571195           
y[1] (numeric)                    = 0.33762773301209179963009505571193           
absolute error                    = 2e-32                                        
relative error                    = 5.9236840000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.722                                       
y[1] (closed_form)                = 0.33723571258749159018441734942847           
y[1] (numeric)                    = 0.33723571258749159018441734942845           
absolute error                    = 2e-32                                        
relative error                    = 5.9305700000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.723                                       
y[1] (closed_form)                = 0.33684437453052315299808335550892           
y[1] (numeric)                    = 0.3368443745305231529980833555089            
absolute error                    = 2e-32                                        
relative error                    = 5.9374600000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.724                                       
y[1] (closed_form)                = 0.33645371725842707214274250826919           
y[1] (numeric)                    = 0.33645371725842707214274250826917           
absolute error                    = 2e-32                                        
relative error                    = 5.9443540000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.725                                       
y[1] (closed_form)                = 0.33606373919303030690012790585914           
y[1] (numeric)                    = 0.33606373919303030690012790585912           
absolute error                    = 2e-32                                        
relative error                    = 5.9512519999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.726                                       
y[1] (closed_form)                = 0.33567443876073025302803519345086           
y[1] (numeric)                    = 0.33567443876073025302803519345084           
absolute error                    = 2e-32                                        
relative error                    = 5.9581540000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.727                                       
y[1] (closed_form)                = 0.33528581439247886861154791401931           
y[1] (numeric)                    = 0.33528581439247886861154791401929           
absolute error                    = 2e-32                                        
relative error                    = 5.9650599999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.728                                       
y[1] (closed_form)                = 0.33489786452376686420059042493516           
y[1] (numeric)                    = 0.33489786452376686420059042493514           
absolute error                    = 2e-32                                        
relative error                    = 5.9719699999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.729                                       
y[1] (closed_form)                = 0.33451058759460795693644499542055           
y[1] (numeric)                    = 0.33451058759460795693644499542053           
absolute error                    = 2e-32                                        
relative error                    = 5.9788840000000000000000000000000e-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)                = 0.33412398204952318837141622793403           
y[1] (numeric)                    = 0.33412398204952318837141622793401           
absolute error                    = 2e-32                                        
relative error                    = 5.9858020000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.731                                       
y[1] (closed_form)                = 0.3337380463375253056873635428563            
y[1] (numeric)                    = 0.33373804633752530568736354285628           
absolute error                    = 2e-32                                        
relative error                    = 5.9927240000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.732                                       
y[1] (closed_form)                = 0.33335277891210320602035118715258           
y[1] (numeric)                    = 0.33335277891210320602035118715256           
absolute error                    = 2e-32                                        
relative error                    = 5.9996500000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.733                                       
y[1] (closed_form)                = 0.3329681782312064436001851303071            
y[1] (numeric)                    = 0.33296817823120644360018513030707           
absolute error                    = 3e-32                                        
relative error                    = 9.0098699999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.734                                       
y[1] (closed_form)                = 0.33258424275722979941511735068714           
y[1] (numeric)                    = 0.33258424275722979941511735068711           
absolute error                    = 3e-32                                        
relative error                    = 9.0202709999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.735                                       
y[1] (closed_form)                = 0.33220097095699791311350044813911           
y[1] (numeric)                    = 0.33220097095699791311350044813908           
absolute error                    = 3e-32                                        
relative error                    = 9.0306780000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.736                                       
y[1] (closed_form)                = 0.33181836130174997685566929920294           
y[1] (numeric)                    = 0.33181836130174997685566929920291           
absolute error                    = 3e-32                                        
relative error                    = 9.0410910000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.737                                       
y[1] (closed_form)                = 0.33143641226712449083081165463              
y[1] (numeric)                    = 0.33143641226712449083081165462997           
absolute error                    = 3e-32                                        
relative error                    = 9.0515100000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.738                                       
y[1] (closed_form)                = 0.33105512233314408015506621930084           
y[1] (numeric)                    = 0.33105512233314408015506621930081           
absolute error                    = 3e-32                                        
relative error                    = 9.0619350000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.739                                       
y[1] (closed_form)                = 0.33067448998420037286855490618434           
y[1] (numeric)                    = 0.33067448998420037286855490618431           
absolute error                    = 3e-32                                        
relative error                    = 9.0723660000000000000000000000000e-30      % 
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)                = 0.33029451370903893875051567230953           
y[1] (numeric)                    = 0.3302945137090389387505156723095            
absolute error                    = 3e-32                                        
relative error                    = 9.0828030000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.741                                       
y[1] (closed_form)                = 0.32991519200074428867315367911525           
y[1] (numeric)                    = 0.32991519200074428867315367911522           
absolute error                    = 3e-32                                        
relative error                    = 9.0932459999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.742                                       
y[1] (closed_form)                = 0.32953652335672493421627152491378           
y[1] (numeric)                    = 0.32953652335672493421627152491376           
absolute error                    = 2e-32                                        
relative error                    = 6.0691300000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.743                                       
y[1] (closed_form)                = 0.32915850627869850726617402610227           
y[1] (numeric)                    = 0.32915850627869850726617402610224           
absolute error                    = 3e-32                                        
relative error                    = 9.1141500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.744                                       
y[1] (closed_form)                = 0.32878113927267693932376952836674           
y[1] (numeric)                    = 0.32878113927267693932376952836671           
absolute error                    = 3e-32                                        
relative error                    = 9.1246110000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.745                                       
y[1] (closed_form)                = 0.32840442084895170024820806127764           
y[1] (numeric)                    = 0.3284044208489517002482080612776            
absolute error                    = 4e-32                                        
relative error                    = 1.2180104000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.746                                       
y[1] (closed_form)                = 0.32802834952207909616380686084414           
y[1] (numeric)                    = 0.3280283495220790961638068608441            
absolute error                    = 4e-32                                        
relative error                    = 1.2194068000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.747                                       
y[1] (closed_form)                = 0.32765292381086562625941592589801           
y[1] (numeric)                    = 0.32765292381086562625941592589797           
absolute error                    = 4e-32                                        
relative error                    = 1.2208040000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.748                                       
y[1] (closed_form)                = 0.32727814223835339821077039638292           
y[1] (numeric)                    = 0.32727814223835339821077039638288           
absolute error                    = 4e-32                                        
relative error                    = 1.2222020000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.749                                       
y[1] (closed_form)                = 0.32690400333180560195776269515352           
y[1] (numeric)                    = 0.32690400333180560195776269515348           
absolute error                    = 4e-32                                        
relative error                    = 1.2236008000000000000000000000000e-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)                = 0.32653050562269204156994560981368           
y[1] (numeric)                    = 0.32653050562269204156994560981364           
absolute error                    = 4e-32                                        
relative error                    = 1.2250004000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.751                                       
y[1] (closed_form)                = 0.32615764764667472493494785717687           
y[1] (numeric)                    = 0.32615764764667472493494785717683           
absolute error                    = 4e-32                                        
relative error                    = 1.2264008000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.752                                       
y[1] (closed_form)                = 0.32578542794359351100584621950445           
y[1] (numeric)                    = 0.32578542794359351100584621950441           
absolute error                    = 4e-32                                        
relative error                    = 1.2278020000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.753                                       
y[1] (closed_form)                = 0.32541384505745181434489311782259           
y[1] (numeric)                    = 0.32541384505745181434489311782255           
absolute error                    = 4e-32                                        
relative error                    = 1.2292040000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.754                                       
y[1] (closed_form)                = 0.32504289753640236670234554205291           
y[1] (numeric)                    = 0.32504289753640236670234554205287           
absolute error                    = 4e-32                                        
relative error                    = 1.2306068000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.755                                       
y[1] (closed_form)                = 0.3246725839327330353704806387998            
y[1] (numeric)                    = 0.32467258393273303537048063879976           
absolute error                    = 4e-32                                        
relative error                    = 1.2320104000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.756                                       
y[1] (closed_form)                = 0.32430290280285269805421501347316           
y[1] (numeric)                    = 0.32430290280285269805421501347312           
absolute error                    = 4e-32                                        
relative error                    = 1.2334148000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.757                                       
y[1] (closed_form)                = 0.32393385270727717400106898171393           
y[1] (numeric)                    = 0.32393385270727717400106898171389           
absolute error                    = 4e-32                                        
relative error                    = 1.2348200000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.758                                       
y[1] (closed_form)                = 0.32356543221061521113453365323169           
y[1] (numeric)                    = 0.32356543221061521113453365323165           
absolute error                    = 4e-32                                        
relative error                    = 1.2362260000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.759                                       
y[1] (closed_form)                = 0.32319763988155452893620789623546           
y[1] (numeric)                    = 0.32319763988155452893620789623542           
absolute error                    = 4e-32                                        
relative error                    = 1.2376328000000000000000000000000e-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)                = 0.32283047429284791682337395939632           
y[1] (numeric)                    = 0.32283047429284791682337395939628           
absolute error                    = 4e-32                                        
relative error                    = 1.2390404000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.761                                       
y[1] (closed_form)                = 0.32246393402129938776997486716098           
y[1] (numeric)                    = 0.32246393402129938776997486716094           
absolute error                    = 4e-32                                        
relative error                    = 1.2404488000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.762                                       
y[1] (closed_form)                = 0.32209801764775038692024369936015           
y[1] (numeric)                    = 0.32209801764775038692024369936011           
absolute error                    = 4e-32                                        
relative error                    = 1.2418580000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.763                                       
y[1] (closed_form)                = 0.32173272375706605494551456323174           
y[1] (numeric)                    = 0.3217327237570660549455145632317            
absolute error                    = 4e-32                                        
relative error                    = 1.2432680000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.764                                       
y[1] (closed_form)                = 0.32136805093812154589601751070236           
y[1] (numeric)                    = 0.32136805093812154589601751070232           
absolute error                    = 4e-32                                        
relative error                    = 1.2446788000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.765                                       
y[1] (closed_form)                = 0.3210039977837883993007248912278            
y[1] (numeric)                    = 0.32100399778378839930072489122776           
absolute error                    = 4e-32                                        
relative error                    = 1.2460904000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.766                                       
y[1] (closed_form)                = 0.32064056289092096626957470556379           
y[1] (numeric)                    = 0.32064056289092096626957470556375           
absolute error                    = 4e-32                                        
relative error                    = 1.2475028000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.767                                       
y[1] (closed_form)                = 0.32027774486034288935364748309734           
y[1] (numeric)                    = 0.3202777448603428893536474830973            
absolute error                    = 4e-32                                        
relative error                    = 1.2489160000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.768                                       
y[1] (closed_form)                = 0.31991554229683363592011708908848           
y[1] (numeric)                    = 0.31991554229683363592011708908844           
absolute error                    = 4e-32                                        
relative error                    = 1.2503300000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.769                                       
y[1] (closed_form)                = 0.31955395380911508480003272232487           
y[1] (numeric)                    = 0.31955395380911508480003272232483           
absolute error                    = 4e-32                                        
relative error                    = 1.2517448000000000000000000000000e-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)                = 0.31919297800983816596821923195147           
y[1] (numeric)                    = 0.31919297800983816596821923195143           
absolute error                    = 4e-32                                        
relative error                    = 1.2531604000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.771                                       
y[1] (closed_form)                = 0.31883261351556955301580580798242           
y[1] (numeric)                    = 0.31883261351556955301580580798238           
absolute error                    = 4e-32                                        
relative error                    = 1.2545768000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.772                                       
y[1] (closed_form)                = 0.31847285894677840817710912631748           
y[1] (numeric)                    = 0.31847285894677840817710912631744           
absolute error                    = 4e-32                                        
relative error                    = 1.2559940000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.773                                       
y[1] (closed_form)                = 0.31811371292782317967380619876381           
y[1] (numeric)                    = 0.31811371292782317967380619876377           
absolute error                    = 4e-32                                        
relative error                    = 1.2574120000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.774                                       
y[1] (closed_form)                = 0.31775517408693845114053453410895           
y[1] (numeric)                    = 0.31775517408693845114053453410891           
absolute error                    = 4e-32                                        
relative error                    = 1.2588308000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=44.3MB, time=1.20
x[1]                              = -1.775                                       
y[1] (closed_form)                = 0.31739724105622184289725279991976           
y[1] (numeric)                    = 0.31739724105622184289725279991972           
absolute error                    = 4e-32                                        
relative error                    = 1.2602504000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.776                                       
y[1] (closed_form)                = 0.31703991247162096483488402838522           
y[1] (numeric)                    = 0.31703991247162096483488402838518           
absolute error                    = 4e-32                                        
relative error                    = 1.2616708000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.777                                       
y[1] (closed_form)                = 0.31668318697292042068194557482749           
y[1] (numeric)                    = 0.31668318697292042068194557482745           
absolute error                    = 4e-32                                        
relative error                    = 1.2630920000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.778                                       
y[1] (closed_form)                = 0.31632706320372886342104555584201           
y[1] (numeric)                    = 0.31632706320372886342104555584197           
absolute error                    = 4e-32                                        
relative error                    = 1.2645140000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.779                                       
y[1] (closed_form)                = 0.31597153981146610162529440648222           
y[1] (numeric)                    = 0.31597153981146610162529440648218           
absolute error                    = 4e-32                                        
relative error                    = 1.2659368000000000000000000000000e-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)                = 0.31561661544735025648584254328919           
y[1] (numeric)                    = 0.31561661544735025648584254328915           
absolute error                    = 4e-32                                        
relative error                    = 1.2673604000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.781                                       
y[1] (closed_form)                = 0.3152622887663849693029109428171            
y[1] (numeric)                    = 0.31526228876638496930291094281706           
absolute error                    = 4e-32                                        
relative error                    = 1.2687848000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.782                                       
y[1] (closed_form)                = 0.31490855842734665921383078388613           
y[1] (numeric)                    = 0.31490855842734665921383078388609           
absolute error                    = 4e-32                                        
relative error                    = 1.2702100000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.783                                       
y[1] (closed_form)                = 0.314555423092771830932751196097             
y[1] (numeric)                    = 0.31455542309277183093275119609696           
absolute error                    = 4e-32                                        
relative error                    = 1.2716360000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.784                                       
y[1] (closed_form)                = 0.31420288142894443227781064689032           
y[1] (numeric)                    = 0.31420288142894443227781064689028           
absolute error                    = 4e-32                                        
relative error                    = 1.2730628000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.785                                       
y[1] (closed_form)                = 0.31385093210588326126269762408567           
y[1] (numeric)                    = 0.31385093210588326126269762408564           
absolute error                    = 3e-32                                        
relative error                    = 9.5586780000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.786                                       
y[1] (closed_form)                = 0.31349957379732942253065006958123           
y[1] (numeric)                    = 0.3134995737973294225306500695812            
absolute error                    = 3e-32                                        
relative error                    = 9.5693910000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.787                                       
y[1] (closed_form)                = 0.31314880518073383291006053166404           
y[1] (numeric)                    = 0.31314880518073383291006053166401           
absolute error                    = 3e-32                                        
relative error                    = 9.5801100000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.788                                       
y[1] (closed_form)                = 0.31279862493724477587196526684069           
y[1] (numeric)                    = 0.31279862493724477587196526684066           
absolute error                    = 3e-32                                        
relative error                    = 9.5908349999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.789                                       
y[1] (closed_form)                = 0.3124490317516955046708005756561            
y[1] (numeric)                    = 0.31244903175169550467080057565607           
absolute error                    = 3e-32                                        
relative error                    = 9.6015659999999999999999999999999e-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)                = 0.31210002431259189395090853877578           
y[1] (numeric)                    = 0.31210002431259189395090853877575           
absolute error                    = 3e-32                                        
relative error                    = 9.6123029999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.791                                       
y[1] (closed_form)                = 0.31175160131210013960236706755844           
y[1] (numeric)                    = 0.31175160131210013960236706755842           
absolute error                    = 2e-32                                        
relative error                    = 6.4153640000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.792                                       
y[1] (closed_form)                = 0.31140376144603450665080583508368           
y[1] (numeric)                    = 0.31140376144603450665080583508366           
absolute error                    = 2e-32                                        
relative error                    = 6.4225300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.793                                       
y[1] (closed_form)                = 0.31105650341384512496695024651228           
y[1] (numeric)                    = 0.31105650341384512496695024651226           
absolute error                    = 2e-32                                        
relative error                    = 6.4297000000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.794                                       
y[1] (closed_form)                = 0.31070982591860583258271017888497           
y[1] (numeric)                    = 0.31070982591860583258271017888495           
absolute error                    = 2e-32                                        
relative error                    = 6.4368740000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.795                                       
y[1] (closed_form)                = 0.31036372766700206640169880689976           
y[1] (numeric)                    = 0.31036372766700206640169880689974           
absolute error                    = 2e-32                                        
relative error                    = 6.4440520000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.796                                       
y[1] (closed_form)                = 0.31001820736931880009312946949374           
y[1] (numeric)                    = 0.31001820736931880009312946949373           
absolute error                    = 1e-32                                        
relative error                    = 3.2256170000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.797                                       
y[1] (closed_form)                = 0.30967326373942852895909525859266           
y[1] (numeric)                    = 0.30967326373942852895909525859265           
absolute error                    = 1e-32                                        
relative error                    = 3.2292100000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.798                                       
y[1] (closed_form)                = 0.30932889549477930156628686233781           
y[1] (numeric)                    = 0.30932889549477930156628686233781           
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]                              = -1.799                                       
y[1] (closed_form)                = 0.30898510135638279793424920637177           
y[1] (numeric)                    = 0.30898510135638279793424920637176           
absolute error                    = 1e-32                                        
relative error                    = 3.2364020000000000000000000000000e-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)                = 0.30864188004880245407331664403807           
y[1] (numeric)                    = 0.30864188004880245407331664403807           
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]                              = -1.801                                       
y[1] (closed_form)                = 0.30829923030014163266639988506605           
y[1] (numeric)                    = 0.30829923030014163266639988506604           
absolute error                    = 1e-32                                        
relative error                    = 3.2436020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.802                                       
y[1] (closed_form)                = 0.30795715084203183968982555767191           
y[1] (numeric)                    = 0.3079571508420318396898255576719            
absolute error                    = 1e-32                                        
relative error                    = 3.2472050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.803                                       
y[1] (closed_form)                = 0.3076156404096209867694513059822            
y[1] (numeric)                    = 0.3076156404096209867694513059822            
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]                              = -1.804                                       
y[1] (closed_form)                = 0.30727469774156169906929566801058           
y[1] (numeric)                    = 0.30727469774156169906929566801058           
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]                              = -1.805                                       
y[1] (closed_form)                = 0.30693432157999966851093269360036           
y[1] (numeric)                    = 0.30693432157999966851093269360035           
absolute error                    = 1e-32                                        
relative error                    = 3.2580260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.806                                       
y[1] (closed_form)                = 0.30659451067056205212290638105957           
y[1] (numeric)                    = 0.30659451067056205212290638105956           
absolute error                    = 1e-32                                        
relative error                    = 3.2616370000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.807                                       
y[1] (closed_form)                = 0.30625526376234591532041956971135           
y[1] (numeric)                    = 0.30625526376234591532041956971134           
absolute error                    = 1e-32                                        
relative error                    = 3.2652500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.808                                       
y[1] (closed_form)                = 0.30591657960790671991654595708296           
y[1] (numeric)                    = 0.30591657960790671991654595708295           
absolute error                    = 1e-32                                        
relative error                    = 3.2688650000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.809                                       
y[1] (closed_form)                = 0.30557845696324685666720244756121           
y[1] (numeric)                    = 0.3055784569632468566672024475612            
absolute error                    = 1e-32                                        
relative error                    = 3.2724820000000000000000000000000e-30      % 
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)                = 0.30524089458780422215310211742556           
y[1] (numeric)                    = 0.30524089458780422215310211742555           
absolute error                    = 1e-32                                        
relative error                    = 3.2761010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.811                                       
y[1] (closed_form)                = 0.30490389124444083980288573238829           
y[1] (numeric)                    = 0.30490389124444083980288573238828           
absolute error                    = 1e-32                                        
relative error                    = 3.2797220000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.812                                       
y[1] (closed_form)                = 0.30456744569943152486260201105884           
y[1] (numeric)                    = 0.30456744569943152486260201105883           
absolute error                    = 1e-32                                        
relative error                    = 3.2833450000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.813                                       
y[1] (closed_form)                = 0.30423155672245259311767372382468           
y[1] (numeric)                    = 0.30423155672245259311767372382466           
absolute error                    = 2e-32                                        
relative error                    = 6.5739399999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.814                                       
y[1] (closed_form)                = 0.30389622308657061317444828400439           
y[1] (numeric)                    = 0.30389622308657061317444828400437           
absolute error                    = 2e-32                                        
relative error                    = 6.5811940000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.815                                       
y[1] (closed_form)                = 0.30356144356823120210938775906692           
y[1] (numeric)                    = 0.3035614435682312021093877590669            
absolute error                    = 2e-32                                        
relative error                    = 6.5884520000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.816                                       
y[1] (closed_form)                = 0.30322721694724786429490423629648           
y[1] (numeric)                    = 0.30322721694724786429490423629645           
absolute error                    = 3e-32                                        
relative error                    = 9.8935710000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.817                                       
y[1] (closed_form)                = 0.30289354200679087321179225137741           
y[1] (numeric)                    = 0.30289354200679087321179225137738           
absolute error                    = 3e-32                                        
relative error                    = 9.9044699999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.818                                       
y[1] (closed_form)                = 0.30256041753337619605915056162778           
y[1] (numeric)                    = 0.30256041753337619605915056162775           
absolute error                    = 3e-32                                        
relative error                    = 9.9153749999999999999999999999998e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.819                                       
y[1] (closed_form)                = 0.3022278423168544609736209494669            
y[1] (numeric)                    = 0.30222784231685446097362094946688           
absolute error                    = 2e-32                                        
relative error                    = 6.6175240000000000000000000000000e-30      % 
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)                = 0.30189581515039996667070200739584           
y[1] (numeric)                    = 0.30189581515039996667070200739582           
absolute error                    = 2e-32                                        
relative error                    = 6.6248020000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.821                                       
y[1] (closed_form)                = 0.30156433483049973432182101432973           
y[1] (numeric)                    = 0.30156433483049973432182101432971           
absolute error                    = 2e-32                                        
relative error                    = 6.6320840000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.822                                       
y[1] (closed_form)                = 0.301233400156942601481767095372             
y[1] (numeric)                    = 0.30123340015694260148176709537198           
absolute error                    = 2e-32                                        
relative error                    = 6.6393700000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.823                                       
y[1] (closed_form)                = 0.30090300993280835788200389368495           
y[1] (numeric)                    = 0.30090300993280835788200389368493           
absolute error                    = 2e-32                                        
relative error                    = 6.6466600000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.824                                       
y[1] (closed_form)                = 0.30057316296445692290629000440941           
y[1] (numeric)                    = 0.30057316296445692290629000440939           
absolute error                    = 2e-32                                        
relative error                    = 6.6539540000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.825                                       
y[1] (closed_form)                = 0.30024385806151756456594045683904           
y[1] (numeric)                    = 0.30024385806151756456594045683903           
absolute error                    = 1e-32                                        
relative error                    = 3.3306260000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.826                                       
y[1] (closed_form)                = 0.29991509403687815979296261228446           
y[1] (numeric)                    = 0.29991509403687815979296261228445           
absolute error                    = 1e-32                                        
relative error                    = 3.3342770000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.827                                       
y[1] (closed_form)                = 0.29958686970667449587019500109349           
y[1] (numeric)                    = 0.29958686970667449587019500109348           
absolute error                    = 1e-32                                        
relative error                    = 3.3379300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.828                                       
y[1] (closed_form)                = 0.29925918389027961281846788275624           
y[1] (numeric)                    = 0.29925918389027961281846788275622           
absolute error                    = 2e-32                                        
relative error                    = 6.6831699999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.829                                       
y[1] (closed_form)                = 0.29893203541029318656168970735152           
y[1] (numeric)                    = 0.2989320354102931865616897073515            
absolute error                    = 2e-32                                        
relative error                    = 6.6904839999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.83                                        
y[1] (closed_form)                = 0.29860542309253095269164421402723           
y[1] (numeric)                    = 0.29860542309253095269164421402721           
absolute error                    = 2e-32                                        
relative error                    = 6.6978020000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.831                                       
y[1] (closed_form)                = 0.29827934576601417065515865180122           
y[1] (numeric)                    = 0.2982793457660141706551586518012            
absolute error                    = 2e-32                                        
relative error                    = 6.7051240000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.832                                       
y[1] (closed_form)                = 0.29795380226295912818717457858159           
y[1] (numeric)                    = 0.29795380226295912818717457858157           
absolute error                    = 2e-32                                        
relative error                    = 6.7124500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.833                                       
y[1] (closed_form)                = 0.29762879141876668581411891460732           
y[1] (numeric)                    = 0.2976287914187666858141189146073            
absolute error                    = 2e-32                                        
relative error                    = 6.7197800000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.834                                       
y[1] (closed_form)                = 0.29730431207201186125283442498522           
y[1] (numeric)                    = 0.29730431207201186125283442498519           
absolute error                    = 3e-32                                        
relative error                    = 1.0090671000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.835                                       
y[1] (closed_form)                = 0.29698036306443345353118561094503           
y[1] (numeric)                    = 0.29698036306443345353118561094501           
absolute error                    = 2e-32                                        
relative error                    = 6.7344520000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.836                                       
y[1] (closed_form)                = 0.29665694324092370665730812896389           
y[1] (numeric)                    = 0.29665694324092370665730812896387           
absolute error                    = 2e-32                                        
relative error                    = 6.7417940000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.837                                       
y[1] (closed_form)                = 0.2963340514495180126653173589524            
y[1] (numeric)                    = 0.29633405144951801266531735895238           
absolute error                    = 2e-32                                        
relative error                    = 6.7491400000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.838                                       
y[1] (closed_form)                = 0.29601168654138465386613463499539           
y[1] (numeric)                    = 0.29601168654138465386613463499537           
absolute error                    = 2e-32                                        
relative error                    = 6.7564900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.839                                       
y[1] (closed_form)                = 0.29568984737081458413292796226524           
y[1] (numeric)                    = 0.29568984737081458413292796226522           
absolute error                    = 2e-32                                        
relative error                    = 6.7638440000000000000000000000001e-30      % 
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)                = 0.29536853279521124905149779906138           
y[1] (numeric)                    = 0.29536853279521124905149779906135           
absolute error                    = 3e-32                                        
relative error                    = 1.0156803000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.841                                       
y[1] (closed_form)                = 0.29504774167508044476676771068327           
y[1] (numeric)                    = 0.29504774167508044476676771068324           
absolute error                    = 3e-32                                        
relative error                    = 1.0167846000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.842                                       
y[1] (closed_form)                = 0.29472747287402021535736442904657           
y[1] (numeric)                    = 0.29472747287402021535736442904655           
absolute error                    = 2e-32                                        
relative error                    = 6.7859300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.843                                       
y[1] (closed_form)                = 0.29440772525871078857109210545685           
y[1] (numeric)                    = 0.29440772525871078857109210545683           
absolute error                    = 2e-32                                        
relative error                    = 6.7932999999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.844                                       
y[1] (closed_form)                = 0.29408849769890454975492135044262           
y[1] (numeric)                    = 0.2940884976989045497549213504426            
absolute error                    = 2e-32                                        
relative error                    = 6.8006740000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.845                                       
y[1] (closed_form)                = 0.29376978906741605381392504052554           
y[1] (numeric)                    = 0.29376978906741605381392504052552           
absolute error                    = 2e-32                                        
relative error                    = 6.8080520000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.846                                       
y[1] (closed_form)                = 0.2934515982401120750343998636037            
y[1] (numeric)                    = 0.29345159824011207503439986360367           
absolute error                    = 3e-32                                        
relative error                    = 1.0223151000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.847                                       
y[1] (closed_form)                = 0.2931339240959016946072151984077            
y[1] (numeric)                    = 0.29313392409590169460721519840767           
absolute error                    = 3e-32                                        
relative error                    = 1.0234230000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.848                                       
y[1] (closed_form)                = 0.29281676551672642568822920525138           
y[1] (numeric)                    = 0.29281676551672642568822920525135           
absolute error                    = 3e-32                                        
relative error                    = 1.0245315000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.849                                       
y[1] (closed_form)                = 0.29250012138755037583340597086348           
y[1] (numeric)                    = 0.29250012138755037583340597086345           
absolute error                    = 3e-32                                        
relative error                    = 1.0256406000000000000000000000000e-29      % 
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)                = 0.29218399059635044664705722511111           
y[1] (numeric)                    = 0.29218399059635044664705722511108           
absolute error                    = 3e-32                                        
relative error                    = 1.0267503000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.851                                       
y[1] (closed_form)                = 0.29186837203410657048241755740029           
y[1] (numeric)                    = 0.29186837203410657048241755740026           
absolute error                    = 3e-32                                        
relative error                    = 1.0278606000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.852                                       
y[1] (closed_form)                = 0.29155326459479198403454323078919           
y[1] (numeric)                    = 0.29155326459479198403454323078916           
absolute error                    = 3e-32                                        
relative error                    = 1.0289715000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.853                                       
y[1] (closed_form)                = 0.29123866717536353866630164753714           
y[1] (numeric)                    = 0.29123866717536353866630164753711           
absolute error                    = 3e-32                                        
relative error                    = 1.0300830000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.854                                       
y[1] (closed_form)                = 0.29092457867575204730899128593609           
y[1] (numeric)                    = 0.29092457867575204730899128593606           
absolute error                    = 3e-32                                        
relative error                    = 1.0311951000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.855                                       
y[1] (closed_form)                = 0.2906109979988526677799005296676            
y[1] (numeric)                    = 0.29061099799885266777990052966757           
absolute error                    = 3e-32                                        
relative error                    = 1.0323078000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.856                                       
y[1] (closed_form)                = 0.29029792405051532235987827227449           
y[1] (numeric)                    = 0.29029792405051532235987827227445           
absolute error                    = 4e-32                                        
relative error                    = 1.3778948000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.857                                       
y[1] (closed_form)                = 0.28998535573953515347474952514898           
y[1] (numeric)                    = 0.28998535573953515347474952514894           
absolute error                    = 4e-32                                        
relative error                    = 1.3793800000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.858                                       
y[1] (closed_form)                = 0.2896732919776430153251655120772            
y[1] (numeric)                    = 0.28967329197764301532516551207716           
absolute error                    = 4e-32                                        
relative error                    = 1.3808660000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.859                                       
y[1] (closed_form)                = 0.28936173167949600131022992104476           
y[1] (numeric)                    = 0.28936173167949600131022992104471           
absolute error                    = 5e-32                                        
relative error                    = 1.7279410000000000000000000000000e-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)                = 0.28905067376266800709099112874577           
y[1] (numeric)                    = 0.28905067376266800709099112874572           
absolute error                    = 5e-32                                        
relative error                    = 1.7298005000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.861                                       
y[1] (closed_form)                = 0.28874011714764032914063433893816           
y[1] (numeric)                    = 0.28874011714764032914063433893811           
absolute error                    = 5e-32                                        
relative error                    = 1.7316610000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.862                                       
y[1] (closed_form)                = 0.28843006075779229862894770618783           
y[1] (numeric)                    = 0.28843006075779229862894770618778           
absolute error                    = 5e-32                                        
relative error                    = 1.7335225000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.863                                       
y[1] (closed_form)                = 0.28812050351939195048937267522769           
y[1] (numeric)                    = 0.28812050351939195048937267522763           
absolute error                    = 6e-32                                        
relative error                    = 2.0824620000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.864                                       
y[1] (closed_form)                = 0.28781144436158672751768097655574           
y[1] (numeric)                    = 0.28781144436158672751768097655569           
absolute error                    = 5e-32                                        
relative error                    = 1.7372485000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.865                                       
y[1] (closed_form)                = 0.28750288221639421935204900429127           
y[1] (numeric)                    = 0.28750288221639421935204900429121           
absolute error                    = 6e-32                                        
relative error                    = 2.0869356000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.866                                       
y[1] (closed_form)                = 0.28719481601869293618502468583041           
y[1] (numeric)                    = 0.28719481601869293618502468583035           
absolute error                    = 6e-32                                        
relative error                    = 2.0891742000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.867                                       
y[1] (closed_form)                = 0.28688724470621311705860245747614           
y[1] (numeric)                    = 0.28688724470621311705860245747608           
absolute error                    = 6e-32                                        
relative error                    = 2.0914140000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.868                                       
y[1] (closed_form)                = 0.28658016721952757259433860879658           
y[1] (numeric)                    = 0.28658016721952757259433860879652           
absolute error                    = 6e-32                                        
relative error                    = 2.0936550000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.869                                       
y[1] (closed_form)                = 0.28627358250204256201115207367995           
y[1] (numeric)                    = 0.28627358250204256201115207367989           
absolute error                    = 6e-32                                        
relative error                    = 2.0958972000000000000000000000000e-29      % 
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)                = 0.28596748949998870428416475044618           
y[1] (numeric)                    = 0.28596748949998870428416475044612           
absolute error                    = 6e-32                                        
relative error                    = 2.0981406000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.871                                       
y[1] (closed_form)                = 0.28566188716241192329864064934375           
y[1] (numeric)                    = 0.28566188716241192329864064934369           
absolute error                    = 6e-32                                        
relative error                    = 2.1003852000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.872                                       
y[1] (closed_form)                = 0.28535677444116442685378461556022           
y[1] (numeric)                    = 0.28535677444116442685378461556016           
absolute error                    = 6e-32                                        
relative error                    = 2.1026310000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.873                                       
y[1] (closed_form)                = 0.28505215029089571937185908161898           
y[1] (numeric)                    = 0.28505215029089571937185908161892           
absolute error                    = 6e-32                                        
relative error                    = 2.1048780000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.874                                       
y[1] (closed_form)                = 0.2847480136690436481687712866937            
y[1] (numeric)                    = 0.28474801366904364816877128669363           
absolute error                    = 7e-32                                        
relative error                    = 2.4583139000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.875                                       
y[1] (closed_form)                = 0.28444436353582548314297368377637           
y[1] (numeric)                    = 0.28444436353582548314297368377631           
absolute error                    = 6e-32                                        
relative error                    = 2.1093756000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.876                                       
y[1] (closed_form)                = 0.28414119885422902974020686047559           
y[1] (numeric)                    = 0.28414119885422902974020686047553           
absolute error                    = 6e-32                                        
relative error                    = 2.1116262000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.877                                       
y[1] (closed_form)                = 0.28383851859000377505229724705021           
y[1] (numeric)                    = 0.28383851859000377505229724705015           
absolute error                    = 6e-32                                        
relative error                    = 2.1138780000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.878                                       
y[1] (closed_form)                = 0.28353632171165206690890119751565           
y[1] (numeric)                    = 0.2835363217116520669089011975156            
absolute error                    = 5e-32                                        
relative error                    = 1.7634425000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.879                                       
y[1] (closed_form)                = 0.28323460719042032582176272757193           
y[1] (numeric)                    = 0.28323460719042032582176272757187           
absolute error                    = 6e-32                                        
relative error                    = 2.1183852000000000000000000000000e-29      % 
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)                = 0.28293337400029028964172429783717           
y[1] (numeric)                    = 0.28293337400029028964172429783712           
absolute error                    = 5e-32                                        
relative error                    = 1.7672005000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.881                                       
y[1] (closed_form)                = 0.28263262111797029078939856343491           
y[1] (numeric)                    = 0.28263262111797029078939856343486           
absolute error                    = 5e-32                                        
relative error                    = 1.7690810000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.882                                       
y[1] (closed_form)                = 0.28233234752288656592107399224998           
y[1] (numeric)                    = 0.28233234752288656592107399224992           
absolute error                    = 6e-32                                        
relative error                    = 2.1251550000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.883                                       
y[1] (closed_form)                = 0.28203255219717459789208870487832           
y[1] (numeric)                    = 0.28203255219717459789208870487826           
absolute error                    = 6e-32                                        
relative error                    = 2.1274140000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.884                                       
y[1] (closed_form)                = 0.2817332341256704898805648300571            
y[1] (numeric)                    = 0.28173323412567048988056483005705           
absolute error                    = 5e-32                                        
relative error                    = 1.7747285000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.885                                       
y[1] (closed_form)                = 0.28143439229590237153505012065092           
y[1] (numeric)                    = 0.28143439229590237153505012065087           
absolute error                    = 5e-32                                        
relative error                    = 1.7766130000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.886                                       
y[1] (closed_form)                = 0.28113602569808183701026455743426           
y[1] (numeric)                    = 0.28113602569808183701026455743421           
absolute error                    = 5e-32                                        
relative error                    = 1.7784985000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.887                                       
y[1] (closed_form)                = 0.28083813332509541475579720116716           
y[1] (numeric)                    = 0.28083813332509541475579720116711           
absolute error                    = 5e-32                                        
relative error                    = 1.7803850000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.888                                       
y[1] (closed_form)                = 0.28054071417249606892324265789883           
y[1] (numeric)                    = 0.28054071417249606892324265789878           
absolute error                    = 5e-32                                        
relative error                    = 1.7822725000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.889                                       
y[1] (closed_form)                = 0.28024376723849473225790721801452           
y[1] (numeric)                    = 0.28024376723849473225790721801446           
absolute error                    = 6e-32                                        
relative error                    = 2.1409932000000000000000000000000e-29      % 
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)                = 0.27994729152395187034185203609864           
y[1] (numeric)                    = 0.27994729152395187034185203609859           
absolute error                    = 5e-32                                        
relative error                    = 1.7860505000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.891                                       
y[1] (closed_form)                = 0.27965128603236907705567465593104           
y[1] (numeric)                    = 0.27965128603236907705567465593099           
absolute error                    = 5e-32                                        
relative error                    = 1.7879410000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.892                                       
y[1] (closed_form)                = 0.27935574976988070112706077244658           
y[1] (numeric)                    = 0.27935574976988070112706077244653           
absolute error                    = 5e-32                                        
relative error                    = 1.7898325000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.893                                       
y[1] (closed_form)                = 0.27906068174524550363476537973182           
y[1] (numeric)                    = 0.27906068174524550363476537973177           
absolute error                    = 5e-32                                        
relative error                    = 1.7917250000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.894                                       
y[1] (closed_form)                = 0.27876608096983834633730640044134           
y[1] (numeric)                    = 0.27876608096983834633730640044129           
absolute error                    = 5e-32                                        
relative error                    = 1.7936185000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.895                                       
y[1] (closed_form)                = 0.2784719464576419106962745466059            
y[1] (numeric)                    = 0.27847194645764191069627454660585           
absolute error                    = 5e-32                                        
relative error                    = 1.7955130000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.896                                       
y[1] (closed_form)                = 0.27817827722523844746478054376621           
y[1] (numeric)                    = 0.27817827722523844746478054376616           
absolute error                    = 5e-32                                        
relative error                    = 1.7974085000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.897                                       
y[1] (closed_form)                = 0.27788507229180155671217497867232           
y[1] (numeric)                    = 0.27788507229180155671217497867228           
absolute error                    = 4e-32                                        
relative error                    = 1.4394440000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.898                                       
y[1] (closed_form)                = 0.27759233067908799815678692429086           
y[1] (numeric)                    = 0.27759233067908799815678692429081           
absolute error                    = 5e-32                                        
relative error                    = 1.8012025000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.899                                       
y[1] (closed_form)                = 0.27730005141142953167903517329312           
y[1] (numeric)                    = 0.27730005141142953167903517329308           
absolute error                    = 4e-32                                        
relative error                    = 1.4424808000000000000000000000000e-29      % 
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)                = 0.27700823351572478788787039117164           
y[1] (numeric)                    = 0.2770082335157247878878703911716            
absolute error                    = 4e-32                                        
relative error                    = 1.4440004000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.901                                       
y[1] (closed_form)                = 0.27671687602143116861410780114683           
y[1] (numeric)                    = 0.27671687602143116861410780114679           
absolute error                    = 4e-32                                        
relative error                    = 1.4455208000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.902                                       
y[1] (closed_form)                = 0.27642597796055677720480815346065           
y[1] (numeric)                    = 0.27642597796055677720480815346061           
absolute error                    = 4e-32                                        
relative error                    = 1.4470420000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.903                                       
y[1] (closed_form)                = 0.27613553836765237849345972977376           
y[1] (numeric)                    = 0.27613553836765237849345972977373           
absolute error                    = 3e-32                                        
relative error                    = 1.0864230000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.904                                       
y[1] (closed_form)                = 0.27584555627980338832130600733694           
y[1] (numeric)                    = 0.27584555627980338832130600733691           
absolute error                    = 3e-32                                        
relative error                    = 1.0875651000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.905                                       
y[1] (closed_form)                = 0.27555603073662189248575237543076           
y[1] (numeric)                    = 0.27555603073662189248575237543073           
absolute error                    = 3e-32                                        
relative error                    = 1.0887078000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.906                                       
y[1] (closed_form)                = 0.27526696078023869499237097618198           
y[1] (numeric)                    = 0.27526696078023869499237097618194           
absolute error                    = 4e-32                                        
relative error                    = 1.4531348000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.907                                       
y[1] (closed_form)                = 0.2749783454552953954876053510786            
y[1] (numeric)                    = 0.27497834545529539548760535107857           
absolute error                    = 3e-32                                        
relative error                    = 1.0909950000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.908                                       
y[1] (closed_form)                = 0.27469018380893649574985613101623           
y[1] (numeric)                    = 0.2746901838089364957498561310162            
absolute error                    = 3e-32                                        
relative error                    = 1.0921395000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.909                                       
y[1] (closed_form)                = 0.27440247489080153511720552910011           
y[1] (numeric)                    = 0.27440247489080153511720552910008           
absolute error                    = 3e-32                                        
relative error                    = 1.0932846000000000000000000000000e-29      % 
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)                = 0.27411521775301725473061189917713           
y[1] (numeric)                    = 0.27411521775301725473061189917711           
absolute error                    = 2e-32                                        
relative error                    = 7.2962020000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.911                                       
y[1] (closed_form)                = 0.27382841145018979047197612654378           
y[1] (numeric)                    = 0.27382841145018979047197612654375           
absolute error                    = 3e-32                                        
relative error                    = 1.0955766000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.912                                       
y[1] (closed_form)                = 0.27354205503939689447704913772706           
y[1] (numeric)                    = 0.27354205503939689447704913772703           
absolute error                    = 3e-32                                        
relative error                    = 1.0967235000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.913                                       
y[1] (closed_form)                = 0.27325614758018018510371437081406           
y[1] (numeric)                    = 0.27325614758018018510371437081403           
absolute error                    = 3e-32                                        
relative error                    = 1.0978710000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.914                                       
y[1] (closed_form)                = 0.27297068813453742523674065355188           
y[1] (numeric)                    = 0.27297068813453742523674065355185           
absolute error                    = 3e-32                                        
relative error                    = 1.0990191000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.915                                       
y[1] (closed_form)                = 0.27268567576691482881065961028854           
y[1] (numeric)                    = 0.27268567576691482881065961028851           
absolute error                    = 3e-32                                        
relative error                    = 1.1001678000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.916                                       
y[1] (closed_form)                = 0.27240110954419939543297747760386           
y[1] (numeric)                    = 0.27240110954419939543297747760383           
absolute error                    = 3e-32                                        
relative error                    = 1.1013171000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.917                                       
y[1] (closed_form)                = 0.27211698853571127299048406891091           
y[1] (numeric)                    = 0.27211698853571127299048406891087           
absolute error                    = 4e-32                                        
relative error                    = 1.4699560000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.918                                       
y[1] (closed_form)                = 0.27183331181319614812197160701058           
y[1] (numeric)                    = 0.27183331181319614812197160701054           
absolute error                    = 4e-32                                        
relative error                    = 1.4714900000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.919                                       
y[1] (closed_form)                = 0.2715500784508176644412232570694            
y[1] (numeric)                    = 0.27155007845081766444122325706936           
absolute error                    = 4e-32                                        
relative error                    = 1.4730248000000000000000000000000e-29      % 
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)                = 0.27126728752514986839467545717354           
y[1] (numeric)                    = 0.2712672875251498683946754571735            
absolute error                    = 4e-32                                        
relative error                    = 1.4745604000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.921                                       
y[1] (closed_form)                = 0.27098493811516968263869957580018           
y[1] (numeric)                    = 0.27098493811516968263869957580014           
absolute error                    = 4e-32                                        
relative error                    = 1.4760968000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.922                                       
y[1] (closed_form)                = 0.27070302930224940682198704144599           
y[1] (numeric)                    = 0.27070302930224940682198704144595           
absolute error                    = 4e-32                                        
relative error                    = 1.4776340000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.923                                       
y[1] (closed_form)                = 0.27042156017014924565905790536868           
y[1] (numeric)                    = 0.27042156017014924565905790536864           
absolute error                    = 4e-32                                        
relative error                    = 1.4791720000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.924                                       
y[1] (closed_form)                = 0.27014052980500986418144582993519           
y[1] (numeric)                    = 0.27014052980500986418144582993515           
absolute error                    = 4e-32                                        
relative error                    = 1.4807108000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.925                                       
y[1] (closed_form)                = 0.26985993729534497005364275833557           
y[1] (numeric)                    = 0.26985993729534497005364275833553           
absolute error                    = 4e-32                                        
relative error                    = 1.4822504000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.926                                       
y[1] (closed_form)                = 0.26957978173203392284141403222071           
y[1] (numeric)                    = 0.26957978173203392284141403222068           
absolute error                    = 3e-32                                        
relative error                    = 1.1128431000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.927                                       
y[1] (closed_form)                = 0.2693000622083143701206194978631            
y[1] (numeric)                    = 0.26930006220831437012061949786307           
absolute error                    = 3e-32                                        
relative error                    = 1.1139990000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.928                                       
y[1] (closed_form)                = 0.26902077781977491031519819433254           
y[1] (numeric)                    = 0.26902077781977491031519819433251           
absolute error                    = 3e-32                                        
relative error                    = 1.1151555000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.929                                       
y[1] (closed_form)                = 0.26874192766434778215349356443706           
y[1] (numeric)                    = 0.26874192766434778215349356443703           
absolute error                    = 3e-32                                        
relative error                    = 1.1163126000000000000000000000000e-29      % 
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)                = 0.26846351084230158063261278621902           
y[1] (numeric)                    = 0.26846351084230158063261278621899           
absolute error                    = 3e-32                                        
relative error                    = 1.1174703000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.931                                       
y[1] (closed_form)                = 0.26818552645623399938102780493901           
y[1] (numeric)                    = 0.26818552645623399938102780493899           
absolute error                    = 2e-32                                        
relative error                    = 7.4575240000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.932                                       
y[1] (closed_form)                = 0.26790797361106459931013696795151           
y[1] (numeric)                    = 0.26790797361106459931013696795149           
absolute error                    = 2e-32                                        
relative error                    = 7.4652500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
memory used=136.5MB, alloc=44.3MB, time=1.85
x[1]                              = -1.933                                       
y[1] (closed_form)                = 0.26763085141402760344601484280702           
y[1] (numeric)                    = 0.267630851414027603446014842807             
absolute error                    = 2e-32                                        
relative error                    = 7.4729800000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.934                                       
y[1] (closed_form)                = 0.26735415897466471783308384734398           
y[1] (numeric)                    = 0.26735415897466471783308384734396           
absolute error                    = 2e-32                                        
relative error                    = 7.4807140000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.935                                       
y[1] (closed_form)                = 0.26707789540481797840194475440318           
y[1] (numeric)                    = 0.26707789540481797840194475440316           
absolute error                    = 2e-32                                        
relative error                    = 7.4884520000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.936                                       
y[1] (closed_form)                = 0.26680205981862262369410396796027           
y[1] (numeric)                    = 0.26680205981862262369410396796025           
absolute error                    = 2e-32                                        
relative error                    = 7.4961940000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.937                                       
y[1] (closed_form)                = 0.2665266513324999933368337166875            
y[1] (numeric)                    = 0.26652665133249999333683371668748           
absolute error                    = 2e-32                                        
relative error                    = 7.5039400000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.938                                       
y[1] (closed_form)                = 0.26625166906515045216189698989176           
y[1] (numeric)                    = 0.26625166906515045216189698989174           
absolute error                    = 2e-32                                        
relative error                    = 7.5116899999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.939                                       
y[1] (closed_form)                = 0.26597711213754633986236216401106           
y[1] (numeric)                    = 0.26597711213754633986236216401105           
absolute error                    = 1e-32                                        
relative error                    = 3.7597220000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.94                                        
y[1] (closed_form)                = 0.26570297967292494608222284987171           
y[1] (numeric)                    = 0.26570297967292494608222284987169           
absolute error                    = 2e-32                                        
relative error                    = 7.5272019999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.941                                       
y[1] (closed_form)                = 0.26542927079678151083402654611223           
y[1] (numeric)                    = 0.26542927079678151083402654611222           
absolute error                    = 1e-32                                        
relative error                    = 3.7674820000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.942                                       
y[1] (closed_form)                = 0.26515598463686225014020122687674           
y[1] (numeric)                    = 0.26515598463686225014020122687673           
absolute error                    = 1e-32                                        
relative error                    = 3.7713650000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.943                                       
y[1] (closed_form)                = 0.26488312032315740679425203628899           
y[1] (numeric)                    = 0.26488312032315740679425203628898           
absolute error                    = 1e-32                                        
relative error                    = 3.7752500000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.944                                       
y[1] (closed_form)                = 0.26461067698789432613848082247349           
y[1] (numeric)                    = 0.26461067698789432613848082247348           
absolute error                    = 1e-32                                        
relative error                    = 3.7791370000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.945                                       
y[1] (closed_form)                = 0.26433865376553055675535933403577           
y[1] (numeric)                    = 0.26433865376553055675535933403576           
absolute error                    = 1e-32                                        
relative error                    = 3.7830260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.946                                       
y[1] (closed_form)                = 0.26406704979274697597016253590982           
y[1] (numeric)                    = 0.26406704979274697597016253590981           
absolute error                    = 1e-32                                        
relative error                    = 3.7869170000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.947                                       
y[1] (closed_form)                = 0.26379586420844094006294169320013           
y[1] (numeric)                    = 0.26379586420844094006294169320013           
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]                              = -1.948                                       
y[1] (closed_form)                = 0.26352509615371945908838763487544           
y[1] (numeric)                    = 0.26352509615371945908838763487543           
absolute error                    = 1e-32                                        
relative error                    = 3.7947050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.949                                       
y[1] (closed_form)                = 0.26325474477189239620260295761441           
y[1] (numeric)                    = 0.2632547447718923962026029576144            
absolute error                    = 1e-32                                        
relative error                    = 3.7986020000000000000000000000000e-30      % 
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)                = 0.2629848092084656913962678773786            
y[1] (numeric)                    = 0.26298480920846569139626787737859           
absolute error                    = 1e-32                                        
relative error                    = 3.8025010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.951                                       
y[1] (closed_form)                = 0.26271528861113460953414799592896           
y[1] (numeric)                    = 0.26271528861113460953414799592895           
absolute error                    = 1e-32                                        
relative error                    = 3.8064020000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.952                                       
y[1] (closed_form)                = 0.26244618212977701260135343496124           
y[1] (numeric)                    = 0.26244618212977701260135343496123           
absolute error                    = 1e-32                                        
relative error                    = 3.8103050000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.953                                       
y[1] (closed_form)                = 0.26217748891644665605721761518113           
y[1] (numeric)                    = 0.26217748891644665605721761518111           
absolute error                    = 2e-32                                        
relative error                    = 7.6284199999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.954                                       
y[1] (closed_form)                = 0.26190920812536650919812043475881           
y[1] (numeric)                    = 0.26190920812536650919812043475879           
absolute error                    = 2e-32                                        
relative error                    = 7.6362340000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.955                                       
y[1] (closed_form)                = 0.26164133891292209943103474439996           
y[1] (numeric)                    = 0.26164133891292209943103474439994           
absolute error                    = 2e-32                                        
relative error                    = 7.6440520000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.956                                       
y[1] (closed_form)                = 0.26137388043765488036002683787004           
y[1] (numeric)                    = 0.26137388043765488036002683787002           
absolute error                    = 2e-32                                        
relative error                    = 7.6518740000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.957                                       
y[1] (closed_form)                = 0.26110683186025562358839119025549           
y[1] (numeric)                    = 0.26110683186025562358839119025547           
absolute error                    = 2e-32                                        
relative error                    = 7.6597000000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.958                                       
y[1] (closed_form)                = 0.26084019234355783413954689450188           
y[1] (numeric)                    = 0.26084019234355783413954689450186           
absolute error                    = 2e-32                                        
relative error                    = 7.6675300000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.959                                       
y[1] (closed_form)                = 0.26057396105253118940026818272072           
y[1] (numeric)                    = 0.2605739610525311894002681827207            
absolute error                    = 2e-32                                        
relative error                    = 7.6753639999999999999999999999999e-30      % 
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)                = 0.26030813715427500149026408520822           
y[1] (numeric)                    = 0.26030813715427500149026408520821           
absolute error                    = 1e-32                                        
relative error                    = 3.8416010000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.961                                       
y[1] (closed_form)                = 0.26004271981801170296256268979868           
y[1] (numeric)                    = 0.26004271981801170296256268979867           
absolute error                    = 1e-32                                        
relative error                    = 3.8455220000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.962                                       
y[1] (closed_form)                = 0.25977770821508035573959362973104           
y[1] (numeric)                    = 0.25977770821508035573959362973103           
absolute error                    = 1e-32                                        
relative error                    = 3.8494450000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.963                                       
y[1] (closed_form)                = 0.25951310151893018319029836221282           
y[1] (numeric)                    = 0.25951310151893018319029836221281           
absolute error                    = 1e-32                                        
relative error                    = 3.8533699999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.964                                       
y[1] (closed_form)                = 0.25924889890511412525403151481465           
y[1] (numeric)                    = 0.25924889890511412525403151481464           
absolute error                    = 1e-32                                        
relative error                    = 3.8572970000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.965                                       
y[1] (closed_form)                = 0.25898509955128241651744808514187           
y[1] (numeric)                    = 0.25898509955128241651744808514186           
absolute error                    = 1e-32                                        
relative error                    = 3.8612260000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.966                                       
y[1] (closed_form)                = 0.25872170263717618715100059324886           
y[1] (numeric)                    = 0.25872170263717618715100059324885           
absolute error                    = 1e-32                                        
relative error                    = 3.8651570000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.967                                       
y[1] (closed_form)                = 0.25845870734462108661209741825597           
y[1] (numeric)                    = 0.25845870734462108661209741825596           
absolute error                    = 1e-32                                        
relative error                    = 3.8690900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.968                                       
y[1] (closed_form)                = 0.25819611285752093002239851279039           
y[1] (numeric)                    = 0.25819611285752093002239851279038           
absolute error                    = 1e-32                                        
relative error                    = 3.8730250000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.969                                       
y[1] (closed_form)                = 0.2579339183618513671271474933208            
y[1] (numeric)                    = 0.25793391836185136712714749332079           
absolute error                    = 1e-32                                        
relative error                    = 3.8769620000000000000000000000000e-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)                = 0.25767212304565357374485976323539           
y[1] (numeric)                    = 0.25767212304565357374485976323538           
absolute error                    = 1e-32                                        
relative error                    = 3.8809010000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.971                                       
y[1] (closed_form)                = 0.25741072609902796561610485059624           
y[1] (numeric)                    = 0.25741072609902796561610485059623           
absolute error                    = 1e-32                                        
relative error                    = 3.8848420000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.972                                       
y[1] (closed_form)                = 0.25714972671412793456053754578872           
y[1] (numeric)                    = 0.25714972671412793456053754578871           
absolute error                    = 1e-32                                        
relative error                    = 3.8887850000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.973                                       
y[1] (closed_form)                = 0.25688912408515360685174671759922           
y[1] (numeric)                    = 0.2568891240851536068517467175992            
absolute error                    = 2e-32                                        
relative error                    = 7.7854599999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.974                                       
y[1] (closed_form)                = 0.2566289174083456237199028813525            
y[1] (numeric)                    = 0.25662891740834562371990288135248           
absolute error                    = 2e-32                                        
relative error                    = 7.7933539999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.975                                       
y[1] (closed_form)                = 0.25636910588197894389259570130538           
y[1] (numeric)                    = 0.25636910588197894389259570130536           
absolute error                    = 2e-32                                        
relative error                    = 7.8012520000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.976                                       
y[1] (closed_form)                = 0.25610968870635666808466064313753           
y[1] (numeric)                    = 0.25610968870635666808466064313751           
absolute error                    = 2e-32                                        
relative error                    = 7.8091539999999999999999999999999e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.977                                       
y[1] (closed_form)                = 0.2558506650838038853481999626458            
y[1] (numeric)                    = 0.25585066508380388534819996264578           
absolute error                    = 2e-32                                        
relative error                    = 7.8170600000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.978                                       
y[1] (closed_form)                = 0.25559203421866154119440713510723           
y[1] (numeric)                    = 0.2555920342186615411944071351072            
absolute error                    = 3e-32                                        
relative error                    = 1.1737455000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.979                                       
y[1] (closed_form)                = 0.25533379531728032739920570762953           
y[1] (numeric)                    = 0.2553337953172803273992057076295            
absolute error                    = 3e-32                                        
relative error                    = 1.1749326000000000000000000000000e-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)                = 0.25507594758801459340511340549092           
y[1] (numeric)                    = 0.25507594758801459340511340549089           
absolute error                    = 3e-32                                        
relative error                    = 1.1761203000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.981                                       
y[1] (closed_form)                = 0.25481849024121627923214015424673           
y[1] (numeric)                    = 0.2548184902412162792321401542467            
absolute error                    = 3e-32                                        
relative error                    = 1.1773086000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.982                                       
y[1] (closed_form)                = 0.25456142248922886981092450344613           
y[1] (numeric)                    = 0.2545614224892288698109245034461            
absolute error                    = 3e-32                                        
relative error                    = 1.1784975000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.983                                       
y[1] (closed_form)                = 0.25430474354638137065170676628631           
y[1] (numeric)                    = 0.25430474354638137065170676628629           
absolute error                    = 2e-32                                        
relative error                    = 7.8645800000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.984                                       
y[1] (closed_form)                = 0.25404845262898230476312903349553           
y[1] (numeric)                    = 0.2540484526289823047631290334955            
absolute error                    = 3e-32                                        
relative error                    = 1.1808771000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.985                                       
y[1] (closed_form)                = 0.25379254895531373073524209017452           
y[1] (numeric)                    = 0.2537925489553137307352420901745            
absolute error                    = 2e-32                                        
relative error                    = 7.8804520000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.986                                       
y[1] (closed_form)                = 0.25353703174562528190148717216711           
y[1] (numeric)                    = 0.25353703174562528190148717216709           
absolute error                    = 2e-32                                        
relative error                    = 7.8883940000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.987                                       
y[1] (closed_form)                = 0.25328190022212822649480645463595           
y[1] (numeric)                    = 0.25328190022212822649480645463592           
absolute error                    = 3e-32                                        
relative error                    = 1.1844510000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.988                                       
y[1] (closed_form)                = 0.25302715360898954871342018068669           
y[1] (numeric)                    = 0.25302715360898954871342018068667           
absolute error                    = 2e-32                                        
relative error                    = 7.9042900000000000000000000000000e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.989                                       
y[1] (closed_form)                = 0.25277279113232605061219042284338           
y[1] (numeric)                    = 0.25277279113232605061219042284336           
absolute error                    = 2e-32                                        
relative error                    = 7.9122440000000000000000000000000e-30      % 
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)                = 0.25251881202019847473587163559717           
y[1] (numeric)                    = 0.25251881202019847473587163559715           
absolute error                    = 2e-32                                        
relative error                    = 7.9202020000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.991                                       
y[1] (closed_form)                = 0.25226521550260564741092641373211           
y[1] (numeric)                    = 0.25226521550260564741092641373208           
absolute error                    = 3e-32                                        
relative error                    = 1.1892246000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.992                                       
y[1] (closed_form)                = 0.25201200081147864261296122921374           
y[1] (numeric)                    = 0.25201200081147864261296122921371           
absolute error                    = 3e-32                                        
relative error                    = 1.1904195000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.993                                       
y[1] (closed_form)                = 0.25175916718067496632721138958472           
y[1] (numeric)                    = 0.2517591671806749663272113895847            
absolute error                    = 2e-32                                        
relative error                    = 7.9441000000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.994                                       
y[1] (closed_form)                = 0.251506713845972761319877053458             
y[1] (numeric)                    = 0.25150671384597276131987705345798           
absolute error                    = 2e-32                                        
relative error                    = 7.9520740000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.995                                       
y[1] (closed_form)                = 0.25125464004506503223848286418229           
y[1] (numeric)                    = 0.25125464004506503223848286418227           
absolute error                    = 2e-32                                        
relative error                    = 7.9600520000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.996                                       
y[1] (closed_form)                = 0.25100294501755389095980263136427           
y[1] (numeric)                    = 0.25100294501755389095980263136425           
absolute error                    = 2e-32                                        
relative error                    = 7.9680340000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.997                                       
y[1] (closed_form)                = 0.2507516280049448221042575118919            
y[1] (numeric)                    = 0.25075162800494482210425751189187           
absolute error                    = 3e-32                                        
relative error                    = 1.1964030000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.998                                       
y[1] (closed_form)                = 0.2505006882506409686360613275785            
y[1] (numeric)                    = 0.25050068825064096863606132757847           
absolute error                    = 3e-32                                        
relative error                    = 1.1976015000000000000000000000000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
 
TOP MAIN SOLVE Loop
x[1]                              = -1.999                                       
y[1] (closed_form)                = 0.25025012499993743746875001564063           
y[1] (numeric)                    = 0.25025012499993743746875001564061           
absolute error                    = 2e-32                                        
relative error                    = 7.9920040000000000000000000000001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = -0.001                                       
Finished!
diff  (  y  ,  x  ,  1  )   =  neg ( 2.0 )   *  x  /   ( x  *   x  +  0.000001 )   /  (  x  *  x  +  0.000001 )  ; 
Iterations                       = 500                                 
Total Elapsed Time               = 2 Seconds
Elapsed Time(since restart)      = 2 Seconds
Expected Time Remaining          = 0 Seconds
Optimized Time Remaining         = 0 Seconds
Expected Total Time              = 2 Seconds
Time to Timeout                  = 2 Minutes 57 Seconds
Percent Done                     = 0                                          % 
> quit
memory used=157.3MB, alloc=44.3MB, time=2.12