|\^/|     Maple 18 (X86 64 WINDOWS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         printf("%s\n",str);
>     fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc

# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         printf("%s",str);
>     fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then printf("%s", str) end if
end proc

# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         print(label,str);
>     fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then print(label, str) end if
end proc

# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         if vallen = 4 then
>         printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
>         else
>         printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
>     fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        if vallen = 4 then
            printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
        else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
        end if
    end if
end proc

# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 0
>         if vallen = 5  then # if number 1
>             printf("%-30s = %-32d  %s\n",prelabel,value, postlabel);
>             else
>             printf("%-30s = %-32d  %s \n",prelabel,value, postlabel);
>         fi;# end if 1;
>     fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        if vallen = 5 then
            printf("%-30s = %-32d  %s\n", prelabel, value, postlabel)
        else printf("%-30s = %-32d  %s \n", prelabel, value, postlabel)
        end if
    end if
end proc

# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 0
>         print(prelabel,"[",elemnt,"]",value, postlabel);
>     fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        print(prelabel, "[", elemnt, "]", value, postlabel)
    end if
end proc

# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
>     global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
>     local  days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
>     fprintf(fd,"<td>");
>     if (secs_in >= 0)  then # if number 0
>         years_int  :=  int_trunc(secs_in / glob_sec_in_year);
>         sec_temp  :=  int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
>         days_int  :=  int_trunc(sec_temp / glob_sec_in_day) ;
>         sec_temp  :=  sec_temp mod int_trunc(glob_sec_in_day) ;
>         hours_int  :=  int_trunc(sec_temp / glob_sec_in_hour);
>         sec_temp  :=  sec_temp mod int_trunc(glob_sec_in_hour);
>         minutes_int  := int_trunc(sec_temp / glob_sec_in_minute);
>         sec_int  := sec_temp mod int_trunc(glob_sec_in_minute);
>         if  (years_int > 0)  then # if number 1
>             fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
>         elif
>         (days_int > 0)  then # if number 2
>             fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
>         elif
>         (hours_int > 0)  then # if number 3
>             fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
>         elif
>         (minutes_int > 0)  then # if number 4
>             fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
>         else
>             fprintf(fd,"%d Seconds",sec_int);
>         fi;# end if 4
>     else
>         fprintf(fd," 0.0 Seconds");
>     fi;# end if 3
>     fprintf(fd,"</td>\n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
    fprintf(fd, "<td>");
    if 0 <= secs_in then
        years_int := int_trunc(secs_in/glob_sec_in_year);
        sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
        days_int := int_trunc(sec_temp/glob_sec_in_day);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
        hours_int := int_trunc(sec_temp/glob_sec_in_hour);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
        minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
        sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
        if 0 < years_int then fprintf(fd,
            "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
            days_int, hours_int, minutes_int, sec_int)
        elif 0 < days_int then fprintf(fd,
            "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
            minutes_int, sec_int)
        elif 0 < hours_int then fprintf(fd,
            "%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
            sec_int)
        elif 0 < minutes_int then
            fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
        else fprintf(fd, "%d Seconds", sec_int)
        end if
    else fprintf(fd, " 0.0 Seconds")
    end if;
    fprintf(fd, "</td>\n")
end proc

# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
>     global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
>     local  days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
>     if (secs_in >= 0)  then # if number 3
>         years_int  :=  int_trunc(secs_in / glob_sec_in_year);
>         sec_temp  :=  (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
>         days_int  :=  int_trunc(sec_temp / glob_sec_in_day) ;
>         sec_temp  :=  (sec_temp mod int_trunc(glob_sec_in_day)) ;
>         hours_int  :=  int_trunc(sec_temp / glob_sec_in_hour);
>         sec_temp  :=  (sec_temp mod int_trunc(glob_sec_in_hour));
>         minutes_int  := int_trunc(sec_temp / glob_sec_in_minute);
>         sec_int  := (sec_temp mod int_trunc(glob_sec_in_minute));
>         if  (years_int > 0)  then # if number 4
>             printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
>         elif
>         (days_int > 0)  then # if number 5
>             printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
>         elif
>         (hours_int > 0)  then # if number 6
>             printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
>         elif
>         (minutes_int > 0)  then # if number 7
>             printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
>         else
>             printf(" = %d Seconds\n",sec_int);
>         fi;# end if 7
>     else
>         printf(" 0.0 Seconds\n");
>     fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
    if 0 <= secs_in then
        years_int := int_trunc(secs_in/glob_sec_in_year);
        sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
        days_int := int_trunc(sec_temp/glob_sec_in_day);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
        hours_int := int_trunc(sec_temp/glob_sec_in_hour);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
        minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
        sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
        if 0 < years_int then printf(
            " = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
            years_int, days_int, hours_int, minutes_int, sec_int)
        elif 0 < days_int then printf(
            " = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
            hours_int, minutes_int, sec_int)
        elif 0 < hours_int then printf(
            " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
            sec_int)
        elif 0 < minutes_int then
            printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
        else printf(" = %d Seconds\n", sec_int)
        end if
    else printf(" 0.0 Seconds\n")
    end if
end proc

# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
>     global ATS_MAX_TERMS;
>     local iii;
>     iii  := 1;
>     while (iii <= ATS_MAX_TERMS) do # do number 1
>         arr_a [iii] := glob__0;
>         iii  :=  iii + 1;
>     od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
    iii := 1;
    while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
    end do
end proc

# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
>     global ATS_MAX_TERMS;
>     local iii_ats, lll_ats,ma_ats, ret_ats;
>     ret_ats  := glob__0;
>     if (jjj_ats <=  mmm_ats)  then # if number 6
>         ma_ats  :=  mmm_ats + 1;
>         iii_ats  :=  jjj_ats;
>         while (iii_ats <= mmm_ats) do # do number 1
>             lll_ats  :=  ma_ats - iii_ats;
>             if ((lll_ats <= ATS_MAX_TERMS  and (iii_ats <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_ats  :=  ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
>             fi;# end if 7;
>             iii_ats  :=  iii_ats + 1;
>         od;# end do number 1
>     fi;# end if 6;
>     ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
    ret_ats := glob__0;
    if jjj_ats <= mmm_ats then
        ma_ats := mmm_ats + 1;
        iii_ats := jjj_ats;
        while iii_ats <= mmm_ats do
            lll_ats := ma_ats - iii_ats;
            if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
                ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
            end if;
            iii_ats := iii_ats + 1
        end do
    end if;
    ret_ats
end proc

# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
>     global ATS_MAX_TERMS;
>     local al_att, iii_att,lll_att, ma_att, ret_att;
>     ret_att  := glob__0;
>     if (jjj_att < mmm_att)  then # if number 6
>         ma_att  :=  mmm_att + 2;
>         iii_att  :=  jjj_att;
>         while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) )   do # do number 1
>             lll_att  :=  ma_att - iii_att;
>             al_att  :=  (lll_att - 1);
>             if ((lll_att <= ATS_MAX_TERMS  and (iii_att <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_att  :=   ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
>             fi;# end if 7;
>             iii_att  :=  iii_att + 1;
>         od;# end do number 1;
>         ret_att  :=  ret_att / c(mmm_att) ;
>     fi;# end if 6;
>     ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
    ret_att := glob__0;
    if jjj_att < mmm_att then
        ma_att := mmm_att + 2;
        iii_att := jjj_att;
        while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
            lll_att := ma_att - iii_att;
            al_att := lll_att - 1;
            if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
                ret_att :=
                ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
            end if;
            iii_att := iii_att + 1
        end do;
        ret_att := ret_att/c(mmm_att)
    end if;
    ret_att
end proc

# End Function number 12
# Begin Function number 13
> logditto := proc(file)
>     fprintf(file,"<td>");
>     fprintf(file,"ditto");
>     fprintf(file,"</td>");
> end;
logditto := proc(file)
    fprintf(file, "<td>"); fprintf(file, "ditto"); fprintf(file, "</td>")
end proc

# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
>     fprintf(file,"<td>");
>     fprintf(file,"%d",n);
>     fprintf(file,"</td>");
> end;
logitem_integer := proc(file, n)
    fprintf(file, "<td>"); fprintf(file, "%d", n); fprintf(file, "</td>")
end proc

# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
>     fprintf(file,"<td>");
>     fprintf(file,str);
>     fprintf(file,"</td>");
> end;
logitem_str := proc(file, str)
    fprintf(file, "<td>"); fprintf(file, str); fprintf(file, "</td>")
end proc

# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
>     global glob_small_float,glob_prec;
>     local good_digits;
>     fprintf(file,"<td>");
>     fprintf(file,"%d",glob_min_good_digits);
>     fprintf(file,"</td>");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
    fprintf(file, "<td>");
    fprintf(file, "%d", glob_min_good_digits);
    fprintf(file, "</td>")
end proc

# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
>     fprintf(file,revs);
> end;
           log_revs := proc(file, revs) fprintf(file, revs) end proc

# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
>     fprintf(file,"<td>");
>     fprintf(file,"%g",x);
>     fprintf(file,"</td>");
> end;
logitem_float := proc(file, x)
    fprintf(file, "<td>"); fprintf(file, "%g", x); fprintf(file, "</td>")
end proc

# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
>     global glob_h_reason;
>     fprintf(file,"<td>");
>     if (glob_h_reason  = 1) then # if number 6
>         fprintf(file,"Max H");
>     elif
>     (glob_h_reason = 2) then # if number 7
>         fprintf(file,"Display Interval");
>     elif
>     (glob_h_reason = 3) then # if number 8
>         fprintf(file,"Optimal");
>     elif
>     (glob_h_reason = 4) then # if number 9
>         fprintf(file,"Pole Accuracy");
>     elif
>     (glob_h_reason = 5) then # if number 10
>         fprintf(file,"Min H (Pole)");
>     elif
>     (glob_h_reason = 6) then # if number 11
>         fprintf(file,"Pole");
>     elif
>     (glob_h_reason = 7) then # if number 12
>         fprintf(file,"Opt Iter");
>     else
>         fprintf(file,"Impossible");
>     fi;# end if 12
>     fprintf(file,"</td>");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
    fprintf(file, "<td>");
    if glob_h_reason = 1 then fprintf(file, "Max H")
    elif glob_h_reason = 2 then fprintf(file, "Display Interval")
    elif glob_h_reason = 3 then fprintf(file, "Optimal")
    elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
    elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
    elif glob_h_reason = 6 then fprintf(file, "Pole")
    elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
    else fprintf(file, "Impossible")
    end if;
    fprintf(file, "</td>")
end proc

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

# End Function number 20
# Begin Function number 21
> logend := proc(file)
>     fprintf(file,"</tr>\n");
> end;
             logend := proc(file) fprintf(file, "</tr>\n") end proc

# End Function number 21
# Begin Function number 22
> chk_data := proc()
>     global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
>     local  errflag;
>     errflag  :=  false;
>     if (glob_max_iter < 2)  then # if number 12
>         omniout_str(ALWAYS,"Illegal max_iter");
>         errflag  :=  true;
>     fi;# end if 12;
>     if (errflag)   then # if number 12
>         quit;
>     fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
    errflag := false;
    if glob_max_iter < 2 then
        omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
    end if;
    if errflag then quit end if
end proc

# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
>     global glob_small_float;
>     local ms2, rrr, sec_left, sub1, sub2;
>     ;
>     ms2 := c(clock_sec2);
>     sub1 := c(t_end2-t_start2);
>     sub2 := c(t2-t_start2);
>     if (sub1 = glob__0)  then # if number 12
>         sec_left := glob__0;
>     else
>         if (sub2 > glob__0)  then # if number 13
>             rrr := (sub1/sub2);
>             sec_left  := rrr * c(ms2) - c(ms2);
>         else
>             sec_left  := glob__0;
>         fi;# end if 13
>     fi;# end if 12;
>     sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
    ms2 := c(clock_sec2);
    sub1 := c(t_end2 - t_start2);
    sub2 := c(t2 - t_start2);
    if sub1 = glob__0 then sec_left := glob__0
    else
        if glob__0 < sub2 then
            rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
        else sec_left := glob__0
        end if
    end if;
    sec_left
end proc

# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
>     global glob_small_float;
>     local rrr, sub1, sub2;
>     sub1  :=  (t_end2-t_start2);
>     sub2  :=  (t2-t_start2);
>     if (sub2 > glob_small_float)  then # if number 12
>         rrr  :=  (glob__100*sub2)/sub1;
>     else
>         rrr  :=  0.0;
>     fi;# end if 12;
>     rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
    sub1 := t_end2 - t_start2;
    sub2 := t2 - t_start2;
    if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
    else rrr := 0.
    end if;
    rrr
end proc

# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (float_abs(term2) > glob__0)  then # if number 12
>         ret :=  float_abs(term1 * glob_h / term2);
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
    if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM ORDER ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (float_abs(term2) > glob__0)  then # if number 12
>         ret := glob__1 +  float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
    if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
        c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 26
# Begin Function number 27
> c := proc(in_val)
>     #To Force Conversion when needed
>     local ret;
>     ret := evalf(in_val);
>     ret;
>     #End Conversion
> end;
        c := proc(in_val) local ret; ret := evalf(in_val); ret end proc

# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret,temp;
>     temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
>     if (float_abs(temp) > glob__0)  then # if number 12
>         ret := float_abs((term2*glob_h*term1)/(temp));
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
    temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
         - term1*term3*c(last_no) + term1*term3);
    if glob__0 < float_abs(temp) then
        ret := float_abs(term2*glob_h*term1/temp)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM ORDER ANALYSIS
>     local ret;
>     ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
>     ret;
>     #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
    ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
         - glob__4*term2*term2*c(last_no) + glob__4*term2*term2
         + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
        /(term2*term2*c(last_no) - glob__2*term2*term2
         - term1*term3*c(last_no) + term1*term3));
    ret
end proc

# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
>     #TOP SIX TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float,glob_six_term_ord_save;
>     local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
>     if ((term5  <> glob__0) and (term4  <> glob__0) and (term3  <> glob__0) and  (term2  <> glob__0) and (term1  <> glob__0)) then # if number 12
>         rm0 := term6/term5;
>         rm1 := term5/term4;
>         rm2 := term4/term3;
>         rm3 := term3/term2;
>         rm4 := term2/term1;
>         nr1 :=  c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
>         nr2 :=  c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
>         dr1 :=  glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
>         dr2 :=  glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
>         ds1 :=  glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
>         ds2 :=  glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
>         if ((float_abs(nr1 * dr2 - nr2 * dr1)  =  glob__0)  or  (float_abs(dr1) = glob__0))  then # if number 13
>             rad_c :=  glob_larger_float;
>             ord_no :=  glob_larger_float;
>         else
>             if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0)  then # if number 14
>                 rcs :=  ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
>                 #(Manuels)  rcs  :=  (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
>                 ord_no :=  (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
>                 if (float_abs(rcs)  <> glob__0)  then # if number 15
>                     if (rcs > glob__0)  then # if number 16
>                         rad_c  :=  sqrt(rcs) * float_abs(glob_h);
>                     else
>                         rad_c  :=  glob_larger_float;
>                         ord_no :=  glob_larger_float;
>                     fi;# end if 16
>                 else
>                     rad_c :=  glob_larger_float;
>                     ord_no :=  glob_larger_float;
>                 fi;# end if 15
>             else
>                 rad_c :=  glob_larger_float;
>                 ord_no :=  glob_larger_float;
>             fi;# end if 14
>         fi;# end if 13
>     else
>         rad_c :=  glob_larger_float;
>         ord_no :=  glob_larger_float;
>     fi;# end if 12;
>     glob_six_term_ord_save :=  ord_no;
>     rad_c;
>     #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
    if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
    term2 <> glob__0 and term1 <> glob__0 then
        rm0 := term6/term5;
        rm1 := term5/term4;
        rm2 := term4/term3;
        rm3 := term3/term2;
        rm4 := term2/term1;
        nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
             + c(last_no - 3)*rm2;
        nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
             + c(last_no - 4)*rm3;
        dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
        dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
        ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
        ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
        if
        float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
        then rad_c := glob_larger_float; ord_no := glob_larger_float
        else
            if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
                rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
                ord_no :=
                    (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
                if float_abs(rcs) <> glob__0 then
                    if glob__0 < rcs then
                        rad_c := sqrt(rcs)*float_abs(glob_h)
                    else
                        rad_c := glob_larger_float;
                        ord_no := glob_larger_float
                    end if
                else
                    rad_c := glob_larger_float; ord_no := glob_larger_float
                end if
            else rad_c := glob_larger_float; ord_no := glob_larger_float
            end if
        end if
    else rad_c := glob_larger_float; ord_no := glob_larger_float
    end if;
    glob_six_term_ord_save := ord_no;
    rad_c
end proc

# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
>     global glob_six_term_ord_save;
>     #TOP SIX TERM ORDER ANALYSIS
>     #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
>     glob_six_term_ord_save;
>     #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
    glob_six_term_ord_save
end proc

# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
>     ret := nnn!;
>     ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
         factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc

# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
>     global ATS_MAX_TERMS,array_fact_1;
>     local ret;
>     if (nnn <= ATS_MAX_TERMS) then # if number 12
>         if (array_fact_1[nnn] = 0) then # if number 13
>             ret := factorial_2(nnn);
>             array_fact_1[nnn] := ret;
>         else
>             ret := array_fact_1[nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
    if nnn <= ATS_MAX_TERMS then
        if array_fact_1[nnn] = 0 then
            ret := factorial_2(nnn); array_fact_1[nnn] := ret
        else ret := array_fact_1[nnn]
        end if
    else ret := factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
>     global ATS_MAX_TERMS,array_fact_2;
>     local ret;
>     if ((nnn <= ATS_MAX_TERMS)  and  (mmm <= ATS_MAX_TERMS)) then # if number 12
>         if (array_fact_2[mmm,nnn] = 0) then # if number 13
>             ret := factorial_1(mmm)/factorial_1(nnn);
>             array_fact_2[mmm,nnn] := ret;
>         else
>             ret := array_fact_2[mmm,nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(mmm)/factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
    if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
        if array_fact_2[mmm, nnn] = 0 then
            ret := factorial_1(mmm)/factorial_1(nnn);
            array_fact_2[mmm, nnn] := ret
        else ret := array_fact_2[mmm, nnn]
        end if
    else ret := factorial_2(mmm)/factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
>     (mmm);
> end;
                      convfloat := proc(mmm) mmm end proc

# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
>     time();
> end;
                 elapsed_time_seconds := proc() time() end proc

# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
>     abs(x);
> end;
                      float_abs := proc(x) abs(x) end proc

# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
>     x^y;
> end;
                        expt := proc(x, y) x^y end proc

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

# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
>     trunc(x);
> end;
                     int_trunc := proc(x) trunc(x) end proc

# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
>     local desired_abs_gbl_error,range,estimated_steps,step_error;
>     global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
>     omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
>     desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
>     omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
>     omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
>     omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
>     range := (x_end - x_start);
>     omniout_float(ALWAYS,"range",32,range,32,"");
>     estimated_steps := range / estimated_h;
>     omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
>     step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
>     omniout_float(ALWAYS,"step_error",32,step_error,32,"");
>     (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
    omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
        glob_desired_digits_correct, 32, "");
    desired_abs_gbl_error :=
        expt(glob__10, c(-glob_desired_digits_correct))*
        c(float_abs(c(estimated_answer)));
    omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
    omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
        ;
    omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
        desired_abs_gbl_error, 32, "");
    range := x_end - x_start;
    omniout_float(ALWAYS, "range", 32, range, 32, "");
    estimated_steps := range/estimated_h;
    omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
    step_error := c(float_abs(desired_abs_gbl_error)/(
        sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
    omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
    step_error
end proc

# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(cos(x) * c(-2.0));
> end;
             exact_soln_y := proc(x) return cos(x)*c(-2.0) end proc

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

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

# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_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)*19*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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_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)*19*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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_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,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre sin 1 $eq_no = 1
>     array_tmp1[1] :=  sin(array_x[1]);
>     array_tmp1_g[1] :=  cos(array_x[1]);
>     #emit pre mult CONST FULL $eq_no = 1 i = 1
>     array_tmp2[1] := array_const_2D0[1] * array_tmp1[1];
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
>     #emit pre 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_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[2] := temporary;
>                 array_y_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
>     array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1);
>     array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
>     #emit pre mult CONST FULL $eq_no = 1 i = 2
>     array_tmp2[2] := array_const_2D0[1] * array_tmp1[2];
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp3[2] := array_tmp2[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_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[3] := temporary;
>                 array_y_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
>     array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2);
>     array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
>     #emit pre mult CONST FULL $eq_no = 1 i = 3
>     array_tmp2[3] := array_const_2D0[1] * array_tmp1[3];
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp3[3] := array_tmp2[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_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[4] := temporary;
>                 array_y_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
>     array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3);
>     array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
>     #emit pre mult CONST FULL $eq_no = 1 i = 4
>     array_tmp2[4] := array_const_2D0[1] * array_tmp1[4];
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp3[4] := array_tmp2[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_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[5] := temporary;
>                 array_y_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
>     array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4);
>     array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
>     #emit pre mult CONST FULL $eq_no = 1 i = 5
>     array_tmp2[5] := array_const_2D0[1] * array_tmp1[5];
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp3[5] := array_tmp2[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_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[6] := temporary;
>                 array_y_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y_higher[2,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #END ATOMHDR5
>     #BEGIN OUTFILE3
>     #Top Atomall While Loop-- outfile3
>     while (kkk <= ATS_MAX_TERMS) do # do number 1
>         #END OUTFILE3
>         #BEGIN OUTFILE4
>         #emit sin LINEAR $eq_no = 1
>         array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1);
>         array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
>         #emit mult CONST FULL $eq_no = 1 i = 1
>         array_tmp2[kkk] := array_const_2D0[1] * array_tmp1[kkk];
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp3[kkk] := array_tmp2[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_tmp3[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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    array_tmp1[1] := sin(array_x[1]);
    array_tmp1_g[1] := cos(array_x[1]);
    array_tmp2[1] := array_const_2D0[1]*array_tmp1[1];
    array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
    if not array_y_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y[2] := temporary; array_y_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1);
    array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
    array_tmp2[2] := array_const_2D0[1]*array_tmp1[2];
    array_tmp3[2] := array_tmp2[2];
    if not array_y_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y[3] := temporary; array_y_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
    array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
    array_tmp2[3] := array_const_2D0[1]*array_tmp1[3];
    array_tmp3[3] := array_tmp2[3];
    if not array_y_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y[4] := temporary; array_y_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
    array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
    array_tmp2[4] := array_const_2D0[1]*array_tmp1[4];
    array_tmp3[4] := array_tmp2[4];
    if not array_y_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y[5] := temporary; array_y_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
    array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
    array_tmp2[5] := array_const_2D0[1]*array_tmp1[5];
    array_tmp3[5] := array_tmp2[5];
    if not array_y_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y[6] := temporary; array_y_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
        array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
            ;
        array_tmp2[kkk] := array_const_2D0[1]*array_tmp1[kkk];
        array_tmp3[kkk] := array_tmp2[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_tmp3[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,
>     #END CONST
>     array_y_init,
>     array_norms,
>     array_fact_1,
>     array_1st_rel_error,
>     array_last_rel_error,
>     array_est_rel_error,
>     array_max_est_error,
>     array_type_pole,
>     array_type_real_pole,
>     array_type_complex_pole,
>     array_est_digits,
>     array_y,
>     array_x,
>     array_tmp0,
>     array_tmp1_g,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_m1,
>     array_y_higher,
>     array_y_higher_work,
>     array_y_higher_work2,
>     array_y_set_initial,
>     array_given_rad_poles,
>     array_given_ord_poles,
>     array_rad_test_poles,
>     array_ord_test_poles,
>     array_fact_2,
>     ATS_MAX_TERMS,
>     glob_last;
>     ATS_MAX_TERMS := 40;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=40;
>     #END BLOCK 1
>     #END FIRST INPUT BLOCK
>     #START OF INITS AFTER INPUT BLOCK
>     glob_html_log := true;
>     #END OF INITS AFTER INPUT BLOCK
>     # before generate arrays
>     array_y_init:= Array(0..(40),[]);
>     array_norms:= Array(0..(40),[]);
>     array_fact_1:= Array(0..(40),[]);
>     array_1st_rel_error:= Array(0..(2),[]);
>     array_last_rel_error:= Array(0..(2),[]);
>     array_est_rel_error:= Array(0..(2),[]);
>     array_max_est_error:= Array(0..(2),[]);
>     array_type_pole:= Array(0..(2),[]);
>     array_type_real_pole:= Array(0..(2),[]);
>     array_type_complex_pole:= Array(0..(2),[]);
>     array_est_digits:= Array(0..(2),[]);
>     array_y:= Array(0..(40),[]);
>     array_x:= Array(0..(40),[]);
>     array_tmp0:= Array(0..(40),[]);
>     array_tmp1_g:= Array(0..(40),[]);
>     array_tmp1:= Array(0..(40),[]);
>     array_tmp2:= Array(0..(40),[]);
>     array_tmp3:= Array(0..(40),[]);
>     array_m1:= Array(0..(40),[]);
>     array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
>     array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
>     array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
>     array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
>     # before generate constants
>     # before generate globals definition
>     #Top Generate Globals Definition
>     #Bottom Generate Globals Deninition
>     # before generate const definition
>     # before arrays initialized
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_fact_1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_1st_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_last_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_est_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_max_est_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_real_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_complex_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_est_digits[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1_g[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_m1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_higher_work2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_set_initial[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_rad_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_ord_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_rad_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_ord_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=40) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1_g);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_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_m1);
>     array_m1[1]   := glob__m1;
>     #END SYMBOLS INITIALIZATED
>     # before generate factorials init
>     #Initing Factorial Tables
>     iiif := 0;
>     while (iiif <= ATS_MAX_TERMS) do # do number 1
>         jjjf := 0;
>         while (jjjf <= ATS_MAX_TERMS) do # do number 2
>             array_fact_1[iiif] := 0;
>             array_fact_2[iiif,jjjf] := 0;
>             jjjf := jjjf + 1;
>         od;# end do number 2;
>         iiif := iiif + 1;
>     od;# end do number 1;
>     #Done Initing Factorial Table
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     glob_iolevel := 5;
>     glob_yes_pole := 4;
>     glob_no_pole := 3;
>     glob_not_given := 0;
>     glob_no_sing_tests := 4;
>     glob_ratio_test := 1;
>     glob_three_term_test := 2;
>     glob_six_term_test := 3;
>     glob_log_10 := log(c(10.0));
>     MAX_UNCHANGED := 10;
>     glob__small := c(0.1e-50);
>     glob_small_float := c(0.1e-50);
>     glob_smallish_float := c(0.1e-60);
>     glob_large_float := c(1.0e100);
>     glob_larger_float := c(1.1e100);
>     glob__m2 := c(-2);
>     glob__m1 := c(-1);
>     glob__0 := c(0);
>     glob__1 := c(1);
>     glob__2 := c(2);
>     glob__3 := c(3);
>     glob__4 := c(4);
>     glob__5 := c(5);
>     glob__8 := c(8);
>     glob__10 := c(10);
>     glob__100 := c(100);
>     glob__pi := c(0.0);
>     glob__0_5 := c(0.5);
>     glob__0_8 := c(0.8);
>     glob__m0_8 := c(-0.8);
>     glob__0_25 := c(0.25);
>     glob__0_125 := c(0.125);
>     glob_prec := c(1.0e-16);
>     glob_check_sign := c(1.0);
>     glob_desired_digits_correct := c(8.0);
>     glob_max_estimated_step_error := c(0.0);
>     glob_ratio_of_radius := c(0.1);
>     glob_percent_done := c(0.0);
>     glob_total_exp_sec := c(0.1);
>     glob_optimal_expect_sec := c(0.1);
>     glob_estimated_size_answer := c(100.0);
>     glob_almost_1 := c(0.9990);
>     glob_clock_sec := c(0.0);
>     glob_clock_start_sec := c(0.0);
>     glob_disp_incr := c(0.1);
>     glob_h := c(0.1);
>     glob_diff_rc_fm := c(0.1);
>     glob_diff_rc_fmm1 := c(0.1);
>     glob_diff_rc_fmm2 := c(0.1);
>     glob_diff_ord_fm := c(0.1);
>     glob_diff_ord_fmm1 := c(0.1);
>     glob_diff_ord_fmm2 := c(0.1);
>     glob_six_term_ord_save := c(0.1);
>     glob_guess_error_rc := c(0.1);
>     glob_guess_error_ord := c(0.1);
>     glob_least_given_sing := c(9.9e200);
>     glob_least_ratio_sing := c(9.9e200);
>     glob_least_3_sing := c(9.9e100);
>     glob_least_6_sing := c(9.9e100);
>     glob_last_good_h := c(0.1);
>     glob_max_h := c(0.1);
>     glob_min_h := c(0.000001);
>     glob_display_interval := c(0.1);
>     glob_abserr := c(0.1e-10);
>     glob_relerr := c(0.1e-10);
>     glob_min_pole_est := c(0.1e+10);
>     glob_max_rel_trunc_err := c(0.1e-10);
>     glob_max_trunc_err := c(0.1e-10);
>     glob_max_hours := c(0.0);
>     glob_optimal_clock_start_sec := c(0.0);
>     glob_optimal_start := c(0.0);
>     glob_upper_ratio_limit := c(1.0001);
>     glob_lower_ratio_limit := c(0.9999);
>     glob_max_sec := c(10000.0);
>     glob_orig_start_sec := c(0.0);
>     glob_normmax := c(0.0);
>     glob_max_minutes := c(0.0);
>     glob_next_display := c(0.0);
>     glob_est_digits := 1;
>     glob_subiter_method := 3;
>     glob_html_log := true;
>     glob_min_good_digits := 99999;
>     glob_good_digits := 0;
>     glob_min_apfp_est_good_digits := 99999;
>     glob_apfp_est_good_digits := 0;
>     glob_max_opt_iter := 10;
>     glob_dump := false;
>     glob_djd_debug := true;
>     glob_display_flag := true;
>     glob_djd_debug2 := true;
>     glob_h_reason := 0;
>     glob_sec_in_minute := 60 ;
>     glob_min_in_hour := 60;
>     glob_hours_in_day := 24;
>     glob_days_in_year := 365;
>     glob_sec_in_hour := 3600;
>     glob_sec_in_day := 86400;
>     glob_sec_in_year := 31536000;
>     glob_not_yet_finished := true;
>     glob_initial_pass := true;
>     glob_not_yet_start_msg := true;
>     glob_reached_optimal_h := false;
>     glob_optimal_done := false;
>     glob_type_given_pole := 0;
>     glob_optimize := false;
>     glob_look_poles := false;
>     glob_dump_closed_form := false;
>     glob_max_iter := 1000;
>     glob_no_eqs := 0;
>     glob_unchanged_h_cnt := 0;
>     glob_warned := false;
>     glob_warned2 := false;
>     glob_start := 0;
>     glob_iter := 0;
>     # before generate set diff initial
>     array_y_set_initial[1,1] := true;
>     array_y_set_initial[1,2] := false;
>     array_y_set_initial[1,3] := false;
>     array_y_set_initial[1,4] := false;
>     array_y_set_initial[1,5] := false;
>     array_y_set_initial[1,6] := false;
>     array_y_set_initial[1,7] := false;
>     array_y_set_initial[1,8] := false;
>     array_y_set_initial[1,9] := false;
>     array_y_set_initial[1,10] := false;
>     array_y_set_initial[1,11] := false;
>     array_y_set_initial[1,12] := false;
>     array_y_set_initial[1,13] := false;
>     array_y_set_initial[1,14] := false;
>     array_y_set_initial[1,15] := false;
>     array_y_set_initial[1,16] := false;
>     array_y_set_initial[1,17] := false;
>     array_y_set_initial[1,18] := false;
>     array_y_set_initial[1,19] := false;
>     array_y_set_initial[1,20] := false;
>     array_y_set_initial[1,21] := false;
>     array_y_set_initial[1,22] := false;
>     array_y_set_initial[1,23] := false;
>     array_y_set_initial[1,24] := false;
>     array_y_set_initial[1,25] := false;
>     array_y_set_initial[1,26] := false;
>     array_y_set_initial[1,27] := false;
>     array_y_set_initial[1,28] := false;
>     array_y_set_initial[1,29] := false;
>     array_y_set_initial[1,30] := false;
>     array_y_set_initial[1,31] := false;
>     array_y_set_initial[1,32] := false;
>     array_y_set_initial[1,33] := false;
>     array_y_set_initial[1,34] := false;
>     array_y_set_initial[1,35] := false;
>     array_y_set_initial[1,36] := false;
>     array_y_set_initial[1,37] := false;
>     array_y_set_initial[1,38] := false;
>     array_y_set_initial[1,39] := false;
>     array_y_set_initial[1,40] := false;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 40;
>     glob_iolevel := INFO;
>     # set default block
>     #Write Set Defaults
>     glob_orig_start_sec   :=  elapsed_time_seconds();
>     glob_display_flag   :=   true;
>     glob_no_eqs   := 1;
>     glob_iter   :=  -1;
>     opt_iter   :=  -1;
>     glob_max_iter   :=  50000;
>     glob_max_hours   :=  (0.0);
>     glob_max_minutes   :=  (15.0);
>     omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
>     omniout_str(ALWAYS,"##############temp/mult_c_sinpostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=40;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(0.1);");
>     omniout_str(ALWAYS,"x_end := c(5.0) ;");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 3;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
>     omniout_str(ALWAYS,"glob_look_poles:=false;");
>     omniout_str(ALWAYS,"glob_h:=c(0.001);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y := proc(x)");
>     omniout_str(ALWAYS,"return(cos(x) * c(-2.0));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(0.1);
>     x_end := c(5.0) ;
>     array_y_init[0 + 1] := exact_soln_y(x_start);
>     glob_look_poles := true;
>     glob_type_given_pole := 3;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=8;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=3;
>     glob_max_iter:=100000;
>     glob_upper_ratio_limit:=c(1.000001);
>     glob_lower_ratio_limit:=c(0.999999);
>     glob_look_poles:=false;
>     glob_h:=c(0.001);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(x_start,x_end));
>     glob__pi := arccos(glob__m1);
>     glob_prec = expt(10.0,c(-Digits));
>     if (glob_optimize)  then # if number 9
>         #BEGIN OPTIMIZE CODE
>         omniout_str(ALWAYS,"START of Optimize");
>         #Start Series -- INITIALIZE FOR OPTIMIZE
>         found_h := false;
>         glob_min_pole_est :=  glob_larger_float;
>         last_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         glob_min_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_max_h := float_abs(glob_max_h) * glob_check_sign;
>         glob_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
>         display_max := c(x_end) - c(x_start)/glob__10;
>         if ((glob_display_interval) > (display_max)) then # if number 10
>             glob_display_interval := c(display_max);
>         fi;# end if 10;
>         chk_data();
>         min_value := glob_larger_float;
>         est_answer := est_size_answer();
>         opt_iter := 1;
>         est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>         omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>         estimated_step_error  := glob_small_float;
>         while ((opt_iter <= 100) and ( not found_h)) do # do number 1
>             omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
>             array_x[1]   := c(x_start);
>             array_x[2]   :=  c(glob_h);
>             glob_next_display := c(x_start);
>             order_diff := 1;
>             #Start Series array_y
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             rows   :=  order_diff;
>             r_order   :=  1;
>             while (r_order <= rows) do # do number 2
>                 term_no   :=  1;
>                 while (term_no <= (rows - r_order + 1)) do # do number 3
>                     it  := term_no + r_order - 1;
>                     if (term_no < ATS_MAX_TERMS) then # if number 10
>                         array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 10;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             atomall();
>             if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
>                 omniout_str(ALWAYS,"SETTING H FOR MIN H");
>                 glob_h := glob_check_sign * float_abs(glob_min_h);
>                 glob_h_reason := 1;
>                 found_h := true;
>             fi;# end if 10;
>             if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
>                 omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>                 glob_h_reason := 2;
>                 glob_h := glob_display_interval;
>                 found_h := true;
>             fi;# end if 10;
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if ( not found_h) then # if number 10
>                 est_answer := est_size_answer();
>                 est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>                 omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>                 estimated_step_error := test_suggested_h();
>                 omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
>                 if (estimated_step_error < est_needed_step_err) then # if number 11
>                     omniout_str(ALWAYS,"Double H and LOOP");
>                     glob_h := glob_h*glob__2;
>                 else
>                     omniout_str(ALWAYS,"Found H for OPTIMAL");
>                     found_h := true;
>                     glob_h_reason := 3;
>                     glob_h := glob_h/glob__2;
>                 fi;# end if 11;
>             fi;# end if 10;
>             opt_iter := opt_iter + 1;
>         od;# end do number 1;
>         if (( not found_h) and (opt_iter = 1)) then # if number 10
>             omniout_str(ALWAYS,"Beginning glob_h too large.");
>             found_h := false;
>         fi;# end if 10;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
>             omniout_str(ALWAYS,"SETTING H FOR MAX H");
>             glob_h := glob_check_sign * float_abs(glob_max_h);
>             glob_h_reason := 1;
>             found_h := true;
>         fi;# end if 10;
>     else
>         found_h := true;
>         glob_h := glob_h * glob_check_sign;
>     fi;# end if 9;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 9
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 9;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 9
>         omniout_str(ALWAYS,"START of Soultion");
>         #Start Series -- INITIALIZE FOR SOLUTION
>         array_x[1]   := c(x_start);
>         array_x[2]   :=  c(glob_h);
>         glob_next_display := c(x_start);
>         glob_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         order_diff := 1;
>         #Start Series array_y
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>             term_no   :=  term_no + 1;
>         od;# end do number 1;
>         rows   :=  order_diff;
>         r_order   :=  1;
>         while (r_order <= rows) do # do number 1
>             term_no   :=  1;
>             while (term_no <= (rows - r_order + 1)) do # do number 2
>                 it  := term_no + r_order - 1;
>                 if (term_no < ATS_MAX_TERMS) then # if number 10
>                     array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 10;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         current_iter   :=  1;
>         glob_clock_start_sec   := elapsed_time_seconds();
>         glob_clock_sec   :=  elapsed_time_seconds();
>         glob_iter   :=  0;
>         omniout_str(DEBUGL," ");
>         glob_reached_optimal_h   :=  true;
>         glob_optimal_clock_start_sec := elapsed_time_seconds();
>         while ((glob_iter < glob_max_iter)  and (glob_check_sign * array_x[1] < glob_check_sign * x_end )  and  (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
>             #left paren 0001C
>             if (reached_interval()) then # if number 10
>                 omniout_str(INFO," ");
>                 omniout_str(INFO,"TOP MAIN SOLVE Loop");
>             fi;# end if 10;
>             glob_iter   :=  glob_iter + 1;
>             glob_clock_sec   := elapsed_time_seconds();
>             track_estimated_error();
>             atomall();
>             track_estimated_error();
>             display_alot(current_iter);
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if (reached_interval()) then # if number 10
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 10;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #END SUM AND ADJUST EQ =1
>             #END PART 1
>             #START PART 2  MOVE TERMS to REGULAR Array
>             term_no := ATS_MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_y[term_no] := array_y_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
>                     ord := ord + 1;
>                 od;# end do number 3;
>                 term_no   :=  term_no - 1;
>             od;# end do number 2;
>             #END PART 2 HEVE MOVED TERMS to REGULAR Array
>             ;
>         od;# end do number 1;#right paren 0001C
>         omniout_str(ALWAYS,"Finished!");
>         if (glob_iter >= glob_max_iter)  then # if number 10
>             omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
>         fi;# end if 10;
>         if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec  )) then # if number 10
>             omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
>         fi;# end if 10;
>         glob_clock_sec   := elapsed_time_seconds();
>         omniout_str(INFO,"diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(x_start,x_end);
>         if (glob_html_log)  then # if number 10
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2015-04-24T20:32:51-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"mult_c_sin.ode.txt\">mult_c_sin</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; ")
>             ;
>             logitem_float(html_log_file,x_start)
>             ;
>             logitem_float(html_log_file,x_end)
>             ;
>             logitem_float(html_log_file,array_x[1])
>             ;
>             logitem_float(html_log_file,glob_h)
>             ;
>             logitem_h_reason(html_log_file)
>             ;
>             logitem_integer(html_log_file,Digits)
>             ;
>             ;
>             logitem_float(html_log_file,glob_desired_digits_correct)
>             ;
>             if (array_est_digits[1] <> -16) then # if number 11
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_min_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_integer(html_log_file,ATS_MAX_TERMS)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 11
>                 logitem_str(html_log_file,"Not Given")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 12
>                 logitem_str(html_log_file,"No Solution")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 13
>                 logitem_str(html_log_file,"Some Pole")
>                 ;
>                 logitem_str(html_log_file,"????")
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 14
>                 logitem_str(html_log_file,"No Pole")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 15
>                 logitem_str(html_log_file,"Real Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 16
>                 logitem_str(html_log_file,"Complex Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             fi;# end if 16;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_ratio_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_3_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_3_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_6_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_6_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             logitem_integer(html_log_file,glob_iter)
>             ;
>             logitem_time(html_log_file,(glob_clock_sec))
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 16
>                 logitem_time(html_log_file,(glob_total_exp_sec))
>                 ;
>                 0;
>             else
>                 logitem_str(html_log_file,"Done")
>                 ;
>                 0;
>             fi;# end if 16;
>             log_revs(html_log_file,"<td> 308.maple.seems.ok </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.mult_c_sin.mxt.txt\">mult_c_sin diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.mult_c_sin.mxt.txt\">mult_c_sin 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_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    ATS_MAX_TERMS := 40;
    Digits := 32;
    max_terms := 40;
    glob_html_log := true;
    array_y_init := Array(0 .. 40, []);
    array_norms := Array(0 .. 40, []);
    array_fact_1 := Array(0 .. 40, []);
    array_1st_rel_error := Array(0 .. 2, []);
    array_last_rel_error := Array(0 .. 2, []);
    array_est_rel_error := Array(0 .. 2, []);
    array_max_est_error := Array(0 .. 2, []);
    array_type_pole := Array(0 .. 2, []);
    array_type_real_pole := Array(0 .. 2, []);
    array_type_complex_pole := Array(0 .. 2, []);
    array_est_digits := Array(0 .. 2, []);
    array_y := Array(0 .. 40, []);
    array_x := Array(0 .. 40, []);
    array_tmp0 := Array(0 .. 40, []);
    array_tmp1_g := Array(0 .. 40, []);
    array_tmp1 := Array(0 .. 40, []);
    array_tmp2 := Array(0 .. 40, []);
    array_tmp3 := Array(0 .. 40, []);
    array_m1 := Array(0 .. 40, []);
    array_y_higher := Array(0 .. 2, 0 .. 41, []);
    array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
    array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
    array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
    array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
    array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
    array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_fact_2 := Array(0 .. 40, 0 .. 41, []);
    term := 1;
    while term <= 40 do array_y_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do
        array_last_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
    term := 1;
    while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_y[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_given_rad_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_given_ord_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 4 do
            array_rad_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 4 do
            array_ord_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 40 do
        term := 1;
        while term <= 40 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y);
    zero_ats_ar(array_x);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1_g);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_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_m1);
    array_m1[1] := glob__m1;
    iiif := 0;
    while iiif <= ATS_MAX_TERMS do
        jjjf := 0;
        while jjjf <= ATS_MAX_TERMS do
            array_fact_1[iiif] := 0;
            array_fact_2[iiif, jjjf] := 0;
            jjjf := jjjf + 1
        end do;
        iiif := iiif + 1
    end do;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := 5;
    glob_yes_pole := 4;
    glob_no_pole := 3;
    glob_not_given := 0;
    glob_no_sing_tests := 4;
    glob_ratio_test := 1;
    glob_three_term_test := 2;
    glob_six_term_test := 3;
    glob_log_10 := log(c(10.0));
    MAX_UNCHANGED := 10;
    glob__small := c(0.1*10^(-50));
    glob_small_float := c(0.1*10^(-50));
    glob_smallish_float := c(0.1*10^(-60));
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob__m2 := c(-2);
    glob__m1 := c(-1);
    glob__0 := c(0);
    glob__1 := c(1);
    glob__2 := c(2);
    glob__3 := c(3);
    glob__4 := c(4);
    glob__5 := c(5);
    glob__8 := c(8);
    glob__10 := c(10);
    glob__100 := c(100);
    glob__pi := c(0.);
    glob__0_5 := c(0.5);
    glob__0_8 := c(0.8);
    glob__m0_8 := c(-0.8);
    glob__0_25 := c(0.25);
    glob__0_125 := c(0.125);
    glob_prec := c(0.10*10^(-15));
    glob_check_sign := c(1.0);
    glob_desired_digits_correct := c(8.0);
    glob_max_estimated_step_error := c(0.);
    glob_ratio_of_radius := c(0.1);
    glob_percent_done := c(0.);
    glob_total_exp_sec := c(0.1);
    glob_optimal_expect_sec := c(0.1);
    glob_estimated_size_answer := c(100.0);
    glob_almost_1 := c(0.9990);
    glob_clock_sec := c(0.);
    glob_clock_start_sec := c(0.);
    glob_disp_incr := c(0.1);
    glob_h := c(0.1);
    glob_diff_rc_fm := c(0.1);
    glob_diff_rc_fmm1 := c(0.1);
    glob_diff_rc_fmm2 := c(0.1);
    glob_diff_ord_fm := c(0.1);
    glob_diff_ord_fmm1 := c(0.1);
    glob_diff_ord_fmm2 := c(0.1);
    glob_six_term_ord_save := c(0.1);
    glob_guess_error_rc := c(0.1);
    glob_guess_error_ord := c(0.1);
    glob_least_given_sing := c(0.99*10^201);
    glob_least_ratio_sing := c(0.99*10^201);
    glob_least_3_sing := c(0.99*10^101);
    glob_least_6_sing := c(0.99*10^101);
    glob_last_good_h := c(0.1);
    glob_max_h := c(0.1);
    glob_min_h := c(0.1*10^(-5));
    glob_display_interval := c(0.1);
    glob_abserr := c(0.1*10^(-10));
    glob_relerr := c(0.1*10^(-10));
    glob_min_pole_est := c(0.1*10^10);
    glob_max_rel_trunc_err := c(0.1*10^(-10));
    glob_max_trunc_err := c(0.1*10^(-10));
    glob_max_hours := c(0.);
    glob_optimal_clock_start_sec := c(0.);
    glob_optimal_start := c(0.);
    glob_upper_ratio_limit := c(1.0001);
    glob_lower_ratio_limit := c(0.9999);
    glob_max_sec := c(10000.0);
    glob_orig_start_sec := c(0.);
    glob_normmax := c(0.);
    glob_max_minutes := c(0.);
    glob_next_display := c(0.);
    glob_est_digits := 1;
    glob_subiter_method := 3;
    glob_html_log := true;
    glob_min_good_digits := 99999;
    glob_good_digits := 0;
    glob_min_apfp_est_good_digits := 99999;
    glob_apfp_est_good_digits := 0;
    glob_max_opt_iter := 10;
    glob_dump := false;
    glob_djd_debug := true;
    glob_display_flag := true;
    glob_djd_debug2 := true;
    glob_h_reason := 0;
    glob_sec_in_minute := 60;
    glob_min_in_hour := 60;
    glob_hours_in_day := 24;
    glob_days_in_year := 365;
    glob_sec_in_hour := 3600;
    glob_sec_in_day := 86400;
    glob_sec_in_year := 31536000;
    glob_not_yet_finished := true;
    glob_initial_pass := true;
    glob_not_yet_start_msg := true;
    glob_reached_optimal_h := false;
    glob_optimal_done := false;
    glob_type_given_pole := 0;
    glob_optimize := false;
    glob_look_poles := false;
    glob_dump_closed_form := false;
    glob_max_iter := 1000;
    glob_no_eqs := 0;
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_start := 0;
    glob_iter := 0;
    array_y_set_initial[1, 1] := true;
    array_y_set_initial[1, 2] := false;
    array_y_set_initial[1, 3] := false;
    array_y_set_initial[1, 4] := false;
    array_y_set_initial[1, 5] := false;
    array_y_set_initial[1, 6] := false;
    array_y_set_initial[1, 7] := false;
    array_y_set_initial[1, 8] := false;
    array_y_set_initial[1, 9] := false;
    array_y_set_initial[1, 10] := false;
    array_y_set_initial[1, 11] := false;
    array_y_set_initial[1, 12] := false;
    array_y_set_initial[1, 13] := false;
    array_y_set_initial[1, 14] := false;
    array_y_set_initial[1, 15] := false;
    array_y_set_initial[1, 16] := false;
    array_y_set_initial[1, 17] := false;
    array_y_set_initial[1, 18] := false;
    array_y_set_initial[1, 19] := false;
    array_y_set_initial[1, 20] := false;
    array_y_set_initial[1, 21] := false;
    array_y_set_initial[1, 22] := false;
    array_y_set_initial[1, 23] := false;
    array_y_set_initial[1, 24] := false;
    array_y_set_initial[1, 25] := false;
    array_y_set_initial[1, 26] := false;
    array_y_set_initial[1, 27] := false;
    array_y_set_initial[1, 28] := false;
    array_y_set_initial[1, 29] := false;
    array_y_set_initial[1, 30] := false;
    array_y_set_initial[1, 31] := false;
    array_y_set_initial[1, 32] := false;
    array_y_set_initial[1, 33] := false;
    array_y_set_initial[1, 34] := false;
    array_y_set_initial[1, 35] := false;
    array_y_set_initial[1, 36] := false;
    array_y_set_initial[1, 37] := false;
    array_y_set_initial[1, 38] := false;
    array_y_set_initial[1, 39] := false;
    array_y_set_initial[1, 40] := false;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 40;
    glob_iolevel := INFO;
    glob_orig_start_sec := elapsed_time_seconds();
    glob_display_flag := true;
    glob_no_eqs := 1;
    glob_iter := -1;
    opt_iter := -1;
    glob_max_iter := 50000;
    glob_max_hours := 0.;
    glob_max_minutes := 15.0;
    omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
    omniout_str(ALWAYS,
        "##############temp/mult_c_sinpostode.ode#################");
    omniout_str(ALWAYS,
        "diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=40;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(0.1);");
    omniout_str(ALWAYS, "x_end := c(5.0) ;");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 3;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
    omniout_str(ALWAYS, "glob_look_poles:=false;");
    omniout_str(ALWAYS, "glob_h:=c(0.001);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y := proc(x)");
    omniout_str(ALWAYS, "return(cos(x) * c(-2.0));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(0.1);
    x_end := c(5.0);
    array_y_init[1] := exact_soln_y(x_start);
    glob_look_poles := true;
    glob_type_given_pole := 3;
    glob_desired_digits_correct := 8;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000;
    glob_upper_ratio_limit := c(1.000001);
    glob_lower_ratio_limit := c(0.999999);
    glob_look_poles := false;
    glob_h := c(0.001);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(x_start, x_end));
    glob__pi := arccos(glob__m1);
    glob_prec = expt(10.0, c(-Digits));
    if glob_optimize then
        omniout_str(ALWAYS, "START of Optimize");
        found_h := false;
        glob_min_pole_est := glob_larger_float;
        last_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        glob_min_h := float_abs(glob_min_h)*glob_check_sign;
        glob_max_h := float_abs(glob_max_h)*glob_check_sign;
        glob_h := float_abs(glob_min_h)*glob_check_sign;
        glob_display_interval :=
            c(float_abs(c(glob_display_interval))*glob_check_sign);
        display_max := c(x_end) - c(x_start)/glob__10;
        if display_max < glob_display_interval then
            glob_display_interval := c(display_max)
        end if;
        chk_data();
        min_value := glob_larger_float;
        est_answer := est_size_answer();
        opt_iter := 1;
        est_needed_step_err :=
            estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
            ;
        omniout_float(ALWAYS, "est_needed_step_err", 32,
            est_needed_step_err, 16, "");
        estimated_step_error := glob_small_float;
        while opt_iter <= 100 and not found_h do
            omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
            array_x[1] := c(x_start);
            array_x[2] := c(glob_h);
            glob_next_display := c(x_start);
            order_diff := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y[term_no] := array_y_init[term_no]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1));
                term_no := term_no + 1
            end do;
            rows := order_diff;
            r_order := 1;
            while r_order <= rows do
                term_no := 1;
                while term_no <= rows - r_order + 1 do
                    it := term_no + r_order - 1;
                    if term_no < ATS_MAX_TERMS then
                        array_y_higher[r_order, term_no] :=
                        array_y_init[it]*expt(glob_h, c(term_no - 1))/
                        c(factorial_1(term_no - 1))
                    end if;
                    term_no := term_no + 1
                end do;
                r_order := r_order + 1
            end do;
            atomall();
            if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
                omniout_str(ALWAYS, "SETTING H FOR MIN H");
                glob_h := float_abs(glob_min_h)*glob_check_sign;
                glob_h_reason := 1;
                found_h := true
            end if;
            if
            glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
            then
                omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
                glob_h_reason := 2;
                glob_h := glob_display_interval;
                found_h := true
            end if;
            if glob_look_poles then check_for_pole() end if;
            if not found_h then
                est_answer := est_size_answer();
                est_needed_step_err := estimated_needed_step_error(x_start,
                    x_end, glob_h, est_answer);
                omniout_float(ALWAYS, "est_needed_step_err", 32,
                    est_needed_step_err, 16, "");
                estimated_step_error := test_suggested_h();
                omniout_float(ALWAYS, "estimated_step_error", 32,
                    estimated_step_error, 32, "");
                if estimated_step_error < est_needed_step_err then
                    omniout_str(ALWAYS, "Double H and LOOP");
                    glob_h := glob_h*glob__2
                else
                    omniout_str(ALWAYS, "Found H for OPTIMAL");
                    found_h := true;
                    glob_h_reason := 3;
                    glob_h := glob_h/glob__2
                end if
            end if;
            opt_iter := opt_iter + 1
        end do;
        if not found_h and opt_iter = 1 then
            omniout_str(ALWAYS, "Beginning glob_h too large.");
            found_h := false
        end if;
        if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
            omniout_str(ALWAYS, "SETTING H FOR MAX H");
            glob_h := float_abs(glob_max_h)*glob_check_sign;
            glob_h_reason := 1;
            found_h := true
        end if
    else found_h := true; glob_h := glob_check_sign*glob_h
    end if;
    if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
    end if;
    if found_h then
        omniout_str(ALWAYS, "START of Soultion");
        array_x[1] := c(x_start);
        array_x[2] := c(glob_h);
        glob_next_display := c(x_start);
        glob_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y[term_no] := array_y_init[term_no]*
                expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
            term_no := term_no + 1
        end do;
        rows := order_diff;
        r_order := 1;
        while r_order <= rows do
            term_no := 1;
            while term_no <= rows - r_order + 1 do
                it := term_no + r_order - 1;
                if term_no < ATS_MAX_TERMS then
                    array_y_higher[r_order, term_no] := array_y_init[it]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1))
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        current_iter := 1;
        glob_clock_start_sec := elapsed_time_seconds();
        glob_clock_sec := elapsed_time_seconds();
        glob_iter := 0;
        omniout_str(DEBUGL, " ");
        glob_reached_optimal_h := true;
        glob_optimal_clock_start_sec := elapsed_time_seconds();
        while glob_iter < glob_max_iter and
        glob_check_sign*array_x[1] < glob_check_sign*x_end and
        glob_clock_sec - glob_orig_start_sec < glob_max_sec do
            if reached_interval() then
                omniout_str(INFO, " ");
                omniout_str(INFO, "TOP MAIN SOLVE Loop")
            end if;
            glob_iter := glob_iter + 1;
            glob_clock_sec := elapsed_time_seconds();
            track_estimated_error();
            atomall();
            track_estimated_error();
            display_alot(current_iter);
            if glob_look_poles then check_for_pole() end if;
            if reached_interval() then glob_next_display :=
                glob_next_display + glob_display_interval
            end if;
            array_x[1] := array_x[1] + glob_h;
            array_x[2] := glob_h;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            term_no := ATS_MAX_TERMS;
            while 1 <= term_no do
                array_y[term_no] := array_y_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y_higher[ord, term_no] :=
                        array_y_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do
        end do;
        omniout_str(ALWAYS, "Finished!");
        if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
            "Maximum Iterations Reached before Solution Completed!")
        end if;
        if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
        then omniout_str(ALWAYS,
            "Maximum Time Reached before Solution Completed!")
        end if;
        glob_clock_sec := elapsed_time_seconds();
        omniout_str(INFO,
            "diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; ");
        omniout_int(INFO, "Iterations                      ", 32, glob_iter,
            4, " ");
        prog_report(x_start, x_end);
        if glob_html_log then
            logstart(html_log_file);
            logitem_str(html_log_file, "2015-04-24T20:32:51-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"mult_c_sin.ode.txt\">mult_c_sin</a>");
            logitem_str(html_log_file,
                "diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; ");
            logitem_float(html_log_file, x_start);
            logitem_float(html_log_file, x_end);
            logitem_float(html_log_file, array_x[1]);
            logitem_float(html_log_file, glob_h);
            logitem_h_reason(html_log_file);
            logitem_integer(html_log_file, Digits);
            logitem_float(html_log_file, glob_desired_digits_correct);
            if array_est_digits[1] <> -16 then
                logitem_integer(html_log_file, array_est_digits[1])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_min_good_digits <> -16 then
                logitem_integer(html_log_file, glob_min_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_good_digits <> -16 then
                logitem_integer(html_log_file, glob_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            logitem_integer(html_log_file, ATS_MAX_TERMS);
            if glob_type_given_pole = 0 then
                logitem_str(html_log_file, "Not Given");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 4 then
                logitem_str(html_log_file, "No Solution");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 5 then
                logitem_str(html_log_file, "Some Pole");
                logitem_str(html_log_file, "????")
            elif glob_type_given_pole = 3 then
                logitem_str(html_log_file, "No Pole");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 1 then
                logitem_str(html_log_file, "Real Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            elif glob_type_given_pole = 2 then
                logitem_str(html_log_file, "Complex Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_ratio_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_3_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_3_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_6_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_6_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            logitem_integer(html_log_file, glob_iter);
            logitem_time(html_log_file, glob_clock_sec);
            if c(glob_percent_done) < glob__100 then
                logitem_time(html_log_file, glob_total_exp_sec); 0
            else logitem_str(html_log_file, "Done"); 0
            end if;
            log_revs(html_log_file, "<td> 308.maple.seems.ok </td>");
            logitem_str(html_log_file, "<a href=\"diffeq.mult_c_sin.mxt.t\
                xt\">mult_c_sin diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.mult_c_sin.mxt.\
                txt\">mult_c_sin 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/mult_c_sinpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;







glob_type_given_pole := 3;

#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(cos(x) * c(-2.0));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0.1                                          
y[1] (closed_form)                = -1.9900083305560515321911239756077           
y[1] (numeric)                    = -1.9900083305560515321911239756077           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4.1MB, alloc=40.3MB, time=0.14
 
TOP MAIN SOLVE Loop
x[1]                              = 0.11                                         
y[1] (closed_form)                = -1.9879121959133937007156792228397           
y[1] (numeric)                    = -1.9879121959133937007156792228395           
absolute error                    = 2e-31                                        
relative error                    = 1.0060806529138739295356804682092e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y[1] (closed_form)                = -1.9856172717077325044961963357153           
y[1] (numeric)                    = -1.9856172717077325044961963357152           
absolute error                    = 1e-31                                        
relative error                    = 5.0362172723243327070511251393704e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.13                                         
y[1] (closed_form)                = -1.9831237874295760791890243423036           
y[1] (numeric)                    = -1.9831237874295760791890243423037           
absolute error                    = 1e-31                                        
relative error                    = 5.0425495692134730704740281089472e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y[1] (closed_form)                = -1.9804319924252743437978964540228           
y[1] (numeric)                    = -1.9804319924252743437978964540228           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y[1] (closed_form)                = -1.9775421558720845734699619973087           
y[1] (numeric)                    = -1.9775421558720845734699619973086           
absolute error                    = 1e-31                                        
relative error                    = 5.0567822133683204545008538115132e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.16                                         
y[1] (closed_form)                = -1.9744545667512538980819050480367           
y[1] (numeric)                    = -1.9744545667512538980819050480365           
absolute error                    = 2e-31                                        
relative error                    = 1.0129379696443348809827832796951e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y[1] (closed_form)                = -1.971169533819121418343859980425            
y[1] (numeric)                    = -1.9711695338191214183438599804249           
absolute error                    = 1e-31                                        
relative error                    = 5.0731303565884052586297828787934e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.18                                         
y[1] (closed_form)                = -1.9676873855762428291854320492231           
y[1] (numeric)                    = -1.9676873855762428291854320492232           
absolute error                    = 1e-31                                        
relative error                    = 5.0821080997434313735652908156550e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y[1] (closed_form)                = -1.9640084702345406379357550083798           
y[1] (numeric)                    = -1.96400847023454063793575500838             
absolute error                    = 2e-31                                        
relative error                    = 1.0183255471200494754242006144117e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.2                                          
y[1] (closed_form)                = -1.9601331556824832622483930334963           
y[1] (numeric)                    = -1.9601331556824832622483930334964           
absolute error                    = 1e-31                                        
relative error                    = 5.1016942247059634489621638842460e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y[1] (closed_form)                = -1.9560618294482964898322771361987           
y[1] (numeric)                    = -1.9560618294482964898322771361988           
absolute error                    = 1e-31                                        
relative error                    = 5.1123128366655367622320430828974e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y[1] (closed_form)                = -1.9517948986612109788120459620894           
y[1] (numeric)                    = -1.9517948986612109788120459620895           
absolute error                    = 1e-31                                        
relative error                    = 5.1234891570109497845197695841652e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=44.5MB, alloc=44.3MB, time=0.61
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y[1] (closed_form)                = -1.9473327900107496739354612961432           
y[1] (numeric)                    = -1.9473327900107496739354612961433           
absolute error                    = 1e-31                                        
relative error                    = 5.1352290945323207758699956975329e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y[1] (closed_form)                = -1.9426759497040592098523504939268           
y[1] (numeric)                    = -1.9426759497040592098523504939267           
absolute error                    = 1e-31                                        
relative error                    = 5.1475388890892311330424515815269e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.25                                         
y[1] (closed_form)                = -1.9378248434212895682891908989884           
y[1] (numeric)                    = -1.9378248434212895682891908989883           
absolute error                    = 1e-31                                        
relative error                    = 5.1604251199219282219922467399379e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y[1] (closed_form)                = -1.9327799562690264511164352929001           
y[1] (numeric)                    = -1.9327799562690264511164352928998           
absolute error                    = 3e-31                                        
relative error                    = 1.5521684143450552422604516676916e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y[1] (closed_form)                = -1.9275417927317810260324654189844           
y[1] (numeric)                    = -1.9275417927317810260324654189841           
absolute error                    = 3e-31                                        
relative error                    = 1.5563864873447402272395457568340e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y[1] (closed_form)                = -1.922110876621541895849180107193            
y[1] (numeric)                    = -1.9221108766215418958491801071926           
absolute error                    = 4e-31                                        
relative error                    = 2.0810454009972227513247622478529e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y[1] (closed_form)                = -1.9164877510253943361402495558637           
y[1] (numeric)                    = -1.9164877510253943361402495558634           
absolute error                    = 3e-31                                        
relative error                    = 1.5653635137479407937787558729909e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.3                                          
y[1] (closed_form)                = -1.9106729782512120392846204551361           
y[1] (numeric)                    = -1.9106729782512120392846204551359           
absolute error                    = 2e-31                                        
relative error                    = 1.0467516015380856009327908455870e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y[1] (closed_form)                = -1.9046671397714267956856108724044           
y[1] (numeric)                    = -1.9046671397714267956856108724042           
absolute error                    = 2e-31                                        
relative error                    = 1.0500522418001151663727238237418e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y[1] (closed_form)                = -1.8984708361648817351506145475322           
y[1] (numeric)                    = -1.8984708361648817351506145475318           
absolute error                    = 4e-31                                        
relative error                    = 2.1069588870168985639438319667824e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y[1] (closed_form)                = -1.8920846870567739430588211567324           
y[1] (numeric)                    = -1.8920846870567739430588211567321           
absolute error                    = 3e-31                                        
relative error                    = 1.5855527083550578520268370405038e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y[1] (closed_form)                = -1.8855093310566924570052881200532           
y[1] (numeric)                    = -1.8855093310566924570052881200529           
absolute error                    = 3e-31                                        
relative error                    = 1.5910820225528746804406741433426e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=84.8MB, alloc=44.3MB, time=1.06
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y[1] (closed_form)                = -1.8787454256947578400700647146073           
y[1] (numeric)                    = -1.8787454256947578400700647146071           
absolute error                    = 2e-31                                        
relative error                    = 1.0645401833834950584242632965676e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y[1] (closed_form)                = -1.8717936473558697167018247362495           
y[1] (numeric)                    = -1.8717936473558697167018247362491           
absolute error                    = 4e-31                                        
relative error                    = 2.1369876992853746943292352547215e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.37                                         
y[1] (closed_form)                = -1.8646546912120688464076258089818           
y[1] (numeric)                    = -1.8646546912120688464076258089814           
absolute error                    = 4e-31                                        
relative error                    = 2.1451693007030203111482463335611e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y[1] (closed_form)                = -1.8573292711530204989850616154491           
y[1] (numeric)                    = -1.8573292711530204989850616154489           
absolute error                    = 2e-31                                        
relative error                    = 1.0768149897074578721590453030593e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y[1] (closed_form)                = -1.8498181197146260829013535057622           
y[1] (numeric)                    = -1.849818119714626082901353505762            
absolute error                    = 2e-31                                        
relative error                    = 1.0811873765776187103041051680289e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y[1] (closed_form)                = -1.8421219880057701655970534641036           
y[1] (numeric)                    = -1.8421219880057701655970534641035           
absolute error                    = 1e-31                                        
relative error                    = 5.4285221419161935155696497757938e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y[1] (closed_form)                = -1.834241645633210210951284116554            
y[1] (numeric)                    = -1.834241645633210210951284116554            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y[1] (closed_form)                = -1.8261778806246165448721775793313           
y[1] (numeric)                    = -1.8261778806246165448721775793314           
absolute error                    = 1e-31                                        
relative error                    = 5.4759178205464032512135787452728e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.43                                         
y[1] (closed_form)                = -1.8179314993497702449518209553269           
y[1] (numeric)                    = -1.8179314993497702449518209553269           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y[1] (closed_form)                = -1.8095033264399268343310747779967           
y[1] (numeric)                    = -1.8095033264399268343310747779969           
absolute error                    = 2e-31                                        
relative error                    = 1.1052756691720828446810853201811e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y[1] (closed_form)                = -1.8008942047053538433376812229729           
y[1] (numeric)                    = -1.800894204705353843337681222973            
absolute error                    = 1e-31                                        
relative error                    = 5.5527970348686364422223033550581e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y[1] (closed_form)                = -1.7921049950510504850727798070008           
y[1] (numeric)                    = -1.792104995051050485072779807001            
absolute error                    = 2e-31                                        
relative error                    = 1.1160060406745461642326441855094e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.47                                         
y[1] (closed_form)                = -1.7831365763906578729080385530668           
y[1] (numeric)                    = -1.7831365763906578729080385530669           
absolute error                    = 1e-31                                        
relative error                    = 5.6080953822626054342681472759509e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=125.1MB, alloc=44.3MB, time=1.52
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y[1] (closed_form)                = -1.7739898455585683887999096623175           
y[1] (numeric)                    = -1.7739898455585683887999096623177           
absolute error                    = 2e-31                                        
relative error                    = 1.1274021691878787428048684309356e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.49                                         
y[1] (closed_form)                = -1.7646657172202429914109363182733           
y[1] (numeric)                    = -1.7646657172202429914109363182735           
absolute error                    = 2e-31                                        
relative error                    = 1.1333591288612230659188985538320e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y[1] (closed_form)                = -1.7551651237807454322325631652077           
y[1] (numeric)                    = -1.7551651237807454322325631652079           
absolute error                    = 2e-31                                        
relative error                    = 1.1394939273245491223133277682049e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.51                                         
y[1] (closed_form)                = -1.745489015291502526211616947151            
y[1] (numeric)                    = -1.7454890152915025262116169471513           
absolute error                    = 3e-31                                        
relative error                    = 1.7187160582038896000689489949602e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.52                                         
y[1] (closed_form)                = -1.735638359355299800775695143977            
y[1] (numeric)                    = -1.7356383593552998007756951439773           
absolute error                    = 3e-31                                        
relative error                    = 1.7284706712257416263216281791913e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.53                                         
y[1] (closed_form)                = -1.7256141410295220236133900371284           
y[1] (numeric)                    = -1.7256141410295220236133900371288           
absolute error                    = 4e-31                                        
relative error                    = 2.3180153111248567922165470502791e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.54                                         
y[1] (closed_form)                = -1.7154173627276482850759375578356           
y[1] (numeric)                    = -1.7154173627276482850759375578359           
absolute error                    = 3e-31                                        
relative error                    = 1.7488455376420840630806391060144e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.55                                         
y[1] (closed_form)                = -1.7050490441190114856099635952355           
y[1] (numeric)                    = -1.7050490441190114856099635952357           
absolute error                    = 2e-31                                        
relative error                    = 1.1729867870360221144899718332545e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.56                                         
y[1] (closed_form)                = -1.6945102220268322521890510077326           
y[1] (numeric)                    = -1.6945102220268322521890510077328           
absolute error                    = 2e-31                                        
relative error                    = 1.1802820508263244778218975785322e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.57                                         
y[1] (closed_form)                = -1.683801950324537480267512727832            
y[1] (numeric)                    = -1.6838019503245374802675127278322           
absolute error                    = 2e-31                                        
relative error                    = 1.1877881478962049113853027126885e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y[1] (closed_form)                = -1.6729252998303738693157746561              
y[1] (numeric)                    = -1.6729252998303738693157746561003           
absolute error                    = 3e-31                                        
relative error                    = 1.7932659637009403627946262823684e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.59                                         
y[1] (closed_form)                = -1.6618813582003269904959930449814           
y[1] (numeric)                    = -1.6618813582003269904959930449817           
absolute error                    = 3e-31                                        
relative error                    = 1.8051830145376557737421752564486e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=165.5MB, alloc=44.3MB, time=1.97
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y[1] (closed_form)                = -1.6506712298193565944819049979108           
y[1] (numeric)                    = -1.650671229819356594481904997911            
absolute error                    = 2e-31                                        
relative error                    = 1.2116283145123167046145551213724e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.61                                         
y[1] (closed_form)                = -1.6392960356909590358014931573096           
y[1] (numeric)                    = -1.6392960356909590358014931573098           
absolute error                    = 2e-31                                        
relative error                    = 1.2200358912946465931687778838392e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.62                                         
y[1] (closed_form)                = -1.6277569133250678573679993087214           
y[1] (numeric)                    = -1.6277569133250678573679993087216           
absolute error                    = 2e-31                                        
relative error                    = 1.2286846909558135601849115214852e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.63                                         
y[1] (closed_form)                = -1.6160550166243037450474179315541           
y[1] (numeric)                    = -1.6160550166243037450474179315543           
absolute error                    = 2e-31                                        
relative error                    = 1.2375816289829659822819115182141e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.64                                         
y[1] (closed_form)                = -1.6041915157685852271722215585206           
y[1] (numeric)                    = -1.6041915157685852271722215585207           
absolute error                    = 1e-31                                        
relative error                    = 6.2336696720459175218826666221322e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y[1] (closed_form)                = -1.5921675970981116578352091413598           
y[1] (numeric)                    = -1.59216759709811165783520914136             
absolute error                    = 2e-31                                        
relative error                    = 1.2561491664854909886649278077748e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.66                                         
y[1] (closed_form)                = -1.5799844629947301855676341824605           
y[1] (numeric)                    = -1.5799844629947301855676341824606           
absolute error                    = 1e-31                                        
relative error                    = 6.3291761623059413489214200885282e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.67                                         
y[1] (closed_form)                = -1.5676433317616985706058842896762           
y[1] (numeric)                    = -1.5676433317616985706058842896764           
absolute error                    = 2e-31                                        
relative error                    = 1.2758004065583108419105880067084e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.68                                         
y[1] (closed_form)                = -1.5551454375018558743647881680886           
y[1] (numeric)                    = -1.5551454375018558743647881680888           
absolute error                    = 2e-31                                        
relative error                    = 1.2860533502337547426689159643017e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.69                                         
y[1] (closed_form)                = -1.5424920299942132039470786309955           
y[1] (numeric)                    = -1.5424920299942132039470786309959           
absolute error                    = 4e-31                                        
relative error                    = 2.5932062676622104529085434785655e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y[1] (closed_form)                = -1.5296843745689768525117199803837           
y[1] (numeric)                    = -1.529684374568976852511719980384            
absolute error                    = 3e-31                                        
relative error                    = 1.9611888896003908048120092529580e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.71                                         
y[1] (closed_form)                = -1.5167237519810163330829158882791           
y[1] (numeric)                    = -1.5167237519810163330829158882794           
absolute error                    = 3e-31                                        
relative error                    = 1.9779475307099619397946020394157e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=205.8MB, alloc=44.3MB, time=2.42
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y[1] (closed_form)                = -1.5036114582817899588909739245039           
y[1] (numeric)                    = -1.5036114582817899588909739245041           
absolute error                    = 2e-31                                        
relative error                    = 1.3301308585965713491100945769746e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.73                                         
y[1] (closed_form)                = -1.4903488046897407775802643171007           
y[1] (numeric)                    = -1.4903488046897407775802643171009           
absolute error                    = 2e-31                                        
relative error                    = 1.3419677284314378095774142725353e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.74                                         
y[1] (closed_form)                = -1.4769371174591758195828491213977           
y[1] (numeric)                    = -1.4769371174591758195828491213978           
absolute error                    = 1e-31                                        
relative error                    = 6.7707689662531696064854064747759e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.75                                         
y[1] (closed_form)                = -1.4633777377476417726236775060002           
y[1] (numeric)                    = -1.4633777377476417726236775060002           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.76                                         
y[1] (closed_form)                = -1.449672021481810344679376733334            
y[1] (numeric)                    = -1.4496720214818103446793767333339           
absolute error                    = 1e-31                                        
relative error                    = 6.8981120224547799759350600885765e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y[1] (closed_form)                = -1.4358213392218867267425811306487           
y[1] (numeric)                    = -1.4358213392218867267425811306486           
absolute error                    = 1e-31                                        
relative error                    = 6.9646548124290243194234616687204e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y[1] (closed_form)                = -1.4218270760245547144325300475291           
y[1] (numeric)                    = -1.4218270760245547144325300475291           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.79                                         
y[1] (closed_form)                = -1.4076906313044721938255617221699           
y[1] (numeric)                    = -1.4076906313044721938255617221699           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y[1] (closed_form)                = -1.3934134186943308418414999632846           
y[1] (numeric)                    = -1.3934134186943308418414999632845           
absolute error                    = 1e-31                                        
relative error                    = 7.1766209983611990024847620408145e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.81                                         
y[1] (closed_form)                = -1.3789968659034940350992784813602           
y[1] (numeric)                    = -1.37899686590349403509927848136             
absolute error                    = 2e-31                                        
relative error                    = 1.4503296196323374815898349922412e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y[1] (closed_form)                = -1.3644424145752271033331159568739           
y[1] (numeric)                    = -1.3644424145752271033331159568735           
absolute error                    = 4e-31                                        
relative error                    = 2.9316004525154433989688989109210e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.83                                         
y[1] (closed_form)                = -1.3497515201425342042249258357289           
y[1] (numeric)                    = -1.3497515201425342042249258357285           
absolute error                    = 4e-31                                        
relative error                    = 2.9635084238153691318662949969539e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.84                                         
y[1] (closed_form)                = -1.3349256516826162358453420737417           
y[1] (numeric)                    = -1.3349256516826162358453420737413           
absolute error                    = 4e-31                                        
relative error                    = 2.9964215572291778484960585808099e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=246.3MB, alloc=44.3MB, time=2.88
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y[1] (closed_form)                = -1.3199662917699643407908320589229           
y[1] (numeric)                    = -1.3199662917699643407908320589226           
absolute error                    = 3e-31                                        
relative error                    = 2.2727853117955391450555323307239e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.86                                         
y[1] (closed_form)                = -1.3048749363281036925440613284477           
y[1] (numeric)                    = -1.3048749363281036925440613284474           
absolute error                    = 3e-31                                        
relative error                    = 2.2990709044055593285178414589012e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y[1] (closed_form)                = -1.2896530944800023895553276109657           
y[1] (numeric)                    = -1.2896530944800023895553276109652           
absolute error                    = 5e-31                                        
relative error                    = 3.8770115943590526293685177850972e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.88                                         
y[1] (closed_form)                = -1.2743022883971604160309972114442           
y[1] (numeric)                    = -1.2743022883971604160309972114437           
absolute error                    = 5e-31                                        
relative error                    = 3.9237157819822225789180651052957e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.89                                         
y[1] (closed_form)                = -1.2588240531473937604071061147605           
y[1] (numeric)                    = -1.25882405314739376040710611476             
absolute error                    = 5e-31                                        
relative error                    = 3.9719609642814457226488366286038e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y[1] (closed_form)                = -1.2432199365413289129694323028143           
y[1] (numeric)                    = -1.2432199365413289129694323028137           
absolute error                    = 6e-31                                        
relative error                    = 4.8261774313981485390720385869191e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y[1] (closed_form)                = -1.2274914989776230930423564523494           
y[1] (numeric)                    = -1.2274914989776230930423564523487           
absolute error                    = 7e-31                                        
relative error                    = 5.7026871516668715436874882038681e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.92                                         
y[1] (closed_form)                = -1.2116403132869256835948094133488           
y[1] (numeric)                    = -1.2116403132869256835948094133482           
absolute error                    = 6e-31                                        
relative error                    = 4.9519646500728093203024089192794e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.93                                         
y[1] (closed_form)                = -1.195667964574596476989814168866            
y[1] (numeric)                    = -1.1956679645745964769898141688655           
absolute error                    = 5e-31                                        
relative error                    = 4.1817629543825209812222471364189e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y[1] (closed_form)                = -1.179576050062196459921979630448            
y[1] (numeric)                    = -1.1795760500621964599219796304477           
absolute error                    = 3e-31                                        
relative error                    = 2.5432866323810292476682675717039e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.95                                         
y[1] (closed_form)                = -1.1633661789277669883323619475209           
y[1] (numeric)                    = -1.1633661789277669883323619475207           
absolute error                    = 2e-31                                        
relative error                    = 1.7191491692180088054618740078577e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y[1] (closed_form)                = -1.1470399721449133242501016007037           
y[1] (numeric)                    = -1.1470399721449133242501016007035           
absolute error                    = 2e-31                                        
relative error                    = 1.7436183991566481011479254485116e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=286.8MB, alloc=44.3MB, time=3.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.97                                         
y[1] (closed_form)                = -1.1305990623207086260730555096997           
y[1] (numeric)                    = -1.1305990623207086260730555096996           
absolute error                    = 1e-31                                        
relative error                    = 8.8448684712984260239665712543228e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.98                                         
y[1] (closed_form)                = -1.1140450935324346017533165347199           
y[1] (numeric)                    = -1.1140450935324346017533165347198           
absolute error                    = 1e-31                                        
relative error                    = 8.9762973312793081933182964276292e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.99                                         
y[1] (closed_form)                = -1.0973797211631751506862528173072           
y[1] (numeric)                    = -1.0973797211631751506862528173071           
absolute error                    = 1e-31                                        
relative error                    = 9.1126159953096559106356852392698e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y[1] (closed_form)                = -1.080604611736279434801873214886            
y[1] (numeric)                    = -1.0806046117362794348018732148858           
absolute error                    = 2e-31                                        
relative error                    = 1.8508157176809256179117532413986e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y[1] (closed_form)                = -1.0637214427487109324134627115584           
y[1] (numeric)                    = -1.0637214427487109324134627115582           
absolute error                    = 2e-31                                        
relative error                    = 1.8801914858761304160058742988837e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y[1] (closed_form)                = -1.0467319025032991397792276160676           
y[1] (numeric)                    = -1.0467319025032991397792276160673           
absolute error                    = 3e-31                                        
relative error                    = 2.8660634044165329681567634169991e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y[1] (closed_form)                = -1.0296376899399106950670045996747           
y[1] (numeric)                    = -1.0296376899399106950670045996745           
absolute error                    = 2e-31                                        
relative error                    = 1.9424308371197244332449996487096e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y[1] (closed_form)                = -1.0124405144655568074689468419843           
y[1] (numeric)                    = -1.0124405144655568074689468419842           
absolute error                    = 1e-31                                        
relative error                    = 9.8771235021928783811416896425128e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y[1] (closed_form)                = -0.9951420957834539805816991456242           
y[1] (numeric)                    = -0.99514209578345398058169914562401          
absolute error                    = 1.9e-31                                      
relative error                    = 1.9092750754395238823873500044170e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y[1] (closed_form)                = -0.97774416372105512383727507991282          
y[1] (numeric)                    = -0.97774416372105512383727507991264          
absolute error                    = 1.8e-31                                      
relative error                    = 1.8409723798806840155425508435042e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y[1] (closed_form)                = -0.96024845805706824873018613635184          
y[1] (numeric)                    = -0.96024845805706824873018613635166          
absolute error                    = 1.8e-31                                      
relative error                    = 1.8745148559176595105285365418384e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y[1] (closed_form)                = -0.94265672834748004782704957705206          
y[1] (numeric)                    = -0.94265672834748004782704957705188          
absolute error                    = 1.8e-31                                      
relative error                    = 1.9094967933401181462999943116344e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=327.3MB, alloc=44.3MB, time=3.80
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y[1] (closed_form)                = -0.92497073375060175405579414775028          
y[1] (numeric)                    = -0.9249707337506017540557941477501           
absolute error                    = 1.8e-31                                      
relative error                    = 1.9460075160446437012306328449831e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y[1] (closed_form)                = -0.90719224285115477554274010356944          
y[1] (numeric)                    = -0.90719224285115477554274010356923          
absolute error                    = 2.1e-31                                      
relative error                    = 2.3148346081532269856853265997174e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y[1] (closed_form)                = -0.88932303348341369728747502386714          
y[1] (numeric)                    = -0.88932303348341369728747502386695          
absolute error                    = 1.9e-31                                      
relative error                    = 2.1364565275655102153590532337523e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y[1] (closed_form)                = -0.87136489255342433522797758792226          
y[1] (numeric)                    = -0.87136489255342433522797758792205          
absolute error                    = 2.1e-31                                      
relative error                    = 2.4100121750902957128886950469435e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y[1] (closed_form)                = -0.85331961586031462074243167130708          
y[1] (numeric)                    = -0.85331961586031462074243167130688          
absolute error                    = 2.0e-31                                      
relative error                    = 2.3437876767705676070253513391040e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y[1] (closed_form)                = -0.83518900791671618435037348164516          
y[1] (numeric)                    = -0.83518900791671618435037348164495          
absolute error                    = 2.1e-31                                      
relative error                    = 2.5144009081707273878601433364520e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y[1] (closed_form)                = -0.81697488176831459630515343761984          
y[1] (numeric)                    = -0.81697488176831459630515343761963          
absolute error                    = 2.1e-31                                      
relative error                    = 2.5704584643466893110588901464424e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y[1] (closed_form)                = -0.79867905881254630890327924678802          
y[1] (numeric)                    = -0.7986790588125463089032792467878           
absolute error                    = 2.2e-31                                      
relative error                    = 2.7545482452875357483025530450983e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.17                                         
y[1] (closed_form)                = -0.780303368616460430665323870101            
y[1] (numeric)                    = -0.78030336861646043066532387010078          
absolute error                    = 2.2e-31                                      
relative error                    = 2.8194162533230811868694119356037e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y[1] (closed_form)                = -0.76184964873376354605919893342552          
y[1] (numeric)                    = -0.76184964873376354605919893342531          
absolute error                    = 2.1e-31                                      
relative error                    = 2.7564493906249306563994538481296e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y[1] (closed_form)                = -0.74331974452106587613135911670094          
y[1] (numeric)                    = -0.74331974452106587613135911670071          
absolute error                    = 2.3e-31                                      
relative error                    = 3.0942269688825915453012812394672e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y[1] (closed_form)                = -0.72471550895334715527674671124616          
y[1] (numeric)                    = -0.72471550895334715527674671124592          
absolute error                    = 2.4e-31                                      
relative error                    = 3.3116443215988877482601195270853e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=367.7MB, alloc=44.3MB, time=4.25
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y[1] (closed_form)                = -0.70603880243866067740602142732958          
y[1] (numeric)                    = -0.70603880243866067740602142732936          
absolute error                    = 2.2e-31                                      
relative error                    = 3.1159760517427536997627838422461e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.22                                         
y[1] (closed_form)                = -0.6872914926320940409510459488704           
y[1] (numeric)                    = -0.68729149263209404095104594887018          
absolute error                    = 2.2e-31                                      
relative error                    = 3.2009708014495331933273173626666e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y[1] (closed_form)                = -0.66847545424900519647909449099532          
y[1] (numeric)                    = -0.66847545424900519647909449099511          
absolute error                    = 2.1e-31                                      
relative error                    = 3.1414766041921952169969188930941e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y[1] (closed_form)                = -0.64959256887755247315538683139476          
y[1] (numeric)                    = -0.64959256887755247315538683139454          
absolute error                    = 2.2e-31                                      
relative error                    = 3.3867382501025773322772009191760e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y[1] (closed_form)                = -0.63064472479053733089507710487608          
y[1] (numeric)                    = -0.63064472479053733089507710487585          
absolute error                    = 2.3e-31                                      
relative error                    = 3.6470613478356188649751194478538e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y[1] (closed_form)                = -0.61163381675657865377268497835296          
y[1] (numeric)                    = -0.61163381675657865377268497835274          
absolute error                    = 2.2e-31                                      
relative error                    = 3.5969234200723861237884732144901e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.27                                         
y[1] (closed_form)                = -0.59256174585063746710227403217592          
y[1] (numeric)                    = -0.5925617458506374671022740321757           
absolute error                    = 2.2e-31                                      
relative error                    = 3.7126932600784817945329155785315e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y[1] (closed_form)                = -0.57343041926391102555877378718518          
y[1] (numeric)                    = -0.57343041926391102555877378718496          
absolute error                    = 2.2e-31                                      
relative error                    = 3.8365596349493444157923609126982e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y[1] (closed_form)                = -0.55424175011311528277321218012236          
y[1] (numeric)                    = -0.55424175011311528277321218012213          
absolute error                    = 2.3e-31                                      
relative error                    = 4.1498136860505233527540086928004e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y[1] (closed_form)                = -0.53499765724917481399596821858574          
y[1] (numeric)                    = -0.53499765724917481399596821858551          
absolute error                    = 2.3e-31                                      
relative error                    = 4.2990842461367573477352186558769e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.31                                         
y[1] (closed_form)                = -0.5157000650653393226763539572324           
y[1] (numeric)                    = -0.51570006506533932267635395723216          
absolute error                    = 2.4e-31                                      
relative error                    = 4.6538679410403398357284019774639e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.32                                         
y[1] (closed_form)                = -0.4963509033047459191479654588547           
y[1] (numeric)                    = -0.49635090330474591914796545885448          
absolute error                    = 2.2e-31                                      
relative error                    = 4.4323481338549312440046261786178e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=408.3MB, alloc=44.3MB, time=4.70
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y[1] (closed_form)                = -0.47695210686744641503156997202116          
y[1] (numeric)                    = -0.47695210686744641503156997202093          
absolute error                    = 2.3e-31                                      
relative error                    = 4.8222871162181729181496015345491e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y[1] (closed_form)                = -0.45750561561691893046527898460028          
y[1] (numeric)                    = -0.45750561561691893046527898460005          
absolute error                    = 2.3e-31                                      
relative error                    = 5.0272606968956822698252186918120e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y[1] (closed_form)                = -0.43801337418608316284004434602126          
y[1] (numeric)                    = -0.43801337418608316284004434602101          
absolute error                    = 2.5e-31                                      
relative error                    = 5.7075882777449483108441764763436e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y[1] (closed_form)                = -0.41847733178283871535195050478372          
y[1] (numeric)                    = -0.41847733178283871535195050478349          
absolute error                    = 2.3e-31                                      
relative error                    = 5.4961160983351510004591764047324e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.37                                         
y[1] (closed_form)                = -0.39889944199514593137639677929062          
y[1] (numeric)                    = -0.3988994419951459313763967792904           
absolute error                    = 2.2e-31                                      
relative error                    = 5.5151744233995971223302011257523e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y[1] (closed_form)                = -0.3792816625956687264183001471964           
y[1] (numeric)                    = -0.3792816625956687264183001471962           
absolute error                    = 2.0e-31                                      
relative error                    = 5.2731260096064537536605461963399e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y[1] (closed_form)                = -0.3596259553459989531923264356081           
y[1] (numeric)                    = -0.3596259553459989531923264356079           
absolute error                    = 2.0e-31                                      
relative error                    = 5.5613338533248644647924530616214e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y[1] (closed_form)                = -0.3399342858004818772334960704073           
y[1] (numeric)                    = -0.33993428580048187723349607040709          
absolute error                    = 2.1e-31                                      
relative error                    = 6.1776645890687120683439838253373e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y[1] (closed_form)                = -0.32020862310966238032712509872184          
y[1] (numeric)                    = -0.32020862310966238032712509872161          
absolute error                    = 2.3e-31                                      
relative error                    = 7.1828171823227732700125036143757e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y[1] (closed_form)                = -0.30045093982337154697396420595182          
y[1] (numeric)                    = -0.3004509398233715469739642059516           
absolute error                    = 2.2e-31                                      
relative error                    = 7.3223269039974755066634047138387e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y[1] (closed_form)                = -0.28066321169347332506779524914984          
y[1] (numeric)                    = -0.28066321169347332506779524914962          
absolute error                    = 2.2e-31                                      
relative error                    = 7.8385763019156665606341994257213e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y[1] (closed_form)                = -0.26084741747629098595504031225834          
y[1] (numeric)                    = -0.26084741747629098595504031225811          
absolute error                    = 2.3e-31                                      
relative error                    = 8.8174152623498839979709414201506e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=448.8MB, alloc=44.3MB, time=5.16
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y[1] (closed_form)                = -0.24100553873473314106573325449604          
y[1] (numeric)                    = -0.24100553873473314106573325449581          
absolute error                    = 2.3e-31                                      
relative error                    = 9.5433491366002764325636593367142e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.46                                         
y[1] (closed_form)                = -0.22113955964013910234929621824674          
y[1] (numeric)                    = -0.22113955964013910234929621824652          
absolute error                    = 2.2e-31                                      
relative error                    = 9.9484687569246538119045146194170e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y[1] (closed_form)                = -0.20125146677386340181394920292482          
y[1] (numeric)                    = -0.20125146677386340181394920292458          
absolute error                    = 2.4e-31                                      
relative error                    = 1.1925378922563404825407409628874e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y[1] (closed_form)                = -0.18134324892861931155245308129568          
y[1] (numeric)                    = -0.18134324892861931155245308129546          
absolute error                    = 2.2e-31                                      
relative error                    = 1.2131689561081859479102756318639e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.49                                         
y[1] (closed_form)                = -0.16141689690960122973663696912743          
y[1] (numeric)                    = -0.16141689690960122973663696912721          
absolute error                    = 2.2e-31                                      
relative error                    = 1.3629304255750080143499645826128e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y[1] (closed_form)                = -0.14147440333540582017637970286854          
y[1] (numeric)                    = -0.14147440333540582017637970286833          
absolute error                    = 2.1e-31                                      
relative error                    = 1.4843674548118398236019389855894e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y[1] (closed_form)                = -0.12151776243877181316319102983239          
y[1] (numeric)                    = -0.12151776243877181316319102983219          
absolute error                    = 2.0e-31                                      
relative error                    = 1.6458499233868991507680269426151e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.52                                         
y[1] (closed_form)                = -0.10154896986715839345225854030545          
y[1] (numeric)                    = -0.10154896986715839345225854030526          
absolute error                    = 1.9e-31                                      
relative error                    = 1.8710184874208876933908430243170e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y[1] (closed_form)                = -0.081570022483182117377978014152242         
y[1] (numeric)                    = -0.081570022483182117377978014152046         
absolute error                    = 1.96e-31                                     
relative error                    = 2.4028435206133569509406657721363e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y[1] (closed_form)                = -0.061582918164932315244953614152794         
y[1] (numeric)                    = -0.061582918164932315244953614152598         
absolute error                    = 1.96e-31                                     
relative error                    = 3.1827007527488352552127837731154e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.55                                         
y[1] (closed_form)                = -0.041589655606184947287825549391112         
y[1] (numeric)                    = -0.041589655606184947287825549390916         
absolute error                    = 1.96e-31                                     
relative error                    = 4.7127103397040906240671000209111e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.56                                         
y[1] (closed_form)                = -0.021592234116534891647841327521812         
y[1] (numeric)                    = -0.021592234116534891647841327521616         
absolute error                    = 1.96e-31                                     
relative error                    = 9.0773376641885892331897508861185e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=489.3MB, alloc=44.3MB, time=5.63
 
TOP MAIN SOLVE Loop
x[1]                              = 1.57                                         
y[1] (closed_form)                = -0.0015926534214666509708170672907084        
y[1] (numeric)                    = -0.0015926534214666509708170672905124        
absolute error                    = 1.960e-31                                    
relative error                    = 1.2306506698708278919196846285447e-26      % 
Desired digits                    = 8                                   
Estimated correct digits          = 9                                   
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.58                                         
y[1] (closed_form)                = 0.018407086537616529610778113965455          
y[1] (numeric)                    = 0.018407086537616529610778113965651          
absolute error                    = 1.96e-31                                     
relative error                    = 1.0648072936445235322194131216922e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.59                                         
y[1] (closed_form)                = 0.038404985803385136190054692486806          
y[1] (numeric)                    = 0.038404985803385136190054692487003          
absolute error                    = 1.97e-31                                     
relative error                    = 5.1295423205868182003640900251891e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y[1] (closed_form)                = 0.058399044602577452411540925892998          
y[1] (numeric)                    = 0.058399044602577452411540925893193          
absolute error                    = 1.95e-31                                     
relative error                    = 3.3390957219768221975163074946208e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.61                                         
y[1] (closed_form)                = 0.078387263545975219170655219202036          
y[1] (numeric)                    = 0.078387263545975219170655219202233          
absolute error                    = 1.97e-31                                     
relative error                    = 2.5131633774210878392431875659014e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.62                                         
y[1] (closed_form)                = 0.098367643828340890287488549424654          
y[1] (numeric)                    = 0.098367643828340890287488549424851          
absolute error                    = 1.97e-31                                     
relative error                    = 2.0026910509697697226405520325808e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.63                                         
y[1] (closed_form)                = 0.1183381874282964905959433948396            
y[1] (numeric)                    = 0.1183381874282964905959433948398            
absolute error                    = 2.0e-31                                      
relative error                    = 1.6900715174565611708855583988679e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.64                                         
y[1] (closed_form)                = 0.13829689730812408872898541491321           
y[1] (numeric)                    = 0.1382968973081240887289854149134            
absolute error                    = 1.9e-31                                      
relative error                    = 1.3738558398507084457650957602485e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.65                                         
y[1] (closed_form)                = 0.15824177761346790471922919468255           
y[1] (numeric)                    = 0.15824177761346790471922919468273           
absolute error                    = 1.8e-31                                      
relative error                    = 1.1374998607490381241603006212275e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.66                                         
y[1] (closed_form)                = 0.17817083387291808237051586330124           
y[1] (numeric)                    = 0.17817083387291808237051586330141           
absolute error                    = 1.7e-31                                      
relative error                    = 9.5414045219799553923165906898223e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.67                                         
y[1] (closed_form)                = 0.19808207319745616818956468489722           
y[1] (numeric)                    = 0.19808207319745616818956468489739           
absolute error                    = 1.7e-31                                      
relative error                    = 8.5823011267928910722500990306101e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.68                                         
y[1] (closed_form)                = 0.21797350447974235249600946834564           
y[1] (numeric)                    = 0.2179735044797423524960094683458            
absolute error                    = 1.6e-31                                      
relative error                    = 7.3403416796865696780405726093583e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=530.0MB, alloc=44.3MB, time=6.08
 
TOP MAIN SOLVE Loop
x[1]                              = 1.69                                         
y[1] (closed_form)                = 0.23784313859322454415278093966618           
y[1] (numeric)                    = 0.23784313859322454415278093966634           
absolute error                    = 1.6e-31                                      
relative error                    = 6.7271227980910075473469486215845e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.7                                          
y[1] (closed_form)                = 0.25768898859104936817528571466974           
y[1] (numeric)                    = 0.25768898859104936817528571466993           
absolute error                    = 1.9e-31                                      
relative error                    = 7.3732292962478376570798943678558e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.71                                         
y[1] (closed_form)                = 0.27750906990475519528537956610222           
y[1] (numeric)                    = 0.2775090699047551952853795661024            
absolute error                    = 1.8e-31                                      
relative error                    = 6.4862744868763530749750381457892e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.72                                         
y[1] (closed_form)                = 0.29730140054272733427275656066238           
y[1] (numeric)                    = 0.29730140054272733427275656066256           
absolute error                    = 1.8e-31                                      
relative error                    = 6.0544618919186994643919399392070e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.73                                         
y[1] (closed_form)                = 0.31706400128839554180989670268514           
y[1] (numeric)                    = 0.31706400128839554180989670268535           
absolute error                    = 2.1e-31                                      
relative error                    = 6.6232684614671184430767005774242e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.74                                         
y[1] (closed_form)                = 0.33679489589815403013475463069018           
y[1] (numeric)                    = 0.33679489589815403013475463069039           
absolute error                    = 2.1e-31                                      
relative error                    = 6.2352488876049801250827789164572e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.75                                         
y[1] (closed_form)                = 0.35649211129898418076535388788526           
y[1] (numeric)                    = 0.35649211129898418076535388788548           
absolute error                    = 2.2e-31                                      
relative error                    = 6.1712445528840763128508664162397e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.76                                         
y[1] (closed_form)                = 0.3761536777857602021396003530082            
y[1] (numeric)                    = 0.37615367778576020213960035300842           
absolute error                    = 2.2e-31                                      
relative error                    = 5.8486733745376765969372053030996e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.77                                         
y[1] (closed_form)                = 0.39577762921821800077897168346078           
y[1] (numeric)                    = 0.39577762921821800077897168346102           
absolute error                    = 2.4e-31                                      
relative error                    = 6.0640112599106090105995699500926e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.78                                         
y[1] (closed_form)                = 0.41536200321756756925310658062526           
y[1] (numeric)                    = 0.41536200321756756925310658062548           
absolute error                    = 2.2e-31                                      
relative error                    = 5.2965846248763273558806487846653e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.79                                         
y[1] (closed_form)                = 0.43490484136272922987034052892922           
y[1] (numeric)                    = 0.43490484136272922987034052892945           
absolute error                    = 2.3e-31                                      
relative error                    = 5.2885132131277004457236408449566e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y[1] (closed_form)                = 0.45440418938617411063334861306116           
y[1] (numeric)                    = 0.45440418938617411063334861306141           
absolute error                    = 2.5e-31                                      
relative error                    = 5.5017098398170402774299944042027e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
memory used=570.5MB, alloc=44.3MB, time=6.55
x[1]                              = 1.81                                         
y[1] (closed_form)                = 0.47385809736934926957549970168396           
y[1] (numeric)                    = 0.47385809736934926957549970168419           
absolute error                    = 2.3e-31                                      
relative error                    = 4.8537737621633638693742450582187e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.82                                         
y[1] (closed_form)                = 0.49326461993766792512834208966174           
y[1] (numeric)                    = 0.49326461993766792512834208966197           
absolute error                    = 2.3e-31                                      
relative error                    = 4.6628116167963611961680670695740e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.83                                         
y[1] (closed_form)                = 0.51262181645504529365967516723706           
y[1] (numeric)                    = 0.51262181645504529365967516723729           
absolute error                    = 2.3e-31                                      
relative error                    = 4.4867384223037647641758494897930e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.84                                         
y[1] (closed_form)                = 0.5319277512179605807605659665632            
y[1] (numeric)                    = 0.53192775121796058076056596656342           
absolute error                    = 2.2e-31                                      
relative error                    = 4.1359000258261329712111528426094e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.85                                         
y[1] (closed_form)                = 0.5511804936490257202438996709496            
y[1] (numeric)                    = 0.55118049364902572024389967094984           
absolute error                    = 2.4e-31                                      
relative error                    = 4.3542905230754482762686787291199e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.86                                         
y[1] (closed_form)                = 0.57037811849004150414187097657824           
y[1] (numeric)                    = 0.57037811849004150414187097657847           
absolute error                    = 2.3e-31                                      
relative error                    = 4.0324127546981919603844841224728e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.87                                         
y[1] (closed_form)                = 0.58951870599452179825029612961978           
y[1] (numeric)                    = 0.58951870599452179825029612962001           
absolute error                    = 2.3e-31                                      
relative error                    = 3.9014877333194803438978897549181e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.88                                         
y[1] (closed_form)                = 0.60860034211966659095862751904448           
y[1] (numeric)                    = 0.60860034211966659095862751904471           
absolute error                    = 2.3e-31                                      
relative error                    = 3.7791631729772515086976772481116e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.89                                         
y[1] (closed_form)                = 0.62762111871776467822076483110246           
y[1] (numeric)                    = 0.62762111871776467822076483110269           
absolute error                    = 2.3e-31                                      
relative error                    = 3.6646313060639509740098756052310e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y[1] (closed_form)                = 0.64657913372700684455766739016062           
y[1] (numeric)                    = 0.64657913372700684455766739016084           
absolute error                    = 2.2e-31                                      
relative error                    = 3.4025224218399620245112623152497e-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)                = 0.66547249136169045893267787879506           
y[1] (numeric)                    = 0.66547249136169045893267787879527           
absolute error                    = 2.1e-31                                      
relative error                    = 3.1556526036154822236915220618307e-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)                = 0.6842993023017964651984732063181            
y[1] (numeric)                    = 0.6842993023017964651984732063183            
absolute error                    = 2.0e-31                                      
relative error                    = 2.9226977044584800174920225286820e-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)                = 0.70305768388191980957457812942374           
y[1] (numeric)                    = 0.70305768388191980957457812942394           
absolute error                    = 2.0e-31                                      
relative error                    = 2.8447167933035558724647682601292e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=611.2MB, alloc=44.3MB, time=7.00
 
TOP MAIN SOLVE Loop
x[1]                              = 1.94                                         
y[1] (closed_form)                = 0.72174576027953441227013537168146           
y[1] (numeric)                    = 0.72174576027953441227013537168165           
absolute error                    = 1.9e-31                                      
relative error                    = 2.6325059384680333968192582572041e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.95                                         
y[1] (closed_form)                = 0.74036166270257385691165691826138           
y[1] (numeric)                    = 0.74036166270257385691165691826158           
absolute error                    = 2.0e-31                                      
relative error                    = 2.7013824469237297099148630459413e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.96                                         
y[1] (closed_form)                = 0.7589035295763090398631304308949            
y[1] (numeric)                    = 0.75890352957630903986313043089511           
absolute error                    = 2.1e-31                                      
relative error                    = 2.7671501293088154368312330748303e-29      % 
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)                = 0.77736950672950409182927962775862           
y[1] (numeric)                    = 0.77736950672950409182927962775883           
absolute error                    = 2.1e-31                                      
relative error                    = 2.7014180281330774180580425215654e-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)                = 0.79575774757983195630494771981438           
y[1] (numeric)                    = 0.79575774757983195630494771981459           
absolute error                    = 2.1e-31                                      
relative error                    = 2.6389940988784704712024422519858e-29      % 
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)                = 0.81406641331853108346727143226058           
y[1] (numeric)                    = 0.81406641331853108346727143226078           
absolute error                    = 2.0e-31                                      
relative error                    = 2.4568020093680393544149682111421e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2                                            
y[1] (closed_form)                = 0.83229367309428477399513645900152           
y[1] (numeric)                    = 0.83229367309428477399513645900172           
absolute error                    = 2.0e-31                                      
relative error                    = 2.4029979617223809897546004014201e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.01                                         
y[1] (closed_form)                = 0.85043770419630478503476468033086           
y[1] (numeric)                    = 0.85043770419630478503476468033106           
absolute error                    = 2.0e-31                                      
relative error                    = 2.3517301621640520727155030697283e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.02                                         
y[1] (closed_form)                = 0.8684966922366008901034057481804            
y[1] (numeric)                    = 0.86849669223660089010340574818059           
absolute error                    = 1.9e-31                                      
relative error                    = 2.1876882399022321378863453678612e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.03                                         
y[1] (closed_form)                = 0.8864688313314181661270334633922            
y[1] (numeric)                    = 0.88646883133141816612703346339238           
absolute error                    = 1.8e-31                                      
relative error                    = 2.0305282446270759551347949170881e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.04                                         
y[1] (closed_form)                = 0.90435232428182386403454041058272           
y[1] (numeric)                    = 0.9043523242818238640345404105829            
absolute error                    = 1.8e-31                                      
relative error                    = 1.9903747153294924322538635392532e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.05                                         
y[1] (closed_form)                = 0.9221453827534258043718599883348            
y[1] (numeric)                    = 0.92214538275342580437185998833497           
absolute error                    = 1.7e-31                                      
relative error                    = 1.8435270964801503657620910539276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=651.8MB, alloc=44.3MB, time=7.47
 
TOP MAIN SOLVE Loop
x[1]                              = 2.06                                         
y[1] (closed_form)                = 0.9398462274552043262462192529758            
y[1] (numeric)                    = 0.93984622745520432624621925297596           
absolute error                    = 1.6e-31                                      
relative error                    = 1.7024061524748317730548018677735e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.07                                         
y[1] (closed_form)                = 0.95745308831743990655465427802346           
y[1] (numeric)                    = 0.95745308831743990655465427802364           
absolute error                    = 1.8e-31                                      
relative error                    = 1.8799876693313426233615701820791e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.08                                         
y[1] (closed_form)                = 0.9749642046687186568831376995447            
y[1] (numeric)                    = 0.97496420466871865688313769954488           
absolute error                    = 1.8e-31                                      
relative error                    = 1.8462216267843584885380697211675e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.09                                         
y[1] (closed_form)                = 0.9923778254119979976741326237409            
y[1] (numeric)                    = 0.99237782541199799767413262374107           
absolute error                    = 1.7e-31                                      
relative error                    = 1.7130572212193716188251236229372e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.1                                          
y[1] (closed_form)                = 1.0096922091997149032418770474383            
y[1] (numeric)                    = 1.0096922091997149032418770474386            
absolute error                    = 3e-31                                        
relative error                    = 2.9712024839508359357913338718801e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.11                                         
y[1] (closed_form)                = 1.0269056246079192069568203141434            
y[1] (numeric)                    = 1.0269056246079192069568203141436            
absolute error                    = 2e-31                                        
relative error                    = 1.9475986420501066201724483171569e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.12                                         
y[1] (closed_form)                = 1.0440163503094145534138037659678            
y[1] (numeric)                    = 1.044016350309414553413803765968             
absolute error                    = 2e-31                                        
relative error                    = 1.9156788104010642135972945821172e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.13                                         
y[1] (closed_form)                = 1.0610226752458896836330524192194            
y[1] (numeric)                    = 1.0610226752458896836330524192197            
absolute error                    = 3e-31                                        
relative error                    = 2.8274607791061171841032831233120e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.14                                         
y[1] (closed_form)                = 1.0779228987990228403088998240172            
y[1] (numeric)                    = 1.0779228987990228403088998240175            
absolute error                    = 3e-31                                        
relative error                    = 2.7831304106652489298174070486430e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.15                                         
y[1] (closed_form)                = 1.0947153309605421828083077645281            
y[1] (numeric)                    = 1.0947153309605421828083077645283            
absolute error                    = 2e-31                                        
relative error                    = 1.8269589759422925385973718785549e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.16                                         
y[1] (closed_form)                = 1.1113982925012252060193974879667            
y[1] (numeric)                    = 1.1113982925012252060193974879667            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.17                                         
y[1] (closed_form)                = 1.127970115138820263248939988833             
y[1] (numeric)                    = 1.127970115138820263248939988833             
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=692.3MB, alloc=44.3MB, time=7.92
 
TOP MAIN SOLVE Loop
x[1]                              = 2.18                                         
y[1] (closed_form)                = 1.144429141704873401156449735325             
y[1] (numeric)                    = 1.144429141704873401156449735325             
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.19                                         
y[1] (closed_form)                = 1.1607737263104438241804103275939            
y[1] (numeric)                    = 1.160773726310443824180410327594             
absolute error                    = 1e-31                                        
relative error                    = 8.6149434410316279101136358407201e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.2                                          
y[1] (closed_form)                = 1.1770022345106914170482852253099            
y[1] (numeric)                    = 1.17700223451069141704828522531              
absolute error                    = 1e-31                                        
relative error                    = 8.4961605906867664521972175024682e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.21                                         
y[1] (closed_form)                = 1.1931130434683198667552183550373            
y[1] (numeric)                    = 1.1931130434683198667552183550374            
absolute error                    = 1e-31                                        
relative error                    = 8.3814354848812152751757071493764e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.22                                         
y[1] (closed_form)                = 1.2091045421158590398354288750003            
y[1] (numeric)                    = 1.2091045421158590398354288750003            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.23                                         
y[1] (closed_form)                = 1.2249751313167703868238078213713            
y[1] (numeric)                    = 1.2249751313167703868238078213711            
absolute error                    = 2e-31                                        
relative error                    = 1.6326862063314927483686831937179e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.24                                         
y[1] (closed_form)                = 1.2407232240253592635015245326209            
y[1] (numeric)                    = 1.2407232240253592635015245326206            
absolute error                    = 3e-31                                        
relative error                    = 2.4179445841812361417985868744650e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.25                                         
y[1] (closed_form)                = 1.2563472454454781778267781147928            
y[1] (numeric)                    = 1.2563472454454781778267781147926            
absolute error                    = 2e-31                                        
relative error                    = 1.5919165718318870562955543564908e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.26                                         
y[1] (closed_form)                = 1.2718456331880050923582531374897            
y[1] (numeric)                    = 1.2718456331880050923582531374893            
absolute error                    = 4e-31                                        
relative error                    = 3.1450357619057982495843435234985e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.27                                         
y[1] (closed_form)                = 1.2872168374270810344722686962486            
y[1] (numeric)                    = 1.2872168374270810344722686962481            
absolute error                    = 5e-31                                        
relative error                    = 3.8843494387426723998405896910622e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.28                                         
y[1] (closed_form)                = 1.3024593210550913907427967009214            
y[1] (numeric)                    = 1.3024593210550913907427967009208            
absolute error                    = 6e-31                                        
relative error                    = 4.6066697846191022459368724641112e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.29                                         
y[1] (closed_form)                = 1.3175715598363753874840620363779            
y[1] (numeric)                    = 1.3175715598363753874840620363773            
absolute error                    = 6e-31                                        
relative error                    = 4.5538323555990530447146537332918e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=732.8MB, alloc=44.3MB, time=8.38
 
TOP MAIN SOLVE Loop
x[1]                              = 2.3                                          
y[1] (closed_form)                = 1.332552042559648386635761142332             
y[1] (numeric)                    = 1.3325520425596483866357611423315            
absolute error                    = 5e-31                                        
relative error                    = 3.7521986686506372625053693372596e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.31                                         
y[1] (closed_form)                = 1.3473992711891217548883286469421            
y[1] (numeric)                    = 1.3473992711891217548883286469417            
absolute error                    = 4e-31                                        
relative error                    = 2.9686820273176158229406161612351e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.32                                         
y[1] (closed_form)                = 1.3621117610143051941872723320165            
y[1] (numeric)                    = 1.3621117610143051941872723320162            
absolute error                    = 3e-31                                        
relative error                    = 2.2024624453473853729019604115502e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.33                                         
y[1] (closed_form)                = 1.376688040798476553508360855632             
y[1] (numeric)                    = 1.3766880407984765535083608556317            
absolute error                    = 3e-31                                        
relative error                    = 2.1791429220667926119166175359994e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.34                                         
y[1] (closed_form)                = 1.3911266529258042750462111441227            
y[1] (numeric)                    = 1.3911266529258042750462111441223            
absolute error                    = 4e-31                                        
relative error                    = 2.8753672367553581454092350248787e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.35                                         
y[1] (closed_form)                = 1.4054261535471077626942582245178            
y[1] (numeric)                    = 1.4054261535471077626942582245175            
absolute error                    = 3e-31                                        
relative error                    = 2.1345838715384660938206846573164e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.36                                         
y[1] (closed_form)                = 1.4195851127242410969007260692902            
y[1] (numeric)                    = 1.4195851127242410969007260692897            
absolute error                    = 5e-31                                        
relative error                    = 3.5221558434103315592627879754304e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.37                                         
y[1] (closed_form)                = 1.4336021145730856576494332176447            
y[1] (numeric)                    = 1.433602114573085657649433217644             
absolute error                    = 7e-31                                        
relative error                    = 4.8828052978176163004221509822665e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.38                                         
y[1] (closed_form)                = 1.4474757574051373564222952147351            
y[1] (numeric)                    = 1.4474757574051373564222952147343            
absolute error                    = 8e-31                                        
relative error                    = 5.5268628569928175956382225138073e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.39                                         
y[1] (closed_form)                = 1.4612046538676743185383165852361            
y[1] (numeric)                    = 1.4612046538676743185383165852355            
absolute error                    = 6e-31                                        
relative error                    = 4.1062009925293844872705227578113e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.4                                          
y[1] (closed_form)                = 1.4747874310824909992176444546696            
y[1] (numeric)                    = 1.4747874310824909992176444546688            
absolute error                    = 8e-31                                        
relative error                    = 5.4245105642974026019377153768576e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.41                                         
y[1] (closed_form)                = 1.4882227307831848600746887911359            
y[1] (numeric)                    = 1.4882227307831848600746887911352            
absolute error                    = 7e-31                                        
relative error                    = 4.7035970189194825877238292838919e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=773.0MB, alloc=44.3MB, time=8.83
 
TOP MAIN SOLVE Loop
x[1]                              = 2.42                                         
y[1] (closed_form)                = 1.5015092094509818774870651378215            
y[1] (numeric)                    = 1.5015092094509818774870651378208            
absolute error                    = 7e-31                                        
relative error                    = 4.6619760677721779328469892664486e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.43                                         
y[1] (closed_form)                = 1.5146455384490873004027104883558            
y[1] (numeric)                    = 1.5146455384490873004027104883551            
absolute error                    = 7e-31                                        
relative error                    = 4.6215433395509884491185286215963e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.44                                         
y[1] (closed_form)                = 1.5276304041555482226213501850748            
y[1] (numeric)                    = 1.527630404155548222621350185074             
absolute error                    = 8e-31                                        
relative error                    = 5.2368687990484734854798067111646e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.45                                         
y[1] (closed_form)                = 1.540462508094614683403806134673             
y[1] (numeric)                    = 1.5404625080946146834038061346722            
absolute error                    = 8e-31                                        
relative error                    = 5.1932455077372403797880698303138e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.46                                         
y[1] (closed_form)                = 1.5531405670665861604085526293724            
y[1] (numeric)                    = 1.5531405670665861604085526293717            
absolute error                    = 7e-31                                        
relative error                    = 4.5069970796145564649950366645999e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.47                                         
y[1] (closed_form)                = 1.5656633132761304704144311681231            
y[1] (numeric)                    = 1.5656633132761304704144311681223            
absolute error                    = 8e-31                                        
relative error                    = 5.1096553979157257364424768741709e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.48                                         
y[1] (closed_form)                = 1.5780294944590622460463840671807            
y[1] (numeric)                    = 1.57802949445906224604638406718              
absolute error                    = 7e-31                                        
relative error                    = 4.4359120184883187395790228706408e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.49                                         
y[1] (closed_form)                = 1.5902378740075683107621826651431            
y[1] (numeric)                    = 1.5902378740075683107621826651425            
absolute error                    = 6e-31                                        
relative error                    = 3.7730204380551966458904321766623e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.5                                          
y[1] (closed_form)                = 1.6022872310938674296670055809347            
y[1] (numeric)                    = 1.6022872310938674296670055809341            
absolute error                    = 6e-31                                        
relative error                    = 3.7446469544064534927192998222247e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.51                                         
y[1] (closed_form)                = 1.6141763607922920702838350157568            
y[1] (numeric)                    = 1.6141763607922920702838350157561            
absolute error                    = 7e-31                                        
relative error                    = 4.3365769503427521823376110383178e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.52                                         
y[1] (closed_form)                = 1.6259040741997799652053285209037            
y[1] (numeric)                    = 1.625904074199779965205328520903             
absolute error                    = 7e-31                                        
relative error                    = 4.3052970412446902491133877016575e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.53                                         
y[1] (closed_form)                = 1.63746919855476342757131034511              
y[1] (numeric)                    = 1.6374691985547634275713103451092            
absolute error                    = 8e-31                                        
relative error                    = 4.8855880813274720360884796876676e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=813.3MB, alloc=44.3MB, time=9.28
 
TOP MAIN SOLVE Loop
x[1]                              = 2.54                                         
y[1] (closed_form)                = 1.6488705773544445305394087116131            
y[1] (numeric)                    = 1.6488705773544445305394087116124            
absolute error                    = 7e-31                                        
relative error                    = 4.2453301648642772420153935857165e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.55                                         
y[1] (closed_form)                = 1.6601070704704444233286209516646            
y[1] (numeric)                    = 1.6601070704704444233286209516637            
absolute error                    = 9e-31                                        
relative error                    = 5.4213370692105794169078220682107e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.56                                         
y[1] (closed_form)                = 1.6711775542628152190005762467649            
y[1] (numeric)                    = 1.6711775542628152190005762467642            
absolute error                    = 7e-31                                        
relative error                    = 4.1886632465500165229829868271517e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.57                                         
y[1] (closed_form)                = 1.6820809216924030528847274431343            
y[1] (numeric)                    = 1.6820809216924030528847274431336            
absolute error                    = 7e-31                                        
relative error                    = 4.1615120353169717464086218434733e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.58                                         
y[1] (closed_form)                = 1.6928160824315510754352649891385            
y[1] (numeric)                    = 1.6928160824315510754352649891379            
absolute error                    = 6e-31                                        
relative error                    = 3.5443897670097954470432390811008e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.59                                         
y[1] (closed_form)                = 1.7033819629731313093127194908166            
y[1] (numeric)                    = 1.7033819629731313093127194908162            
absolute error                    = 4e-31                                        
relative error                    = 2.3482695525425702351749188536074e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.6                                          
y[1] (closed_form)                = 1.7137775067378944675954043032904            
y[1] (numeric)                    = 1.7137775067378944675954043032899            
absolute error                    = 5e-31                                        
relative error                    = 2.9175315817496612578319463133169e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.61                                         
y[1] (closed_form)                = 1.7240016741801269982283348974453            
y[1] (numeric)                    = 1.7240016741801269982283348974449            
absolute error                    = 4e-31                                        
relative error                    = 2.3201833617141095280137822456223e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.62                                         
y[1] (closed_form)                = 1.7340534428916047890932273534967            
y[1] (numeric)                    = 1.7340534428916047890932273534964            
absolute error                    = 3e-31                                        
relative error                    = 1.7300504850631233902563068698153e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.63                                         
y[1] (closed_form)                = 1.7439318077038331384156967803899            
y[1] (numeric)                    = 1.7439318077038331384156967803896            
absolute error                    = 3e-31                                        
relative error                    = 1.7202507499131991666384218340733e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.64                                         
y[1] (closed_form)                = 1.753635780788562766597814632532             
y[1] (numeric)                    = 1.7536357807885627665978146325317            
absolute error                    = 3e-31                                        
relative error                    = 1.7107315172657921143915128600645e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.65                                         
y[1] (closed_form)                = 1.7631643917565718179586047321076            
y[1] (numeric)                    = 1.7631643917565718179586047321075            
absolute error                    = 1e-31                                        
relative error                    = 5.6716208918201839247010974742375e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=853.6MB, alloc=44.3MB, time=9.73
 
TOP MAIN SOLVE Loop
x[1]                              = 2.66                                         
y[1] (closed_form)                = 1.7725166877547039742646220077652            
y[1] (numeric)                    = 1.7725166877547039742646220077651            
absolute error                    = 1e-31                                        
relative error                    = 5.6416958266651228079658128334323e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.67                                         
y[1] (closed_form)                = 1.7816917335611529763201257168595            
y[1] (numeric)                    = 1.7816917335611529763201257168594            
absolute error                    = 1e-31                                        
relative error                    = 5.6126432040028153181372445884784e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.68                                         
y[1] (closed_form)                = 1.7906886116789840252440916372413            
y[1] (numeric)                    = 1.7906886116789840252440916372413            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.69                                         
y[1] (closed_form)                = 1.7995064224278827113718697686577            
y[1] (numeric)                    = 1.7995064224278827113718697686577            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.7                                          
y[1] (closed_form)                = 1.8081442840341222959650545638867            
y[1] (numeric)                    = 1.8081442840341222959650545638866            
absolute error                    = 1e-31                                        
relative error                    = 5.5305320976316984817127443030506e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.71                                         
y[1] (closed_form)                = 1.8166013327187403490763691874322            
y[1] (numeric)                    = 1.8166013327187403490763691874321            
absolute error                    = 1e-31                                        
relative error                    = 5.5047851280797634114327210999805e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.72                                         
y[1] (closed_form)                = 1.8248767227839159259792575999741            
y[1] (numeric)                    = 1.8248767227839159259792575999741            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.73                                         
y[1] (closed_form)                = 1.8329696266975386445165222497856            
y[1] (numeric)                    = 1.8329696266975386445165222497856            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.74                                         
y[1] (closed_form)                = 1.8408792351759612065307465035586            
y[1] (numeric)                    = 1.8408792351759612065307465035587            
absolute error                    = 1e-31                                        
relative error                    = 5.4321868642535618830343701369341e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.75                                         
y[1] (closed_form)                = 1.8486047572649270881933189790534            
y[1] (numeric)                    = 1.8486047572649270881933189790536            
absolute error                    = 2e-31                                        
relative error                    = 1.0818970318777429012207368086543e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.76                                         
y[1] (closed_form)                = 1.8561454204186653065304663942802            
y[1] (numeric)                    = 1.8561454204186653065304663942803            
absolute error                    = 1e-31                                        
relative error                    = 5.3875089149773819600165670049442e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.77                                         
y[1] (closed_form)                = 1.8635004705771443527355544156581            
y[1] (numeric)                    = 1.8635004705771443527355544156583            
absolute error                    = 2e-31                                        
relative error                    = 1.0732489911207698303910363424691e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=893.9MB, alloc=44.3MB, time=10.19
 
TOP MAIN SOLVE Loop
x[1]                              = 2.78                                         
y[1] (closed_form)                = 1.8706691722414775669387033382352            
y[1] (numeric)                    = 1.8706691722414775669387033382354            
absolute error                    = 2e-31                                        
relative error                    = 1.0691361303632086628055214573001e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.79                                         
y[1] (closed_form)                = 1.8776508085474724139590792392482            
y[1] (numeric)                    = 1.8776508085474724139590792392484            
absolute error                    = 2e-31                                        
relative error                    = 1.0651607801064860492742727778761e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.8                                          
y[1] (closed_form)                = 1.8844446813373163051735762347323            
y[1] (numeric)                    = 1.8844446813373163051735762347327            
absolute error                    = 4e-31                                        
relative error                    = 2.1226412425974517098801367850977e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.81                                         
y[1] (closed_form)                = 1.8910501112293917979794409567177            
y[1] (numeric)                    = 1.8910501112293917979794409567181            
absolute error                    = 4e-31                                        
relative error                    = 2.1152268658811782836468148462742e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.82                                         
y[1] (closed_form)                = 1.8974664376862141913890721275201            
y[1] (numeric)                    = 1.8974664376862141913890721275205            
absolute error                    = 4e-31                                        
relative error                    = 2.1080741775214912973366635412409e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.83                                         
y[1] (closed_form)                = 1.9036930190804847240540502254491            
y[1] (numeric)                    = 1.9036930190804847240540502254495            
absolute error                    = 4e-31                                        
relative error                    = 2.1011791081379634871127195378521e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.84                                         
y[1] (closed_form)                = 1.9097292327592527694536389871725            
y[1] (numeric)                    = 1.909729232759252769453638987173             
absolute error                    = 5e-31                                        
relative error                    = 2.6181722069446468529370716879611e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.85                                         
y[1] (closed_form)                = 1.9155744751061806120817082143499            
y[1] (numeric)                    = 1.9155744751061806120817082143504            
absolute error                    = 5e-31                                        
relative error                    = 2.6101830364610852144202173411781e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.86                                         
y[1] (closed_form)                = 1.9212281616019045782063463327855            
y[1] (numeric)                    = 1.921228161601904578206346332786             
absolute error                    = 5e-31                                        
relative error                    = 2.6025019307602904604126950551129e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.87                                         
y[1] (closed_form)                = 1.9266897268824864851393875174759            
y[1] (numeric)                    = 1.9266897268824864851393875174764            
absolute error                    = 5e-31                                        
relative error                    = 2.5951246483731120340020038132103e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.88                                         
y[1] (closed_form)                = 1.931958624795949563919635809531             
y[1] (numeric)                    = 1.9319586247959495639196358095315            
absolute error                    = 5e-31                                        
relative error                    = 2.5880471433636898658737589358428e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.89                                         
y[1] (closed_form)                = 1.9370343284568932018646310144186            
y[1] (numeric)                    = 1.937034328456893201864631014419             
absolute error                    = 4e-31                                        
relative error                    = 2.0650124477590104179367267496684e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=934.0MB, alloc=44.3MB, time=10.64
 
TOP MAIN SOLVE Loop
x[1]                              = 2.9                                          
y[1] (closed_form)                = 1.9419163302991810435622133386911            
y[1] (numeric)                    = 1.9419163302991810435622133386915            
absolute error                    = 4e-31                                        
relative error                    = 2.0598209807441809861239563218980e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.91                                         
y[1] (closed_form)                = 1.9466041421266971815356942132055            
y[1] (numeric)                    = 1.946604142126697181535694213206             
absolute error                    = 5e-31                                        
relative error                    = 2.5685756501768343121923665511038e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.92                                         
y[1] (closed_form)                = 1.9510972951621653610058634703165            
y[1] (numeric)                    = 1.9510972951621653610058634703169            
absolute error                    = 4e-31                                        
relative error                    = 2.0501284123135131433354795506711e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.93                                         
y[1] (closed_form)                = 1.9553953400940263168700392093527            
y[1] (numeric)                    = 1.9553953400940263168700392093531            
absolute error                    = 4e-31                                        
relative error                    = 2.0456221399237136795442936937857e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.94                                         
y[1] (closed_form)                = 1.9594978471213685552035267626566            
y[1] (numeric)                    = 1.9594978471213685552035267626572            
absolute error                    = 6e-31                                        
relative error                    = 3.0620089778686898421153760826910e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.95                                         
y[1] (closed_form)                = 1.9634044059969080862427788094039            
y[1] (numeric)                    = 1.9634044059969080862427788094044            
absolute error                    = 5e-31                                        
relative error                    = 2.5465971170932952763580793262475e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.96                                         
y[1] (closed_form)                = 1.9671146260680128109127746459523            
y[1] (numeric)                    = 1.9671146260680128109127746459528            
absolute error                    = 5e-31                                        
relative error                    = 2.5417939217880257124468104584671e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.97                                         
y[1] (closed_form)                = 1.9706281363157674584941527496123            
y[1] (numeric)                    = 1.9706281363157674584941527496127            
absolute error                    = 4e-31                                        
relative error                    = 2.0298096461153197331692060521674e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.98                                         
y[1] (closed_form)                = 1.9739445853920751689688839287908            
y[1] (numeric)                    = 1.9739445853920751689688839287913            
absolute error                    = 5e-31                                        
relative error                    = 2.5329991718115399484296806747349e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.99                                         
y[1] (closed_form)                = 1.9770636416547920099171683744217            
y[1] (numeric)                    = 1.9770636416547920099171683744221            
absolute error                    = 4e-31                                        
relative error                    = 2.0232024481781581670835491953362e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3                                            
y[1] (closed_form)                = 1.9799849932008909145431455894625            
y[1] (numeric)                    = 1.979984993200890914543145589463             
absolute error                    = 5e-31                                        
relative error                    = 2.5252716647699843782575912036580e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.01                                         
y[1] (closed_form)                = 1.9827083478976517244632511483648            
y[1] (numeric)                    = 1.9827083478976517244632511483653            
absolute error                    = 5e-31                                        
relative error                    = 2.5218030706844545930805915480806e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=974.3MB, alloc=44.3MB, time=11.09
 
TOP MAIN SOLVE Loop
x[1]                              = 3.02                                         
y[1] (closed_form)                = 1.9852334334118742182789330665261            
y[1] (numeric)                    = 1.9852334334118742182789330665265            
absolute error                    = 4e-31                                        
relative error                    = 2.0148764032879977981244725613442e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.03                                         
y[1] (closed_form)                = 1.9875599972371112046552146174169            
y[1] (numeric)                    = 1.9875599972371112046552146174174            
absolute error                    = 5e-31                                        
relative error                    = 2.5156473298669996481759346109232e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.04                                         
y[1] (closed_form)                = 1.9896878067189189566184899096864            
y[1] (numeric)                    = 1.9896878067189189566184899096868            
absolute error                    = 4e-31                                        
relative error                    = 2.0103656395201881395128191980257e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.05                                         
y[1] (closed_form)                = 1.9916166490781224620511644031298            
y[1] (numeric)                    = 1.9916166490781224620511644031303            
absolute error                    = 5e-31                                        
relative error                    = 2.5105232989061399128987905026074e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.06                                         
y[1] (closed_form)                = 1.9933463314320931638774785435863            
y[1] (numeric)                    = 1.9933463314320931638774785435869            
absolute error                    = 6e-31                                        
relative error                    = 3.0100138171621083975233696398276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.07                                         
y[1] (closed_form)                = 1.9948766808140370621842273254535            
y[1] (numeric)                    = 1.9948766808140370621842273254541            
absolute error                    = 6e-31                                        
relative error                    = 3.0077047156376688354313035576519e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.08                                         
y[1] (closed_form)                = 1.9962075441902912494822370747196            
y[1] (numeric)                    = 1.9962075441902912494822370747201            
absolute error                    = 5e-31                                        
relative error                    = 2.5047495760407606562652585944511e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.09                                         
y[1] (closed_form)                = 1.9973387884756271494694870361715            
y[1] (numeric)                    = 1.9973387884756271494694870361718            
absolute error                    = 3e-31                                        
relative error                    = 1.5019985679493091097067396838789e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.1                                          
y[1] (closed_form)                = 1.9982703005465589289847521090829            
y[1] (numeric)                    = 1.9982703005465589289847521090832            
absolute error                    = 3e-31                                        
relative error                    = 1.5012983975088114734883761056682e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.11                                         
y[1] (closed_form)                = 1.9990019872526557523216616734337            
y[1] (numeric)                    = 1.9990019872526557523216616734339            
absolute error                    = 2e-31                                        
relative error                    = 1.0004992555053513850774541731278e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.12                                         
y[1] (closed_form)                = 1.9995337754258567466871699479512            
y[1] (numeric)                    = 1.9995337754258567466871699479514            
absolute error                    = 2e-31                                        
relative error                    = 1.0002331666410805977636579275350e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.13                                         
y[1] (closed_form)                = 1.9998656118877877473156544782784            
y[1] (numeric)                    = 1.9998656118877877473156544782786            
absolute error                    = 2e-31                                        
relative error                    = 1.0000671985714507066524953955074e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1014.6MB, alloc=44.3MB, time=11.55
 
TOP MAIN SOLVE Loop
x[1]                              = 3.14                                         
y[1] (closed_form)                = 1.9999974634550790905702286126901            
y[1] (numeric)                    = 1.9999974634550790905702286126903            
absolute error                    = 2e-31                                        
relative error                    = 1.0000012682740689717888714570959e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.15                                         
y[1] (closed_form)                = 1.9999293169426839232563893135895            
y[1] (numeric)                    = 1.9999293169426839232563893135899            
absolute error                    = 4e-31                                        
relative error                    = 2.0000706855554516604478288694140e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.16                                         
y[1] (closed_form)                = 1.9996611791651966963198341885479            
y[1] (numeric)                    = 1.9996611791651966963198341885484            
absolute error                    = 5e-31                                        
relative error                    = 2.5004235978053851503222069451043e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.17                                         
y[1] (closed_form)                = 1.9991930769361717110801767002706            
y[1] (numeric)                    = 1.999193076936171711080176700271             
absolute error                    = 4e-31                                        
relative error                    = 2.0008072487576486856484747461864e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.18                                         
y[1] (closed_form)                = 1.9985250570654417861453683077206            
y[1] (numeric)                    = 1.9985250570654417861453683077211            
absolute error                    = 5e-31                                        
relative error                    = 2.5018450393320611701328199511378e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.19                                         
y[1] (closed_form)                = 1.997657186354437313137901659399             
y[1] (numeric)                    = 1.9976571863544373131379016593995            
absolute error                    = 5e-31                                        
relative error                    = 2.5029319515650206882495050144123e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.2                                          
y[1] (closed_form)                = 1.9965895515895061693233214445672            
y[1] (numeric)                    = 1.9965895515895061693233214445676            
absolute error                    = 4e-31                                        
relative error                    = 2.0034162739234799024546068656658e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.21                                         
y[1] (closed_form)                = 1.9953222595332351551442133304085            
y[1] (numeric)                    = 1.9953222595332351551442133304089            
absolute error                    = 4e-31                                        
relative error                    = 2.0046887067434000426513713834122e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.22                                         
y[1] (closed_form)                = 1.9938554369137738245086854749517            
y[1] (numeric)                    = 1.9938554369137738245086854749523            
absolute error                    = 6e-31                                        
relative error                    = 3.0092452486360853998590568384776e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.23                                         
y[1] (closed_form)                = 1.9921892304121617754414169891699            
y[1] (numeric)                    = 1.9921892304121617754414169891704            
absolute error                    = 5e-31                                        
relative error                    = 2.5098017415572293090821558028979e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.24                                         
y[1] (closed_form)                = 1.9903238066476606683576476874849            
y[1] (numeric)                    = 1.9903238066476606683576476874854            
absolute error                    = 5e-31                                        
relative error                    = 2.5121540441309360657673761370317e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.25                                         
y[1] (closed_form)                = 1.9882593521610924387460584503432            
y[1] (numeric)                    = 1.9882593521610924387460584503435            
absolute error                    = 3e-31                                        
relative error                    = 1.5088574821686212636897580143247e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1054.8MB, alloc=44.3MB, time=12.00
 
TOP MAIN SOLVE Loop
x[1]                              = 3.26                                         
y[1] (closed_form)                = 1.9859960733961853704253891343433            
y[1] (numeric)                    = 1.9859960733961853704253891343435            
absolute error                    = 2e-31                                        
relative error                    = 1.0070513365013189495923246723329e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.27                                         
y[1] (closed_form)                = 1.9835341966789298947519234809895            
y[1] (numeric)                    = 1.9835341966789298947519234809897            
absolute error                    = 2e-31                                        
relative error                    = 1.0083012449942325783113608911906e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.28                                         
y[1] (closed_form)                = 1.9808739681949461801807168322634            
y[1] (numeric)                    = 1.9808739681949461801807168322635            
absolute error                    = 1e-31                                        
relative error                    = 5.0482767508487232191881281099957e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.29                                         
y[1] (closed_form)                = 1.978015653964865775402750251079             
y[1] (numeric)                    = 1.978015653964865775402750251079             
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]                              = 3.3                                          
y[1] (closed_form)                = 1.9749595398177297678731821022057            
y[1] (numeric)                    = 1.9749595398177297678731821022058            
absolute error                    = 1e-31                                        
relative error                    = 5.0633948687996444514938517923536e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.31                                         
y[1] (closed_form)                = 1.9717059313624061178926761411711            
y[1] (numeric)                    = 1.971705931362406117892676141171             
absolute error                    = 1e-31                                        
relative error                    = 5.0717502244821145644888401491348e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.32                                         
y[1] (closed_form)                = 1.9682551539570290264845791694624            
y[1] (numeric)                    = 1.9682551539570290264845791694623            
absolute error                    = 1e-31                                        
relative error                    = 5.0806421006421610199162350853551e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.33                                         
y[1] (closed_form)                = 1.9646075526764633931056934297185            
y[1] (numeric)                    = 1.9646075526764633931056934297183            
absolute error                    = 2e-31                                        
relative error                    = 1.0180150215117111105941744917833e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.34                                         
y[1] (closed_form)                = 1.9607634922777976167177598021398            
y[1] (numeric)                    = 1.9607634922777976167177598021395            
absolute error                    = 3e-31                                        
relative error                    = 1.5300162471481619839353830866090e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.35                                         
y[1] (closed_form)                = 1.9567233571638681909107887505431            
y[1] (numeric)                    = 1.9567233571638681909107887505427            
absolute error                    = 4e-31                                        
relative error                    = 2.0442337877530712725080405457988e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.36                                         
y[1] (closed_form)                = 1.9524875513448197405883306155566            
y[1] (numeric)                    = 1.9524875513448197405883306155562            
absolute error                    = 4e-31                                        
relative error                    = 2.0486686315848262296579784720237e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.37                                         
y[1] (closed_form)                = 1.9480564983977043441789835319417            
y[1] (numeric)                    = 1.9480564983977043441789835319413            
absolute error                    = 4e-31                                        
relative error                    = 2.0533285370778719174383274372345e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1095.0MB, alloc=44.3MB, time=12.45
 
TOP MAIN SOLVE Loop
x[1]                              = 3.38                                         
y[1] (closed_form)                = 1.9434306414241241814082506999811            
y[1] (numeric)                    = 1.9434306414241241814082506999807            
absolute error                    = 4e-31                                        
relative error                    = 2.0582159788675786514994062928818e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.39                                         
y[1] (closed_form)                = 1.938610443005921742330672149345             
y[1] (numeric)                    = 1.9386104430059217423306721493447            
absolute error                    = 3e-31                                        
relative error                    = 1.5475001750987865191781570077453e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.4                                          
y[1] (closed_form)                = 1.9335963851589220285644030795314            
y[1] (numeric)                    = 1.9335963851589220285644030795311            
absolute error                    = 3e-31                                        
relative error                    = 1.5515130370671593910769382832276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.41                                         
y[1] (closed_form)                = 1.9283889692847313724695672819059            
y[1] (numeric)                    = 1.9283889692847313724695672819058            
absolute error                    = 1e-31                                        
relative error                    = 5.1856757942922434410113844975597e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.42                                         
y[1] (closed_form)                = 1.9229887161205976943483002912028            
y[1] (numeric)                    = 1.9229887161205976943483002912029            
absolute error                    = 1e-31                                        
relative error                    = 5.2002385225503648894626245969838e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.43                                         
y[1] (closed_form)                = 1.9173961656873372115989792824511            
y[1] (numeric)                    = 1.9173961656873372115989792824512            
absolute error                    = 1e-31                                        
relative error                    = 5.2154062780318835108871485139554e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.44                                         
y[1] (closed_form)                = 1.911611877235332807110330025945             
y[1] (numeric)                    = 1.9116118772353328071103300259449            
absolute error                    = 1e-31                                        
relative error                    = 5.2311874178468132526872087945843e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.45                                         
y[1] (closed_form)                = 1.9056364291886094570135702798955            
y[1] (numeric)                    = 1.9056364291886094570135702798956            
absolute error                    = 1e-31                                        
relative error                    = 5.2475906982203554252998574589777e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.46                                         
y[1] (closed_form)                = 1.8994704190869923102032107515641            
y[1] (numeric)                    = 1.8994704190869923102032107515642            
absolute error                    = 1e-31                                        
relative error                    = 5.2646252868768776987941812544462e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.47                                         
y[1] (closed_form)                = 1.8931144635263532037703601070534            
y[1] (numeric)                    = 1.8931144635263532037703601070534            
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]                              = 3.48                                         
y[1] (closed_form)                = 1.8865691980969515896471962947646            
y[1] (numeric)                    = 1.8865691980969515896471962947643            
absolute error                    = 3e-31                                        
relative error                    = 1.5901881590276174593539207714396e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.49                                         
y[1] (closed_form)                = 1.8798352773198760383185573455335            
y[1] (numeric)                    = 1.8798352773198760383185573455333            
absolute error                    = 2e-31                                        
relative error                    = 1.0639230065154674313518926496524e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1135.3MB, alloc=44.3MB, time=12.91
 
TOP MAIN SOLVE Loop
x[1]                              = 3.5                                          
y[1] (closed_form)                = 1.8729133745815926753973152533435            
y[1] (numeric)                    = 1.8729133745815926753973152533433            
absolute error                    = 2e-31                                        
relative error                    = 1.0678550471918106588133042517524e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.51                                         
y[1] (closed_form)                = 1.8658041820666070961653326115152            
y[1] (numeric)                    = 1.8658041820666070961653326115148            
absolute error                    = 4e-31                                        
relative error                    = 2.1438476976557685356492653159076e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.52                                         
y[1] (closed_form)                = 1.8585084106882464918324330245445            
y[1] (numeric)                    = 1.8585084106882464918324330245441            
absolute error                    = 4e-31                                        
relative error                    = 2.1522635985912553006800333494479e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.53                                         
y[1] (closed_form)                = 1.851026790017568909243078029368             
y[1] (numeric)                    = 1.8510267900175689092430780293677            
absolute error                    = 3e-31                                        
relative error                    = 1.6207220858059680923182223765428e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.54                                         
y[1] (closed_form)                = 1.8433600682104067530455377722595            
y[1] (numeric)                    = 1.8433600682104067530455377722593            
absolute error                    = 2e-31                                        
relative error                    = 1.0849752224163477356592689867444e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.55                                         
y[1] (closed_form)                = 1.8355090119325518259125416454209            
y[1] (numeric)                    = 1.8355090119325518259125416454207            
absolute error                    = 2e-31                                        
relative error                    = 1.0896160067850936871968472812362e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.56                                         
y[1] (closed_form)                = 1.8274744062830893882470412262073            
y[1] (numeric)                    = 1.8274744062830893882470412262072            
absolute error                    = 1e-31                                        
relative error                    = 5.4720328589110350394166707891683e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.57                                         
y[1] (closed_form)                = 1.8192570547158889039032268720735            
y[1] (numeric)                    = 1.8192570547158889039032268720733            
absolute error                    = 2e-31                                        
relative error                    = 1.0993498663729725074662779247150e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.58                                         
y[1] (closed_form)                = 1.810857778959259322782801709098             
y[1] (numeric)                    = 1.8108577789592593227828017090978            
absolute error                    = 2e-31                                        
relative error                    = 1.1044489651470282574808011818836e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.59                                         
y[1] (closed_form)                = 1.8022774189337769347112996786957            
y[1] (numeric)                    = 1.8022774189337769347112996786953            
absolute error                    = 4e-31                                        
relative error                    = 2.2194141467779086721968958785723e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.6                                          
y[1] (closed_form)                = 1.7935168326682940117405834505319            
y[1] (numeric)                    = 1.7935168326682940117405834505316            
absolute error                    = 3e-31                                        
relative error                    = 1.6726912986574917305357179065306e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.61                                         
y[1] (closed_form)                = 1.7845768962141366379432993870768            
y[1] (numeric)                    = 1.7845768962141366379432993870766            
absolute error                    = 2e-31                                        
relative error                    = 1.1207138253570745036371142603232e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1175.5MB, alloc=44.3MB, time=13.36
 
TOP MAIN SOLVE Loop
x[1]                              = 3.62                                         
y[1] (closed_form)                = 1.775458503557500306844808544136             
y[1] (numeric)                    = 1.7754585035575003068448085441358            
absolute error                    = 2e-31                                        
relative error                    = 1.1264695829232753754025252345354e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.63                                         
y[1] (closed_form)                = 1.766162566530052046859847088796             
y[1] (numeric)                    = 1.7661625665300520468598470887957            
absolute error                    = 3e-31                                        
relative error                    = 1.6985978849580343298286092385223e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.64                                         
y[1] (closed_form)                = 1.7566900147177480144468744882682            
y[1] (numeric)                    = 1.7566900147177480144468744882677            
absolute error                    = 5e-31                                        
relative error                    = 2.8462619802636967201830422751425e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.65                                         
y[1] (closed_form)                = 1.7470417953678756731448089490565            
y[1] (numeric)                    = 1.7470417953678756731448089490561            
absolute error                    = 4e-31                                        
relative error                    = 2.2895846055919443655873565192064e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.66                                         
y[1] (closed_form)                = 1.7372188732943298541967818403199            
y[1] (numeric)                    = 1.7372188732943298541967818403193            
absolute error                    = 6e-31                                        
relative error                    = 3.4537962327234310782191911690125e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.67                                         
y[1] (closed_form)                = 1.7272222307811321710759123729596            
y[1] (numeric)                    = 1.7272222307811321710759123729591            
absolute error                    = 5e-31                                        
relative error                    = 2.8948214716636444743779204617744e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.68                                         
y[1] (closed_form)                = 1.7170528674842034358912497370723            
y[1] (numeric)                    = 1.7170528674842034358912497370718            
absolute error                    = 5e-31                                        
relative error                    = 2.9119662502447665965966587027984e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.69                                         
y[1] (closed_form)                = 1.7067118003313989003503860567443            
y[1] (numeric)                    = 1.7067118003313989003503860567439            
absolute error                    = 4e-31                                        
relative error                    = 2.3436880199828139510216791342077e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.7                                          
y[1] (closed_form)                = 1.6962000634208163176713402127088            
y[1] (numeric)                    = 1.6962000634208163176713402127083            
absolute error                    = 5e-31                                        
relative error                    = 2.9477654834632158505528434201635e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.71                                         
y[1] (closed_form)                = 1.6855187079173869945527783452195            
y[1] (numeric)                    = 1.6855187079173869945527783452189            
absolute error                    = 6e-31                                        
relative error                    = 3.5597350369451256247924205429640e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.72                                         
y[1] (closed_form)                = 1.6746688019477601740112001789793            
y[1] (numeric)                    = 1.6746688019477601740112001789786            
absolute error                    = 7e-31                                        
relative error                    = 4.1799309761180819243789810447127e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.73                                         
y[1] (closed_form)                = 1.6636514304934912605592113958433            
y[1] (numeric)                    = 1.6636514304934912605592113958426            
absolute error                    = 7e-31                                        
relative error                    = 4.2076121666445357294215852763678e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1215.7MB, alloc=44.3MB, time=13.81
 
TOP MAIN SOLVE Loop
x[1]                              = 3.74                                         
y[1] (closed_form)                = 1.6524676952825445688133547124051            
y[1] (numeric)                    = 1.6524676952825445688133547124043            
absolute error                    = 8e-31                                        
relative error                    = 4.8412444145433854816585550698790e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.75                                         
y[1] (closed_form)                = 1.6411187146791214451662248045814            
y[1] (numeric)                    = 1.6411187146791214451662248045807            
absolute error                    = 7e-31                                        
relative error                    = 4.2653830813017508967598001449688e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.76                                         
y[1] (closed_form)                = 1.6296056235718247796188902751262            
y[1] (numeric)                    = 1.6296056235718247796188902751255            
absolute error                    = 7e-31                                        
relative error                    = 4.2955178226847076040644600061836e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.77                                         
y[1] (closed_form)                = 1.6179295732601710912292434923924            
y[1] (numeric)                    = 1.6179295732601710912292434923918            
absolute error                    = 6e-31                                        
relative error                    = 3.7084432469516213445706500905240e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.78                                         
y[1] (closed_form)                = 1.6060917313394615358731605184754            
y[1] (numeric)                    = 1.6060917313394615358731605184748            
absolute error                    = 6e-31                                        
relative error                    = 3.7357766576608117273915275878861e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.79                                         
y[1] (closed_form)                = 1.5940932815840233491217545036803            
y[1] (numeric)                    = 1.5940932815840233491217545036797            
absolute error                    = 6e-31                                        
relative error                    = 3.7638951680656367675908407364284e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.8                                          
y[1] (closed_form)                = 1.5819354238288333999931363487015            
y[1] (numeric)                    = 1.5819354238288333999931363487007            
absolute error                    = 8e-31                                        
relative error                    = 5.0570964399022181600283054041128e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.81                                         
y[1] (closed_form)                = 1.5696193738495356931246607487299            
y[1] (numeric)                    = 1.5696193738495356931246607487291            
absolute error                    = 8e-31                                        
relative error                    = 5.0967770488075557010466449568099e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.82                                         
y[1] (closed_form)                = 1.5571463632408648175154553133124            
y[1] (numeric)                    = 1.5571463632408648175154553133116            
absolute error                    = 8e-31                                        
relative error                    = 5.1376031109559430440083564979626e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.83                                         
y[1] (closed_form)                = 1.544517639293487499393045054047             
y[1] (numeric)                    = 1.544517639293487499393045054046             
absolute error                    = 1.0e-30                                      
relative error                    = 6.4745133014954264833469466715167e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.84                                         
y[1] (closed_form)                = 1.5317344648692745749461538804954            
y[1] (numeric)                    = 1.5317344648692745749461538804944            
absolute error                    = 1.0e-30                                      
relative error                    = 6.5285467092061854490849149312284e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.85                                         
y[1] (closed_form)                = 1.5187981182750158556224701479056            
y[1] (numeric)                    = 1.5187981182750158556224701479047            
absolute error                    = 9e-31                                        
relative error                    = 5.9257381818604071010054540559790e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1256.0MB, alloc=44.3MB, time=14.26
 
TOP MAIN SOLVE Loop
x[1]                              = 3.86                                         
y[1] (closed_form)                = 1.5057098931345905143996092187297            
y[1] (numeric)                    = 1.5057098931345905143996092187287            
absolute error                    = 1.0e-30                                      
relative error                    = 6.6413855986440892010213652896653e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.87                                         
y[1] (closed_form)                = 1.4924710982596057758841216186546            
y[1] (numeric)                    = 1.4924710982596057758841216186536            
absolute error                    = 1.0e-30                                      
relative error                    = 6.7002972531000155642241600406923e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.88                                         
y[1] (closed_form)                = 1.4790830575185168462617361540826            
y[1] (numeric)                    = 1.4790830575185168462617361540816            
absolute error                    = 1.0e-30                                      
relative error                    = 6.7609455393108027747553392791550e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.89                                         
y[1] (closed_form)                = 1.4655471097042411709967766052634            
y[1] (numeric)                    = 1.4655471097042411709967766052624            
absolute error                    = 1.0e-30                                      
relative error                    = 6.8233903460244808770235299703525e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.9                                          
y[1] (closed_form)                = 1.4518646084002802587446609692287            
y[1] (numeric)                    = 1.4518646084002802587446609692277            
absolute error                    = 1.0e-30                                      
relative error                    = 6.8876945840138502981930502450700e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.91                                         
y[1] (closed_form)                = 1.4380369218453624591835272277488            
y[1] (numeric)                    = 1.4380369218453624591835272277477            
absolute error                    = 1.1e-30                                      
relative error                    = 7.6493168102278194081443311750476e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.92                                         
y[1] (closed_form)                = 1.4240654327966202303744051685852            
y[1] (numeric)                    = 1.4240654327966202303744051685839            
absolute error                    = 1.3e-30                                      
relative error                    = 9.1287940150827409513752565915022e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.93                                         
y[1] (closed_form)                = 1.4099515383913155778091796790539            
y[1] (numeric)                    = 1.4099515383913155778091796790527            
absolute error                    = 1.2e-30                                      
relative error                    = 8.5109308180133636545280653043605e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.94                                         
y[1] (closed_form)                = 1.3956966500071274924872122988712            
y[1] (numeric)                    = 1.3956966500071274924872122988701            
absolute error                    = 1.1e-30                                      
relative error                    = 7.8813687773369847976998304461734e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.95                                         
y[1] (closed_form)                = 1.3813021931210153591603866232805            
y[1] (numeric)                    = 1.3813021931210153591603866232794            
absolute error                    = 1.1e-30                                      
relative error                    = 7.9634999891991731519920399241316e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.96                                         
y[1] (closed_form)                = 1.366769607166672448288139617503             
y[1] (numeric)                    = 1.366769607166672448288139617502             
absolute error                    = 1.0e-30                                      
relative error                    = 7.3165220733361956834052140777348e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.97                                         
y[1] (closed_form)                = 1.3521003453905837462344949786387            
y[1] (numeric)                    = 1.3521003453905837462344949786376            
absolute error                    = 1.1e-30                                      
relative error                    = 8.1354908587220347931675582277963e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1296.1MB, alloc=44.3MB, time=14.72
 
TOP MAIN SOLVE Loop
x[1]                              = 3.98                                         
y[1] (closed_form)                = 1.3372958747067025178041274333497            
y[1] (numeric)                    = 1.3372958747067025178041274333487            
absolute error                    = 1.0e-30                                      
relative error                    = 7.4777767501849305362226399490806e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.99                                         
y[1] (closed_form)                = 1.3223576755497601333401019040203            
y[1] (numeric)                    = 1.3223576755497601333401019040193            
absolute error                    = 1.0e-30                                      
relative error                    = 7.5622505052141631453095386467577e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4                                            
y[1] (closed_form)                = 1.3072872417272238292783363661955            
y[1] (numeric)                    = 1.3072872417272238292783363661946            
absolute error                    = 9e-31                                        
relative error                    = 6.8844854540987890858327991532181e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.01                                         
y[1] (closed_form)                = 1.2920860802699172062593648293701            
y[1] (numeric)                    = 1.2920860802699172062593648293692            
absolute error                    = 9e-31                                        
relative error                    = 6.9654801931771426916097453815408e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.02                                         
y[1] (closed_form)                = 1.2767557112813184026231067615307            
y[1] (numeric)                    = 1.2767557112813184026231067615298            
absolute error                    = 9e-31                                        
relative error                    = 7.0491166951333525316975941165958e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.03                                         
y[1] (closed_form)                = 1.2612976677855510133437090437049            
y[1] (numeric)                    = 1.2612976677855510133437090437039            
absolute error                    = 1.0e-30                                      
relative error                    = 7.9283425755927307646459463621400e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.04                                         
y[1] (closed_form)                = 1.2457134955740829551858931583454            
y[1] (numeric)                    = 1.2457134955740829551858931583444            
absolute error                    = 1.0e-30                                      
relative error                    = 8.0275280275353627658299672170210e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.05                                         
y[1] (closed_form)                = 1.2300047530511486080685414569647            
y[1] (numeric)                    = 1.230004753051148608068541456964             
absolute error                    = 7e-31                                        
relative error                    = 5.6910349188780016734048551010817e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.06                                         
y[1] (closed_form)                = 1.2141730110779096902925716955787            
y[1] (numeric)                    = 1.214173011077909690292571695578             
absolute error                    = 7e-31                                        
relative error                    = 5.7652409797723891762603925643068e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.07                                         
y[1] (closed_form)                = 1.1982198528153704514157115460792            
y[1] (numeric)                    = 1.1982198528153704514157115460786            
absolute error                    = 6e-31                                        
relative error                    = 5.0074282994913114884796287958636e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.08                                         
y[1] (closed_form)                = 1.1821468735660628911239820364958            
y[1] (numeric)                    = 1.1821468735660628911239820364951            
absolute error                    = 7e-31                                        
relative error                    = 5.9214300325337816092125741914690e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.09                                         
y[1] (closed_form)                = 1.1659556806145178354460742272886            
y[1] (numeric)                    = 1.1659556806145178354460742272878            
absolute error                    = 8e-31                                        
relative error                    = 6.8613242621568547666629466224331e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1336.4MB, alloc=44.3MB, time=15.17
 
TOP MAIN SOLVE Loop
x[1]                              = 4.1                                          
y[1] (closed_form)                = 1.1496478930665378230700573593196            
y[1] (numeric)                    = 1.1496478930665378230700573593188            
absolute error                    = 8e-31                                        
relative error                    = 6.9586523389009389693790083787290e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.11                                         
y[1] (closed_form)                = 1.1332251416872878743398479877489            
y[1] (numeric)                    = 1.133225141687287874339847987748             
absolute error                    = 9e-31                                        
relative error                    = 7.9419346332183117598071063522235e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.12                                         
y[1] (closed_form)                = 1.1166890687382203337196165455186            
y[1] (numeric)                    = 1.1166890687382203337196165455175            
absolute error                    = 1.1e-30                                      
relative error                    = 9.8505486513172569961106271524463e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.13                                         
y[1] (closed_form)                = 1.100041327812850093105989384141             
y[1] (numeric)                    = 1.1000413278128500931059893841399            
absolute error                    = 1.1e-30                                      
relative error                    = 9.9996243067255276412476458799684e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.14                                         
y[1] (closed_form)                = 1.0832835836713966183288615471946            
y[1] (numeric)                    = 1.0832835836713966183288615471935            
absolute error                    = 1.1e-30                                      
relative error                    = 1.0154312467949981798592239829371e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.15                                         
y[1] (closed_form)                = 1.0664175120743093145003723433254            
y[1] (numeric)                    = 1.0664175120743093145003723433244            
absolute error                    = 1.0e-30                                      
relative error                    = 9.3771903469109455259785146056201e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.16                                         
y[1] (closed_form)                = 1.0494447996146928775367804214184            
y[1] (numeric)                    = 1.0494447996146928775367804214177            
absolute error                    = 7e-31                                        
relative error                    = 6.6701936133945045108133190600704e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.17                                         
y[1] (closed_form)                = 1.0323671435496493891784410855156            
y[1] (numeric)                    = 1.0323671435496493891784410855149            
absolute error                    = 7e-31                                        
relative error                    = 6.7805334988979631871398842097068e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.18                                         
y[1] (closed_form)                = 1.0151862516305540211578360660934            
y[1] (numeric)                    = 1.0151862516305540211578360660927            
absolute error                    = 7e-31                                        
relative error                    = 6.8952864449817587266374747979165e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.19                                         
y[1] (closed_form)                = 0.9979038419322813208038025029849            
y[1] (numeric)                    = 0.99790384193228132080380250298415           
absolute error                    = 7.5e-31                                      
relative error                    = 7.5157542088198082598268418414807e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.2                                          
y[1] (closed_form)                = 0.98052164268139915531108976275426           
y[1] (numeric)                    = 0.98052164268139915531108976275352           
absolute error                    = 7.4e-31                                      
relative error                    = 7.5470032255111390769349688122020e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.21                                         
y[1] (closed_form)                = 0.9630413920833474951376458989737            
y[1] (numeric)                    = 0.96304139208334749513764589897296           
absolute error                    = 7.4e-31                                      
relative error                    = 7.6839895572832852004107934779800e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1376.6MB, alloc=44.3MB, time=15.63
 
TOP MAIN SOLVE Loop
x[1]                              = 4.22                                         
y[1] (closed_form)                = 0.94546483814861931850727682631042           
y[1] (numeric)                    = 0.94546483814861931850727682630967           
absolute error                    = 7.5e-31                                      
relative error                    = 7.9326059493510868246806992976710e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.23                                         
y[1] (closed_form)                = 0.92779373851796101878237917908968           
y[1] (numeric)                    = 0.92779373851796101878237917908893           
absolute error                    = 7.5e-31                                      
relative error                    = 8.0836932699937688072106446469356e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.24                                         
y[1] (closed_form)                = 0.91002986028660979452034373941188           
y[1] (numeric)                    = 0.91002986028660979452034373941112           
absolute error                    = 7.6e-31                                      
relative error                    = 8.3513743138125317381956165528676e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.25                                         
y[1] (closed_form)                = 0.89217497982758559832815544108968           
y[1] (numeric)                    = 0.89217497982758559832815544108892           
absolute error                    = 7.6e-31                                      
relative error                    = 8.5185083328258247248099096891289e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.26                                         
y[1] (closed_form)                = 0.87423088261405531517304827097196           
y[1] (numeric)                    = 0.87423088261405531517304827097123           
absolute error                    = 7.3e-31                                      
relative error                    = 8.3501968932647671155470516949849e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.27                                         
y[1] (closed_form)                = 0.85619936304078693358335464418858           
y[1] (numeric)                    = 0.85619936304078693358335464418785           
absolute error                    = 7.3e-31                                      
relative error                    = 8.5260516593636481101204512690293e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.28                                         
y[1] (closed_form)                = 0.83808222424471156417364147367208           
y[1] (numeric)                    = 0.83808222424471156417364147367134           
absolute error                    = 7.4e-31                                      
relative error                    = 8.8296825608835184760695626924186e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.29                                         
y[1] (closed_form)                = 0.8198812779246112491427492675585            
y[1] (numeric)                    = 0.81988127792461124914274926755777           
absolute error                    = 7.3e-31                                      
relative error                    = 8.9037281330276222527934265387728e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.3                                          
y[1] (closed_form)                = 0.80159834415995059381352479267206           
y[1] (numeric)                    = 0.80159834415995059381352479267135           
absolute error                    = 7.1e-31                                      
relative error                    = 8.8573037253970038260657932456513e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.31                                         
y[1] (closed_form)                = 0.7832352512288703369001201936885            
y[1] (numeric)                    = 0.78323525122887033690012019368777           
absolute error                    = 7.3e-31                                      
relative error                    = 9.3203159440877312477615734164866e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.32                                         
y[1] (closed_form)                = 0.76479383542536105999416031886016           
y[1] (numeric)                    = 0.76479383542536105999416031885944           
absolute error                    = 7.2e-31                                      
relative error                    = 9.4143018242236780019850175293119e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.33                                         
y[1] (closed_form)                = 0.74627594087563531874647490132572           
y[1] (numeric)                    = 0.74627594087563531874647490132502           
absolute error                    = 7.0e-31                                      
relative error                    = 9.3799084448396137212866773506835e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1417.0MB, alloc=44.3MB, time=16.08
 
TOP MAIN SOLVE Loop
x[1]                              = 4.34                                         
y[1] (closed_form)                = 0.72768341935371655837825470884734           
y[1] (numeric)                    = 0.72768341935371655837825470884664           
absolute error                    = 7.0e-31                                      
relative error                    = 9.6195678145545316864634261037500e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.35                                         
y[1] (closed_form)                = 0.70901813009626325447640515487174           
y[1] (numeric)                    = 0.70901813009626325447640515487104           
absolute error                    = 7.0e-31                                      
relative error                    = 9.8728081876405774744242699636199e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.36                                         
y[1] (closed_form)                = 0.69028193961664679650470513392686           
y[1] (numeric)                    = 0.69028193961664679650470513392615           
absolute error                    = 7.1e-31                                      
relative error                    = 1.0285652271219840617894162756406e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.37                                         
y[1] (closed_form)                = 0.67147672151830170608748538484566           
y[1] (numeric)                    = 0.67147672151830170608748538484496           
absolute error                    = 7.0e-31                                      
relative error                    = 1.0424784323382100538369944968852e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.38                                         
y[1] (closed_form)                = 0.65260435630736685488845704768816           
y[1] (numeric)                    = 0.65260435630736685488845704768748           
absolute error                    = 6.8e-31                                      
relative error                    = 1.0419789470110895309396542991326e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.39                                         
y[1] (closed_form)                = 0.63366673120463641780677073351148           
y[1] (numeric)                    = 0.6336667312046364178067707335108            
absolute error                    = 6.8e-31                                      
relative error                    = 1.0731193015408610906753985183736e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.4                                          
y[1] (closed_form)                = 0.61466573995683936623827948443542           
y[1] (numeric)                    = 0.61466573995683936623827948443476           
absolute error                    = 6.6e-31                                      
relative error                    = 1.0737543303557864106799698301162e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.41                                         
y[1] (closed_form)                = 0.59560328264726637329541293298128           
y[1] (numeric)                    = 0.59560328264726637329541293298062           
absolute error                    = 6.6e-31                                      
relative error                    = 1.1081201518341382950048199769034e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.42                                         
y[1] (closed_form)                = 0.57648126550576306813733028698644           
y[1] (numeric)                    = 0.57648126550576306813733028698577           
absolute error                    = 6.7e-31                                      
relative error                    = 1.1622233714953257705115739043086e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.43                                         
y[1] (closed_form)                = 0.55730160071810863992658069786728           
y[1] (numeric)                    = 0.55730160071810863992658069786662           
absolute error                    = 6.6e-31                                      
relative error                    = 1.1842779549700911830531178106196e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.44                                         
y[1] (closed_form)                = 0.53806620623479885339302471232678           
y[1] (numeric)                    = 0.5380662062347988533930247123261            
absolute error                    = 6.8e-31                                      
relative error                    = 1.2637849991702781855426802154563e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.45                                         
y[1] (closed_form)                = 0.51877700557925259754411345948892           
y[1] (numeric)                    = 0.51877700557925259754411345948822           
absolute error                    = 7.0e-31                                      
relative error                    = 1.3493273457993741068157181283441e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1457.2MB, alloc=44.3MB, time=16.53
 
TOP MAIN SOLVE Loop
x[1]                              = 4.46                                         
y[1] (closed_form)                = 0.49943592765546114670682720222532           
y[1] (numeric)                    = 0.49943592765546114670682720222462           
absolute error                    = 7.0e-31                                      
relative error                    = 1.4015811863717164832198373731870e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.47                                         
y[1] (closed_form)                = 0.48004490655509936881487731066032           
y[1] (numeric)                    = 0.48004490655509936881487731065961           
absolute error                    = 7.1e-31                                      
relative error                    = 1.4790282956965537024144556176666e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.48                                         
y[1] (closed_form)                = 0.4606058813641181696596028136977            
y[1] (numeric)                    = 0.46060588136411816965960281369701           
absolute error                    = 6.9e-31                                      
relative error                    = 1.4980268987371900002530866676035e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.49                                         
y[1] (closed_form)                = 0.4411207959688375136989640130322            
y[1] (numeric)                    = 0.4411207959688375136989640130315            
absolute error                    = 7.0e-31                                      
relative error                    = 1.5868669226137566154045440291837e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.5                                          
y[1] (closed_form)                = 0.42159159886155941196096364958766           
y[1] (numeric)                    = 0.42159159886155941196096364958697           
absolute error                    = 6.9e-31                                      
relative error                    = 1.6366550041870722409643883375512e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.51                                         
y[1] (closed_form)                = 0.40202024294572031558071664348154           
y[1] (numeric)                    = 0.40202024294572031558071664348084           
absolute error                    = 7.0e-31                                      
relative error                    = 1.7412058528965968119277923873573e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.52                                         
y[1] (closed_form)                = 0.38240868534060239956944223639776           
y[1] (numeric)                    = 0.38240868534060239956944223639707           
absolute error                    = 6.9e-31                                      
relative error                    = 1.8043523237068563672311619337608e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.53                                         
y[1] (closed_form)                = 0.3627588871856232655242615827628            
y[1] (numeric)                    = 0.36275888718562326552426158276212           
absolute error                    = 6.8e-31                                      
relative error                    = 1.8745233377343691561946713177158e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.54                                         
y[1] (closed_form)                = 0.3430728134442236341454384391956            
y[1] (numeric)                    = 0.3430728134442236341454384391949            
absolute error                    = 7.0e-31                                      
relative error                    = 2.0403831856347461908270950766462e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.55                                         
y[1] (closed_form)                = 0.32335243270737263862838485001588           
y[1] (numeric)                    = 0.32335243270737263862838485001517           
absolute error                    = 7.1e-31                                      
relative error                    = 2.1957465854061952567035384814399e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.56                                         
y[1] (closed_form)                = 0.3035997169967103682373475852198            
y[1] (numeric)                    = 0.30359971699671036823734758521908           
absolute error                    = 7.2e-31                                      
relative error                    = 2.3715437126306725296571620028848e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.57                                         
y[1] (closed_form)                = 0.28381664156734734764237062874918           
y[1] (numeric)                    = 0.28381664156734734764237062874848           
absolute error                    = 7.0e-31                                      
relative error                    = 2.4663810977901934435671635288390e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1497.5MB, alloc=44.3MB, time=16.98
 
TOP MAIN SOLVE Loop
x[1]                              = 4.58                                         
y[1] (closed_form)                = 0.2640051847103406719072668013646            
y[1] (numeric)                    = 0.26400518471034067190726680136388           
absolute error                    = 7.2e-31                                      
relative error                    = 2.7272191672673567814673257967132e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.59                                         
y[1] (closed_form)                = 0.244167327554866549350497048793             
y[1] (numeric)                    = 0.24416732755486654935049704879229           
absolute error                    = 7.1e-31                                      
relative error                    = 2.9078419586685149169733527377076e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.6                                          
y[1] (closed_form)                = 0.22430505387010903485981564245838           
y[1] (numeric)                    = 0.22430505387010903485981564245766           
absolute error                    = 7.2e-31                                      
relative error                    = 3.2099143000894614994091908174762e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.61                                         
y[1] (closed_form)                = 0.20442034986688476462225765634538           
y[1] (numeric)                    = 0.20442034986688476462225765634467           
absolute error                    = 7.1e-31                                      
relative error                    = 3.4732354213381424629873637166973e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.62                                         
y[1] (closed_form)                = 0.18451520399902352963068355123164           
y[1] (numeric)                    = 0.18451520399902352963068355123094           
absolute error                    = 7.0e-31                                      
relative error                    = 3.7937253127590746416606135813402e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.63                                         
y[1] (closed_form)                = 0.16459160676452454974401457480525           
y[1] (numeric)                    = 0.16459160676452454974401457480453           
absolute error                    = 7.2e-31                                      
relative error                    = 4.3744636446139006124649919666981e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.64                                         
y[1] (closed_form)                = 0.14465155050650833250805040152024           
y[1] (numeric)                    = 0.14465155050650833250805040151952           
absolute error                    = 7.2e-31                                      
relative error                    = 4.9774786200276844878282031874832e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.65                                         
y[1] (closed_form)                = 0.12469702921398402138511403235415           
y[1] (numeric)                    = 0.12469702921398402138511403235343           
absolute error                    = 7.2e-31                                      
relative error                    = 5.7739948139779446569509364283826e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.66                                         
y[1] (closed_form)                = 0.10473003832245215649167433359191           
y[1] (numeric)                    = 0.1047300383224521564916743335912            
absolute error                    = 7.1e-31                                      
relative error                    = 6.7793348629739717449052514238856e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.67                                         
y[1] (closed_form)                = 0.084752574514362787401708640210552          
y[1] (numeric)                    = 0.084752574514362787401708640209832          
absolute error                    = 7.20e-31                                     
relative error                    = 8.4953171526132644599123875305281e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.68                                         
y[1] (closed_form)                = 0.064766635519448892038240735889134          
y[1] (numeric)                    = 0.064766635519448892038240735888412          
absolute error                    = 7.22e-31                                     
relative error                    = 1.1147715088321814906907766301551e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.69                                         
y[1] (closed_form)                = 0.044774219914955068144776792884014          
y[1] (numeric)                    = 0.044774219914955068144776792883292          
absolute error                    = 7.22e-31                                     
relative error                    = 1.6125350734672303713426600130521e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1537.9MB, alloc=44.3MB, time=17.44
 
TOP MAIN SOLVE Loop
x[1]                              = 4.7                                          
y[1] (closed_form)                = 0.024777326925781474301016592654222          
y[1] (numeric)                    = 0.024777326925781474301016592653499          
absolute error                    = 7.23e-31                                     
relative error                    = 2.9179903149588710348037000448146e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.71                                         
y[1] (closed_form)                = 0.0047779562245630059221922954493916         
y[1] (numeric)                    = 0.0047779562245630059221922954486682         
absolute error                    = 7.234e-31                                    
relative error                    = 1.5140364750122056576952390403646e-26      % 
Desired digits                    = 8                                   
Estimated correct digits          = 9                                   
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.72                                         
y[1] (closed_form)                = -0.015221892268296301842165306349265         
y[1] (numeric)                    = -0.015221892268296301842165306349988         
absolute error                    = 7.23e-31                                     
relative error                    = 4.7497379908925160107759085103750e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.73                                         
y[1] (closed_form)                = -0.03522021858461364791696036988569          
y[1] (numeric)                    = -0.035220218584613647916960369886411         
absolute error                    = 7.21e-31                                     
relative error                    = 2.0471196062223674846081390105850e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.74                                         
y[1] (closed_form)                = -0.05521502290842261694704263443799          
y[1] (numeric)                    = -0.055215022908422616947042634438711         
absolute error                    = 7.21e-31                                     
relative error                    = 1.3058040403167470706692656764847e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.75                                         
y[1] (closed_form)                = -0.075204305775953109430992624746668         
y[1] (numeric)                    = -0.075204305775953109430992624747389         
absolute error                    = 7.21e-31                                     
relative error                    = 9.5872170158446267905226935515783e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.76                                         
y[1] (closed_form)                = -0.095186068275576052516817432821052         
y[1] (numeric)                    = -0.095186068275576052516817432821774         
absolute error                    = 7.22e-31                                     
relative error                    = 7.5851436358282606974099161815709e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.77                                         
y[1] (closed_form)                = -0.11515831224769289715509754557452          
y[1] (numeric)                    = -0.11515831224769289715509754557523          
absolute error                    = 7.1e-31                                      
relative error                    = 6.1654255445570258504190762714772e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.78                                         
y[1] (closed_form)                = -0.13511904048454991282644342931911          
y[1] (numeric)                    = -0.13511904048454991282644342931981          
absolute error                    = 7.0e-31                                      
relative error                    = 5.1806170136328120571092810212353e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.79                                         
y[1] (closed_form)                = -0.15506625692995729858030048269519          
y[1] (numeric)                    = -0.15506625692995729858030048269591          
absolute error                    = 7.2e-31                                      
relative error                    = 4.6431764992252352178346499812872e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.8                                          
y[1] (closed_form)                = -0.17499796687889313864043051529898          
y[1] (numeric)                    = -0.17499796687889313864043051529968          
absolute error                    = 7.0e-31                                      
relative error                    = 4.0000464718794880257194314363424e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.81                                         
y[1] (closed_form)                = -0.19491217717697224234784527907679          
y[1] (numeric)                    = -0.19491217717697224234784527907748          
absolute error                    = 6.9e-31                                      
relative error                    = 3.5400558856489934534978298251738e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1578.0MB, alloc=44.3MB, time=17.89
 
TOP MAIN SOLVE Loop
x[1]                              = 4.82                                         
y[1] (closed_form)                = -0.21480689641975992172342123833954          
y[1] (numeric)                    = -0.21480689641975992172342123834023          
absolute error                    = 6.9e-31                                      
relative error                    = 3.2121873715434744718807767769113e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.83                                         
y[1] (closed_form)                = -0.23468013515191077543853357790764          
y[1] (numeric)                    = -0.23468013515191077543853357790834          
absolute error                    = 7.0e-31                                      
relative error                    = 2.9827833512490653209595546462457e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.84                                         
y[1] (closed_form)                = -0.25452990606611256548126081946536          
y[1] (numeric)                    = -0.25452990606611256548126081946606          
absolute error                    = 7.0e-31                                      
relative error                    = 2.7501679893685237078522555505901e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.85                                         
y[1] (closed_form)                = -0.27435422420181529229627943693056          
y[1] (numeric)                    = -0.27435422420181529229627943693126          
absolute error                    = 7.0e-31                                      
relative error                    = 2.5514460440203726218111467753429e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.86                                         
y[1] (closed_form)                = -0.2941511071437255956565414919708           
y[1] (numeric)                    = -0.2941511071437255956565414919715           
absolute error                    = 7.0e-31                                      
relative error                    = 2.3797292717921744653177932865620e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.87                                         
y[1] (closed_form)                = -0.31391857522004663199205957125608          
y[1] (numeric)                    = -0.31391857522004663199205957125675          
absolute error                    = 6.7e-31                                      
relative error                    = 2.1343114198653327871294107855191e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.88                                         
y[1] (closed_form)                = -0.33365465170044360435326549406324          
y[1] (numeric)                    = -0.33365465170044360435326549406394          
absolute error                    = 7.0e-31                                      
relative error                    = 2.0979776437478312788773260139180e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.89                                         
y[1] (closed_form)                = -0.35335736299371514862091717942768          
y[1] (numeric)                    = -0.35335736299371514862091717942836          
absolute error                    = 6.8e-31                                      
relative error                    = 1.9243974265567930215174231180216e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.9                                          
y[1] (closed_form)                = -0.37302473884515080898865828824384          
y[1] (numeric)                    = -0.37302473884515080898865828824451          
absolute error                    = 6.7e-31                                      
relative error                    = 1.7961275224647470199204979879135e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.91                                         
y[1] (closed_form)                = -0.3926548125335548671351463990388           
y[1] (numeric)                    = -0.39265481253355486713514639903946          
absolute error                    = 6.6e-31                                      
relative error                    = 1.6808656838851269021571143460136e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.92                                         
y[1] (closed_form)                = -0.41224562106791682286701848162354          
y[1] (numeric)                    = -0.41224562106791682286701848162421          
absolute error                    = 6.7e-31                                      
relative error                    = 1.6252446739503839274589809857359e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.93                                         
y[1] (closed_form)                = -0.43179520538370885934852089297154          
y[1] (numeric)                    = -0.43179520538370885934852089297218          
absolute error                    = 6.4e-31                                      
relative error                    = 1.4821841280782004489156652564199e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1618.3MB, alloc=44.3MB, time=18.34
 
TOP MAIN SOLVE Loop
x[1]                              = 4.94                                         
y[1] (closed_form)                = -0.45130161053879066333486160807944          
y[1] (numeric)                    = -0.45130161053879066333486160808006          
absolute error                    = 6.2e-31                                      
relative error                    = 1.3738040935856780593466622535112e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.95                                         
y[1] (closed_form)                = -0.47076288590890201009051482326948          
y[1] (numeric)                    = -0.47076288590890201009051482327012          
absolute error                    = 6.4e-31                                      
relative error                    = 1.3594954469793256015320494991955e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.96                                         
y[1] (closed_form)                = -0.49017708538272356389689604587064          
y[1] (numeric)                    = -0.4901770853827235638968960458713           
absolute error                    = 6.6e-31                                      
relative error                    = 1.3464521693923758739424604759064e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.97                                         
y[1] (closed_form)                = -0.50954226755648638823190702802508          
y[1] (numeric)                    = -0.50954226755648638823190702802574          
absolute error                    = 6.6e-31                                      
relative error                    = 1.2952801799250820755270462934927e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.98                                         
y[1] (closed_form)                = -0.52885649592811070483250664136156          
y[1] (numeric)                    = -0.52885649592811070483250664136221          
absolute error                    = 6.5e-31                                      
relative error                    = 1.2290668735368181073685375492143e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.99                                         
y[1] (closed_form)                = -0.5481178390908544879261831953939           
y[1] (numeric)                    = -0.54811783909085448792618319539455          
absolute error                    = 6.5e-31                                      
relative error                    = 1.1858763821263949202685075232876e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
Finished!
diff  (  y  ,  x  ,  1  )   =   2.0  *  sin ( x )  ; 
Iterations                       = 4900                                
Total Elapsed Time               = 18 Seconds
Elapsed Time(since restart)      = 18 Seconds
Time to Timeout                  = 2 Minutes 41 Seconds
Percent Done                     = 100                                        % 
> quit
memory used=1641.2MB, alloc=44.3MB, time=18.59