|\^/|     Maple 2016 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
>     global glob_iolevel;
>     if (glob_iolevel >= iolevel)  then # if number 1
>         printf("%s\n",str);
>     fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc

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

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

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

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

# End Function number 6
# Begin Function number 7
> logitem_time := proc(fd,secs_in)
>     global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
>     local  days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
>     fprintf(fd,"<td>");
>     if (secs_in >= 0)  then # if number 0
>         years_int  :=  int_trunc(secs_in / glob_sec_in_year);
>         sec_temp  :=  int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
>         days_int  :=  int_trunc(sec_temp / glob_sec_in_day) ;
>         sec_temp  :=  sec_temp mod int_trunc(glob_sec_in_day) ;
>         hours_int  :=  int_trunc(sec_temp / glob_sec_in_hour);
>         sec_temp  :=  sec_temp mod int_trunc(glob_sec_in_hour);
>         minutes_int  := int_trunc(sec_temp / glob_sec_in_minute);
>         sec_int  := sec_temp mod int_trunc(glob_sec_in_minute);
>         if  (years_int > 0)  then # if number 1
>             fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
>         elif
>         (days_int > 0)  then # if number 2
>             fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
>         elif
>         (hours_int > 0)  then # if number 3
>             fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
>         elif
>         (minutes_int > 0)  then # if number 4
>             fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
>         else
>             fprintf(fd,"%d Seconds",sec_int);
>         fi;# end if 4
>     else
>         fprintf(fd," 0.0 Seconds");
>     fi;# end if 3
>     fprintf(fd,"</td>\n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
    fprintf(fd, "<td>");
    if 0 <= secs_in then
        years_int := int_trunc(secs_in/glob_sec_in_year);
        sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
        days_int := int_trunc(sec_temp/glob_sec_in_day);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
        hours_int := int_trunc(sec_temp/glob_sec_in_hour);
        sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
        minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
        sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
        if 0 < years_int then fprintf(fd,
            "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
            days_int, hours_int, minutes_int, sec_int)
        elif 0 < days_int then fprintf(fd,
            "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
            minutes_int, sec_int)
        elif 0 < hours_int then fprintf(fd,
            "%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
            sec_int)
        elif 0 < minutes_int then
            fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
        else fprintf(fd, "%d Seconds", sec_int)
        end if
    else fprintf(fd, " 0.0 Seconds")
    end if;
    fprintf(fd, "</td>\n")
end proc

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

# End Function number 8
# Begin Function number 9
> zero_ats_ar := proc(arr_a)
>     global ATS_MAX_TERMS;
>     local iii;
>     iii  := 1;
>     while (iii <= ATS_MAX_TERMS) do # do number 1
>         arr_a [iii] := glob__0;
>         iii  :=  iii + 1;
>     od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
    iii := 1;
    while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
    end do
end proc

# End Function number 9
# Begin Function number 10
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
>     global ATS_MAX_TERMS;
>     local iii_ats, lll_ats,ma_ats, ret_ats;
>     ret_ats  := glob__0;
>     if (jjj_ats <=  mmm_ats)  then # if number 6
>         ma_ats  :=  mmm_ats + 1;
>         iii_ats  :=  jjj_ats;
>         while (iii_ats <= mmm_ats) do # do number 1
>             lll_ats  :=  ma_ats - iii_ats;
>             if ((lll_ats <= ATS_MAX_TERMS  and (iii_ats <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_ats  :=  ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
>             fi;# end if 7;
>             iii_ats  :=  iii_ats + 1;
>         od;# end do number 1
>     fi;# end if 6;
>     ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
    ret_ats := glob__0;
    if jjj_ats <= mmm_ats then
        ma_ats := mmm_ats + 1;
        iii_ats := jjj_ats;
        while iii_ats <= mmm_ats do
            lll_ats := ma_ats - iii_ats;
            if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
                ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
            end if;
            iii_ats := iii_ats + 1
        end do
    end if;
    ret_ats
end proc

# End Function number 10
# Begin Function number 11
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
>     global ATS_MAX_TERMS;
>     local al_att, iii_att,lll_att, ma_att, ret_att;
>     ret_att  := glob__0;
>     if (jjj_att < mmm_att)  then # if number 6
>         ma_att  :=  mmm_att + 2;
>         iii_att  :=  jjj_att;
>         while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) )   do # do number 1
>             lll_att  :=  ma_att - iii_att;
>             al_att  :=  (lll_att - 1);
>             if ((lll_att <= ATS_MAX_TERMS  and (iii_att <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_att  :=   ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
>             fi;# end if 7;
>             iii_att  :=  iii_att + 1;
>         od;# end do number 1;
>         ret_att  :=  ret_att / c(mmm_att) ;
>     fi;# end if 6;
>     ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
    ret_att := glob__0;
    if jjj_att < mmm_att then
        ma_att := mmm_att + 2;
        iii_att := jjj_att;
        while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
            lll_att := ma_att - iii_att;
            al_att := lll_att - 1;
            if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
                ret_att :=
                ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
            end if;
            iii_att := iii_att + 1
        end do;
        ret_att := ret_att/c(mmm_att)
    end if;
    ret_att
end proc

# End Function number 11
# Begin Function number 12
> logditto := proc(file)
>     fprintf(file,"<td>");
>     fprintf(file,"ditto");
>     fprintf(file,"</td>");
> end;
logditto := proc(file)
    fprintf(file, "<td>"); fprintf(file, "ditto"); fprintf(file, "</td>")
end proc

# End Function number 12
# Begin Function number 13
> logitem_integer := proc(file,n)
>     fprintf(file,"<td>");
>     fprintf(file,"%d",n);
>     fprintf(file,"</td>");
> end;
logitem_integer := proc(file, n)
    fprintf(file, "<td>"); fprintf(file, "%d", n); fprintf(file, "</td>")
end proc

# End Function number 13
# Begin Function number 14
> logitem_str := proc(file,str)
>     fprintf(file,"<td>");
>     fprintf(file,str);
>     fprintf(file,"</td>");
> end;
logitem_str := proc(file, str)
    fprintf(file, "<td>"); fprintf(file, str); fprintf(file, "</td>")
end proc

# End Function number 14
# Begin Function number 15
> logitem_good_digits := proc(file,rel_error)
>     global glob_small_float,glob_prec;
>     local good_digits;
>     fprintf(file,"<td>");
>     fprintf(file,"%d",glob_min_good_digits);
>     fprintf(file,"</td>");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
    fprintf(file, "<td>");
    fprintf(file, "%d", glob_min_good_digits);
    fprintf(file, "</td>")
end proc

# End Function number 15
# Begin Function number 16
> log_revs := proc(file,revs)
>     fprintf(file,revs);
> end;
           log_revs := proc(file, revs) fprintf(file, revs) end proc

# End Function number 16
# Begin Function number 17
> logitem_float := proc(file,x)
>     fprintf(file,"<td>");
>     fprintf(file,"%g",x);
>     fprintf(file,"</td>");
> end;
logitem_float := proc(file, x)
    fprintf(file, "<td>"); fprintf(file, "%g", x); fprintf(file, "</td>")
end proc

# End Function number 17
# Begin Function number 18
> logitem_h_reason := proc(file)
>     global glob_h_reason;
>     fprintf(file,"<td>");
>     if (glob_h_reason  = 1) then # if number 6
>         fprintf(file,"Max H");
>     elif
>     (glob_h_reason = 2) then # if number 7
>         fprintf(file,"Display Interval");
>     elif
>     (glob_h_reason = 3) then # if number 8
>         fprintf(file,"Optimal");
>     elif
>     (glob_h_reason = 4) then # if number 9
>         fprintf(file,"Pole Accuracy");
>     elif
>     (glob_h_reason = 5) then # if number 10
>         fprintf(file,"Min H (Pole)");
>     elif
>     (glob_h_reason = 6) then # if number 11
>         fprintf(file,"Pole");
>     elif
>     (glob_h_reason = 7) then # if number 12
>         fprintf(file,"Opt Iter");
>     else
>         fprintf(file,"Impossible");
>     fi;# end if 12
>     fprintf(file,"</td>");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
    fprintf(file, "<td>");
    if glob_h_reason = 1 then fprintf(file, "Max H")
    elif glob_h_reason = 2 then fprintf(file, "Display Interval")
    elif glob_h_reason = 3 then fprintf(file, "Optimal")
    elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
    elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
    elif glob_h_reason = 6 then fprintf(file, "Pole")
    elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
    else fprintf(file, "Impossible")
    end if;
    fprintf(file, "</td>")
end proc

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

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

# End Function number 20
# Begin Function number 21
> chk_data := proc()
>     global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
>     local  errflag;
>     errflag  :=  false;
>     if (glob_max_iter < 2)  then # if number 12
>         omniout_str(ALWAYS,"Illegal max_iter");
>         errflag  :=  true;
>     fi;# end if 12;
>     if (errflag)   then # if number 12
>         quit;
>     fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
    errflag := false;
    if glob_max_iter < 2 then
        omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
    end if;
    if errflag then quit end if
end proc

# End Function number 21
# Begin Function number 22
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
>     global glob_small_float;
>     local ms2, rrr, sec_left, sub1, sub2;
>     ;
>     ms2 := c(clock_sec2);
>     sub1 := c(t_end2-t_start2);
>     sub2 := c(t2-t_start2);
>     if (sub1 = glob__0)  then # if number 12
>         sec_left := glob__0;
>     else
>         if (sub2 > glob__0)  then # if number 13
>             rrr := (sub1/sub2);
>             sec_left  := rrr * c(ms2) - c(ms2);
>         else
>             sec_left  := glob__0;
>         fi;# end if 13
>     fi;# end if 12;
>     sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
    ms2 := c(clock_sec2);
    sub1 := c(t_end2 - t_start2);
    sub2 := c(t2 - t_start2);
    if sub1 = glob__0 then sec_left := glob__0
    else
        if glob__0 < sub2 then
            rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
        else sec_left := glob__0
        end if
    end if;
    sec_left
end proc

# End Function number 22
# Begin Function number 23
> comp_percent := proc(t_end2,t_start2, t2)
>     global glob_small_float;
>     local rrr, sub1, sub2;
>     sub1  :=  (t_end2-t_start2);
>     sub2  :=  (t2-t_start2);
>     if (sub2 > glob_small_float)  then # if number 12
>         rrr  :=  (glob__100*sub2)/sub1;
>     else
>         rrr  :=  0.0;
>     fi;# end if 12;
>     rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
    sub1 := t_end2 - t_start2;
    sub2 := t2 - t_start2;
    if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
    else rrr := 0.
    end if;
    rrr
end proc

# End Function number 23
# Begin Function number 24
> comp_rad_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (float_abs(term2) > glob__0)  then # if number 12
>         ret :=  float_abs(term1 * glob_h / term2);
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
    if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 24
# Begin Function number 25
> comp_ord_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM ORDER ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (float_abs(term2) > glob__0)  then # if number 12
>         ret := glob__1 +  float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
    if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
        c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 25
# Begin Function number 26
> c := proc(in_val)
>     #To Force Conversion when needed
>     local ret;
>     ret := evalf(in_val);
>     ret;
>     #End Conversion
> end;
        c := proc(in_val) local ret; ret := evalf(in_val); ret end proc

# End Function number 26
# Begin Function number 27
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret,temp;
>     temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
>     if (float_abs(temp) > glob__0)  then # if number 12
>         ret := float_abs((term2*glob_h*term1)/(temp));
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
    temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
         - term1*term3*c(last_no) + term1*term3);
    if glob__0 < float_abs(temp) then
        ret := float_abs(term2*glob_h*term1/temp)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 27
# Begin Function number 28
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM ORDER ANALYSIS
>     local ret;
>     ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
>     ret;
>     #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
    ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
         - glob__4*term2*term2*c(last_no) + glob__4*term2*term2
         + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
        /(term2*term2*c(last_no) - glob__2*term2*term2
         - term1*term3*c(last_no) + term1*term3));
    ret
end proc

# End Function number 28
# Begin Function number 29
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
>     #TOP SIX TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float,glob_six_term_ord_save;
>     local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
>     if ((term5  <> glob__0) and (term4  <> glob__0) and (term3  <> glob__0) and  (term2  <> glob__0) and (term1  <> glob__0)) then # if number 12
>         rm0 := term6/term5;
>         rm1 := term5/term4;
>         rm2 := term4/term3;
>         rm3 := term3/term2;
>         rm4 := term2/term1;
>         nr1 :=  c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
>         nr2 :=  c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
>         dr1 :=  glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
>         dr2 :=  glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
>         ds1 :=  glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
>         ds2 :=  glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
>         if ((float_abs(nr1 * dr2 - nr2 * dr1)  =  glob__0)  or  (float_abs(dr1) = glob__0))  then # if number 13
>             rad_c :=  glob_larger_float;
>             ord_no :=  glob_larger_float;
>         else
>             if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0)  then # if number 14
>                 rcs :=  ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
>                 #(Manuels)  rcs  :=  (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
>                 ord_no :=  (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
>                 if (float_abs(rcs)  <> glob__0)  then # if number 15
>                     if (rcs > glob__0)  then # if number 16
>                         rad_c  :=  sqrt(rcs) * float_abs(glob_h);
>                     else
>                         rad_c  :=  glob_larger_float;
>                         ord_no :=  glob_larger_float;
>                     fi;# end if 16
>                 else
>                     rad_c :=  glob_larger_float;
>                     ord_no :=  glob_larger_float;
>                 fi;# end if 15
>             else
>                 rad_c :=  glob_larger_float;
>                 ord_no :=  glob_larger_float;
>             fi;# end if 14
>         fi;# end if 13
>     else
>         rad_c :=  glob_larger_float;
>         ord_no :=  glob_larger_float;
>     fi;# end if 12;
>     glob_six_term_ord_save :=  ord_no;
>     rad_c;
>     #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
    if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
    term2 <> glob__0 and term1 <> glob__0 then
        rm0 := term6/term5;
        rm1 := term5/term4;
        rm2 := term4/term3;
        rm3 := term3/term2;
        rm4 := term2/term1;
        nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
             + c(last_no - 3)*rm2;
        nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
             + c(last_no - 4)*rm3;
        dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
        dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
        ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
        ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
        if
        float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
        then rad_c := glob_larger_float; ord_no := glob_larger_float
        else
            if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
                rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
                ord_no :=
                    (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
                if float_abs(rcs) <> glob__0 then
                    if glob__0 < rcs then
                        rad_c := sqrt(rcs)*float_abs(glob_h)
                    else
                        rad_c := glob_larger_float;
                        ord_no := glob_larger_float
                    end if
                else
                    rad_c := glob_larger_float; ord_no := glob_larger_float
                end if
            else rad_c := glob_larger_float; ord_no := glob_larger_float
            end if
        end if
    else rad_c := glob_larger_float; ord_no := glob_larger_float
    end if;
    glob_six_term_ord_save := ord_no;
    rad_c
end proc

# End Function number 29
# Begin Function number 30
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
>     global glob_six_term_ord_save;
>     #TOP SIX TERM ORDER ANALYSIS
>     #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
>     glob_six_term_ord_save;
>     #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
    glob_six_term_ord_save
end proc

# End Function number 30
# Begin Function number 31
> factorial_2 := proc(nnn)
>     ret := nnn!;
>     ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
         factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc

# End Function number 31
# Begin Function number 32
> factorial_1 := proc(nnn)
>     global ATS_MAX_TERMS,array_fact_1;
>     local ret;
>     if (nnn <= ATS_MAX_TERMS) then # if number 12
>         if (array_fact_1[nnn] = 0) then # if number 13
>             ret := factorial_2(nnn);
>             array_fact_1[nnn] := ret;
>         else
>             ret := array_fact_1[nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
    if nnn <= ATS_MAX_TERMS then
        if array_fact_1[nnn] = 0 then
            ret := factorial_2(nnn); array_fact_1[nnn] := ret
        else ret := array_fact_1[nnn]
        end if
    else ret := factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 32
# Begin Function number 33
> factorial_3 := proc(mmm,nnn)
>     global ATS_MAX_TERMS,array_fact_2;
>     local ret;
>     if ((nnn <= ATS_MAX_TERMS)  and  (mmm <= ATS_MAX_TERMS)) then # if number 12
>         if (array_fact_2[mmm,nnn] = 0) then # if number 13
>             ret := factorial_1(mmm)/factorial_1(nnn);
>             array_fact_2[mmm,nnn] := ret;
>         else
>             ret := array_fact_2[mmm,nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(mmm)/factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
    if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
        if array_fact_2[mmm, nnn] = 0 then
            ret := factorial_1(mmm)/factorial_1(nnn);
            array_fact_2[mmm, nnn] := ret
        else ret := array_fact_2[mmm, nnn]
        end if
    else ret := factorial_2(mmm)/factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 33
# Begin Function number 34
> convfloat := proc(mmm)
>     (mmm);
> end;
                      convfloat := proc(mmm) mmm end proc

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

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

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

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

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

# End Function number 39
# Begin Function number 40
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
>     local desired_abs_gbl_error,range,estimated_steps,step_error;
>     global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
>     omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
>     desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
>     omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
>     omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
>     omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
>     range := (x_end - x_start);
>     omniout_float(ALWAYS,"range",32,range,32,"");
>     estimated_steps := range / estimated_h;
>     omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
>     step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
>     omniout_float(ALWAYS,"step_error",32,step_error,32,"");
>     (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
    omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
        glob_desired_digits_correct, 32, "");
    desired_abs_gbl_error :=
        expt(glob__10, c(-glob_desired_digits_correct))*
        c(float_abs(c(estimated_answer)));
    omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
    omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
        ;
    omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
        desired_abs_gbl_error, 32, "");
    range := x_end - x_start;
    omniout_float(ALWAYS, "range", 32, range, 32, "");
    estimated_steps := range/estimated_h;
    omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
    step_error := c(float_abs(desired_abs_gbl_error)/(
        sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
    omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
    step_error
end proc

# End Function number 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3));
> end;
exact_soln_y := proc(x)
    return
    c(0.05)*c(x)*c(x) + c(0.2)*c(x) - cos(c(0.3)*c(x) + c(0.1))/c(0.3)
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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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)*29*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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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)*29*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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> 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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, 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_0D3,
> array_const_0D1,
> array_const_0D2,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
>     array_tmp1[1] := array_const_0D3[1] * array_x[1];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 1
>     array_tmp2[1] := array_tmp1[1] + array_const_0D1[1];
>     #emit pre sin 1 $eq_no = 1
>     array_tmp3[1] :=  sin(array_tmp2[1]);
>     array_tmp3_g[1] :=  cos(array_tmp2[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
>     array_tmp5[1] := array_const_0D1[1] * array_x[1];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 1
>     array_tmp6[1] := array_tmp5[1] + array_const_0D2[1];
>     #emit pre add FULL - LINEAR $eq_no = 1 i = 1
>     array_tmp7[1] := array_tmp4[1] + array_tmp6[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_tmp7[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[2] := temporary;
>                 array_y_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
>     array_tmp1[2] := array_const_0D3[1] * array_x[2];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
>     array_tmp3[2] := array_tmp3_g[1] * array_tmp2[2] / c(1);
>     array_tmp3_g[2] := neg(array_tmp3[1]) * array_tmp2[2] / c(1);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp4[2] := array_tmp3[2];
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
>     array_tmp5[2] := array_const_0D1[1] * array_x[2];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 2
>     array_tmp6[2] := array_tmp5[2];
>     #emit pre add FULL - LINEAR $eq_no = 1 i = 2
>     array_tmp7[2] := array_tmp4[2] + array_tmp6[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_tmp7[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_tmp3[3] := array_tmp3_g[2] * array_tmp2[2] / c(2);
>     array_tmp3_g[3] := neg(array_tmp3[2]) * array_tmp2[2] / c(2);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp4[3] := array_tmp3[3];
>     #emit pre add FULL - LINEAR $eq_no = 1 i = 3
>     array_tmp7[3] := array_tmp4[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[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_tmp3[4] := array_tmp3_g[3] * array_tmp2[2] / c(3);
>     array_tmp3_g[4] := neg(array_tmp3[3]) * array_tmp2[2] / c(3);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp4[4] := array_tmp3[4];
>     #emit pre add FULL - LINEAR $eq_no = 1 i = 4
>     array_tmp7[4] := array_tmp4[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[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_tmp3[5] := array_tmp3_g[4] * array_tmp2[2] / c(4);
>     array_tmp3_g[5] := neg(array_tmp3[4]) * array_tmp2[2] / c(4);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp4[5] := array_tmp3[5];
>     #emit pre add FULL - LINEAR $eq_no = 1 i = 5
>     array_tmp7[5] := array_tmp4[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_y_set_initial[1,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[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_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_tmp2[2] / c(kkk - 1);
>         array_tmp3_g[kkk] := neg(array_tmp3[kkk - 1]) * array_tmp2[2] / c(kkk - 1);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp4[kkk] := array_tmp3[kkk];
>         #emit FULL - NOT FULL add $eq_no = 1
>         array_tmp7[kkk] := array_tmp4[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y_set_initial[1,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp7[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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    array_tmp1[1] := array_const_0D3[1]*array_x[1];
    array_tmp2[1] := array_tmp1[1] + array_const_0D1[1];
    array_tmp3[1] := sin(array_tmp2[1]);
    array_tmp3_g[1] := cos(array_tmp2[1]);
    array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
    array_tmp5[1] := array_const_0D1[1]*array_x[1];
    array_tmp6[1] := array_tmp5[1] + array_const_0D2[1];
    array_tmp7[1] := array_tmp4[1] + array_tmp6[1];
    if not array_y_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y[2] := temporary; array_y_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := array_const_0D3[1]*array_x[2];
    array_tmp2[2] := array_tmp1[2];
    array_tmp3[2] := array_tmp3_g[1]*array_tmp2[2]/c(1);
    array_tmp3_g[2] := neg(array_tmp3[1])*array_tmp2[2]/c(1);
    array_tmp4[2] := array_tmp3[2];
    array_tmp5[2] := array_const_0D1[1]*array_x[2];
    array_tmp6[2] := array_tmp5[2];
    array_tmp7[2] := array_tmp4[2] + array_tmp6[2];
    if not array_y_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y[3] := temporary; array_y_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp3[3] := array_tmp3_g[2]*array_tmp2[2]/c(2);
    array_tmp3_g[3] := neg(array_tmp3[2])*array_tmp2[2]/c(2);
    array_tmp4[3] := array_tmp3[3];
    array_tmp7[3] := array_tmp4[3];
    if not array_y_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y[4] := temporary; array_y_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp3[4] := array_tmp3_g[3]*array_tmp2[2]/c(3);
    array_tmp3_g[4] := neg(array_tmp3[3])*array_tmp2[2]/c(3);
    array_tmp4[4] := array_tmp3[4];
    array_tmp7[4] := array_tmp4[4];
    if not array_y_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y[5] := temporary; array_y_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp3[5] := array_tmp3_g[4]*array_tmp2[2]/c(4);
    array_tmp3_g[5] := neg(array_tmp3[4])*array_tmp2[2]/c(4);
    array_tmp4[5] := array_tmp3[5];
    array_tmp7[5] := array_tmp4[5];
    if not array_y_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y[6] := temporary; array_y_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_tmp2[2]/c(kkk - 1);
        array_tmp3_g[kkk] :=
            neg(array_tmp3[kkk - 1])*array_tmp2[2]/c(kkk - 1);
        array_tmp4[kkk] := array_tmp3[kkk];
        array_tmp7[kkk] := array_tmp4[kkk];
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp7[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_0D3,
>     array_const_0D1,
>     array_const_0D2,
>     #END CONST
>     array_y_init,
>     array_norms,
>     array_fact_1,
>     array_1st_rel_error,
>     array_last_rel_error,
>     array_est_rel_error,
>     array_max_est_error,
>     array_type_pole,
>     array_type_real_pole,
>     array_type_complex_pole,
>     array_est_digits,
>     array_y,
>     array_x,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3_g,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_tmp6,
>     array_tmp7,
>     array_m1,
>     array_y_higher,
>     array_y_higher_work,
>     array_y_higher_work2,
>     array_y_set_initial,
>     array_given_rad_poles,
>     array_given_ord_poles,
>     array_rad_test_poles,
>     array_ord_test_poles,
>     array_fact_2,
>     ATS_MAX_TERMS,
>     glob_last;
>     ATS_MAX_TERMS := 40;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=40;
>     #END BLOCK 1
>     #END FIRST INPUT BLOCK
>     #START OF INITS AFTER INPUT BLOCK
>     glob_html_log := true;
>     #END OF INITS AFTER INPUT BLOCK
>     # before generate arrays
>     array_y_init:= Array(0..(40),[]);
>     array_norms:= Array(0..(40),[]);
>     array_fact_1:= Array(0..(40),[]);
>     array_1st_rel_error:= Array(0..(2),[]);
>     array_last_rel_error:= Array(0..(2),[]);
>     array_est_rel_error:= Array(0..(2),[]);
>     array_max_est_error:= Array(0..(2),[]);
>     array_type_pole:= Array(0..(2),[]);
>     array_type_real_pole:= Array(0..(2),[]);
>     array_type_complex_pole:= Array(0..(2),[]);
>     array_est_digits:= Array(0..(2),[]);
>     array_y:= Array(0..(40),[]);
>     array_x:= Array(0..(40),[]);
>     array_tmp0:= Array(0..(40),[]);
>     array_tmp1:= Array(0..(40),[]);
>     array_tmp2:= Array(0..(40),[]);
>     array_tmp3_g:= Array(0..(40),[]);
>     array_tmp3:= Array(0..(40),[]);
>     array_tmp4:= Array(0..(40),[]);
>     array_tmp5:= Array(0..(40),[]);
>     array_tmp6:= Array(0..(40),[]);
>     array_tmp7:= Array(0..(40),[]);
>     array_m1:= Array(0..(40),[]);
>     array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
>     array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
>     array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
>     array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
>     array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
>     # before generate constants
>     # before generate globals definition
>     #Top Generate Globals Definition
>     #Bottom Generate Globals Deninition
>     # before generate const definition
>     # before arrays initialized
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_fact_1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_1st_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_last_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_est_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_max_est_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_real_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_complex_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_est_digits[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp3_g[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp5[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp6[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp7[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_m1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_higher_work2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y_set_initial[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_rad_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_ord_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_rad_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_ord_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=40) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3_g);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5);
>     zero_ats_ar(array_tmp6);
>     zero_ats_ar(array_tmp7);
>     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_0D3);
>     array_const_0D3[1]   := c(0.3);
>     zero_ats_ar(array_const_0D1);
>     array_const_0D1[1]   := c(0.1);
>     zero_ats_ar(array_const_0D2);
>     array_const_0D2[1]   := c(0.2);
>     zero_ats_ar(array_m1);
>     array_m1[1]   := glob__m1;
>     #END SYMBOLS INITIALIZATED
>     # before generate factorials init
>     #Initing Factorial Tables
>     iiif := 0;
>     while (iiif <= ATS_MAX_TERMS) do # do number 1
>         jjjf := 0;
>         while (jjjf <= ATS_MAX_TERMS) do # do number 2
>             array_fact_1[iiif] := 0;
>             array_fact_2[iiif,jjjf] := 0;
>             jjjf := jjjf + 1;
>         od;# end do number 2;
>         iiif := iiif + 1;
>     od;# end do number 1;
>     #Done Initing Factorial Table
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     glob_iolevel := 5;
>     glob_yes_pole := 4;
>     glob_no_pole := 3;
>     glob_not_given := 0;
>     glob_no_sing_tests := 4;
>     glob_ratio_test := 1;
>     glob_three_term_test := 2;
>     glob_six_term_test := 3;
>     glob_log_10 := log(c(10.0));
>     MAX_UNCHANGED := 10;
>     glob__small := c(0.1e-50);
>     glob_small_float := c(0.1e-50);
>     glob_smallish_float := c(0.1e-60);
>     glob_large_float := c(1.0e100);
>     glob_larger_float := c(1.1e100);
>     glob__m2 := c(-2);
>     glob__m1 := c(-1);
>     glob__0 := c(0);
>     glob__1 := c(1);
>     glob__2 := c(2);
>     glob__3 := c(3);
>     glob__4 := c(4);
>     glob__5 := c(5);
>     glob__8 := c(8);
>     glob__10 := c(10);
>     glob__100 := c(100);
>     glob__pi := c(0.0);
>     glob__0_5 := c(0.5);
>     glob__0_8 := c(0.8);
>     glob__m0_8 := c(-0.8);
>     glob__0_25 := c(0.25);
>     glob__0_125 := c(0.125);
>     glob_prec := c(1.0e-16);
>     glob_check_sign := c(1.0);
>     glob_desired_digits_correct := c(8.0);
>     glob_max_estimated_step_error := c(0.0);
>     glob_ratio_of_radius := c(0.1);
>     glob_percent_done := c(0.0);
>     glob_total_exp_sec := c(0.1);
>     glob_optimal_expect_sec := c(0.1);
>     glob_estimated_size_answer := c(100.0);
>     glob_almost_1 := c(0.9990);
>     glob_clock_sec := c(0.0);
>     glob_clock_start_sec := c(0.0);
>     glob_disp_incr := c(0.1);
>     glob_h := c(0.1);
>     glob_diff_rc_fm := c(0.1);
>     glob_diff_rc_fmm1 := c(0.1);
>     glob_diff_rc_fmm2 := c(0.1);
>     glob_diff_ord_fm := c(0.1);
>     glob_diff_ord_fmm1 := c(0.1);
>     glob_diff_ord_fmm2 := c(0.1);
>     glob_six_term_ord_save := c(0.1);
>     glob_guess_error_rc := c(0.1);
>     glob_guess_error_ord := c(0.1);
>     glob_least_given_sing := c(9.9e200);
>     glob_least_ratio_sing := c(9.9e200);
>     glob_least_3_sing := c(9.9e100);
>     glob_least_6_sing := c(9.9e100);
>     glob_last_good_h := c(0.1);
>     glob_max_h := c(0.1);
>     glob_min_h := c(0.000001);
>     glob_display_interval := c(0.1);
>     glob_abserr := c(0.1e-10);
>     glob_relerr := c(0.1e-10);
>     glob_min_pole_est := c(0.1e+10);
>     glob_max_rel_trunc_err := c(0.1e-10);
>     glob_max_trunc_err := c(0.1e-10);
>     glob_max_hours := c(0.0);
>     glob_optimal_clock_start_sec := c(0.0);
>     glob_optimal_start := c(0.0);
>     glob_upper_ratio_limit := c(1.0001);
>     glob_lower_ratio_limit := c(0.9999);
>     glob_max_sec := c(10000.0);
>     glob_orig_start_sec := c(0.0);
>     glob_normmax := c(0.0);
>     glob_max_minutes := c(0.0);
>     glob_next_display := c(0.0);
>     glob_est_digits := 1;
>     glob_subiter_method := 3;
>     glob_html_log := true;
>     glob_min_good_digits := 99999;
>     glob_good_digits := 0;
>     glob_min_apfp_est_good_digits := 99999;
>     glob_apfp_est_good_digits := 0;
>     glob_max_opt_iter := 10;
>     glob_dump := false;
>     glob_djd_debug := true;
>     glob_display_flag := true;
>     glob_djd_debug2 := true;
>     glob_h_reason := 0;
>     glob_sec_in_minute := 60 ;
>     glob_min_in_hour := 60;
>     glob_hours_in_day := 24;
>     glob_days_in_year := 365;
>     glob_sec_in_hour := 3600;
>     glob_sec_in_day := 86400;
>     glob_sec_in_year := 31536000;
>     glob_not_yet_finished := true;
>     glob_initial_pass := true;
>     glob_not_yet_start_msg := true;
>     glob_reached_optimal_h := false;
>     glob_optimal_done := false;
>     glob_type_given_pole := 0;
>     glob_optimize := false;
>     glob_look_poles := false;
>     glob_dump_closed_form := false;
>     glob_max_iter := 1000;
>     glob_no_eqs := 0;
>     glob_unchanged_h_cnt := 0;
>     glob_warned := false;
>     glob_warned2 := false;
>     glob_start := 0;
>     glob_iter := 0;
>     # before generate set diff initial
>     array_y_set_initial[1,1] := true;
>     array_y_set_initial[1,2] := false;
>     array_y_set_initial[1,3] := false;
>     array_y_set_initial[1,4] := false;
>     array_y_set_initial[1,5] := false;
>     array_y_set_initial[1,6] := false;
>     array_y_set_initial[1,7] := false;
>     array_y_set_initial[1,8] := false;
>     array_y_set_initial[1,9] := false;
>     array_y_set_initial[1,10] := false;
>     array_y_set_initial[1,11] := false;
>     array_y_set_initial[1,12] := false;
>     array_y_set_initial[1,13] := false;
>     array_y_set_initial[1,14] := false;
>     array_y_set_initial[1,15] := false;
>     array_y_set_initial[1,16] := false;
>     array_y_set_initial[1,17] := false;
>     array_y_set_initial[1,18] := false;
>     array_y_set_initial[1,19] := false;
>     array_y_set_initial[1,20] := false;
>     array_y_set_initial[1,21] := false;
>     array_y_set_initial[1,22] := false;
>     array_y_set_initial[1,23] := false;
>     array_y_set_initial[1,24] := false;
>     array_y_set_initial[1,25] := false;
>     array_y_set_initial[1,26] := false;
>     array_y_set_initial[1,27] := false;
>     array_y_set_initial[1,28] := false;
>     array_y_set_initial[1,29] := false;
>     array_y_set_initial[1,30] := false;
>     array_y_set_initial[1,31] := false;
>     array_y_set_initial[1,32] := false;
>     array_y_set_initial[1,33] := false;
>     array_y_set_initial[1,34] := false;
>     array_y_set_initial[1,35] := false;
>     array_y_set_initial[1,36] := false;
>     array_y_set_initial[1,37] := false;
>     array_y_set_initial[1,38] := false;
>     array_y_set_initial[1,39] := false;
>     array_y_set_initial[1,40] := false;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 40;
>     glob_iolevel := INFO;
>     # set default block
>     #Write Set Defaults
>     glob_orig_start_sec   :=  elapsed_time_seconds();
>     glob_display_flag   :=   true;
>     glob_no_eqs   := 1;
>     glob_iter   :=  -1;
>     opt_iter   :=  -1;
>     glob_max_iter   :=  50000;
>     glob_max_hours   :=  (0.0);
>     glob_max_minutes   :=  (15.0);
>     omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
>     omniout_str(ALWAYS,"##############temp/add_full_linpostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =   sin ( 0.3  *  x  +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=40;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(1.0);");
>     omniout_str(ALWAYS,"x_end := c(5.0) ;");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_display_interval := c(0.1);");
>     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,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
>     omniout_str(ALWAYS,"glob_look_poles:=false;");
>     omniout_str(ALWAYS,"glob_h:=c(0.001);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y := proc(x)");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3));");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(1.0);
>     x_end := c(5.0) ;
>     array_y_init[0 + 1] := exact_soln_y(x_start);
>     glob_display_interval := c(0.1);
>     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  )   =   sin ( 0.3  *  x  +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(x_start,x_end);
>         if (glob_html_log)  then # if number 10
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2016-08-26T16:21:49-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"add_full_lin.ode.txt\">add_full_lin</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =   sin ( 0.3  *  x  +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ; ")
>             ;
>             logitem_float(html_log_file,x_start)
>             ;
>             logitem_float(html_log_file,x_end)
>             ;
>             logitem_float(html_log_file,array_x[1])
>             ;
>             logitem_float(html_log_file,glob_h)
>             ;
>             logitem_h_reason(html_log_file)
>             ;
>             logitem_integer(html_log_file,Digits)
>             ;
>             ;
>             logitem_float(html_log_file,glob_desired_digits_correct)
>             ;
>             if (array_est_digits[1] <> -16) then # if number 11
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_min_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_integer(html_log_file,ATS_MAX_TERMS)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 11
>                 logitem_str(html_log_file,"Not Given")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 12
>                 logitem_str(html_log_file,"No Solution")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 13
>                 logitem_str(html_log_file,"Some Pole")
>                 ;
>                 logitem_str(html_log_file,"????")
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 14
>                 logitem_str(html_log_file,"No Pole")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 15
>                 logitem_str(html_log_file,"Real Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 16
>                 logitem_str(html_log_file,"Complex Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             fi;# end if 16;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_ratio_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_3_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_3_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_6_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_6_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             logitem_integer(html_log_file,glob_iter)
>             ;
>             logitem_time(html_log_file,(glob_clock_sec))
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 16
>                 logitem_time(html_log_file,(glob_total_exp_sec))
>                 ;
>                 0;
>             else
>                 logitem_str(html_log_file,"Done")
>                 ;
>                 0;
>             fi;# end if 16;
>             log_revs(html_log_file,"<td> 308.maple.seems.ok </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.add_full_lin.mxt.txt\">add_full_lin diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.add_full_lin.mxt.txt\">add_full_lin 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_0D3,
array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    ATS_MAX_TERMS := 40;
    Digits := 32;
    max_terms := 40;
    glob_html_log := true;
    array_y_init := Array(0 .. 40, []);
    array_norms := Array(0 .. 40, []);
    array_fact_1 := Array(0 .. 40, []);
    array_1st_rel_error := Array(0 .. 2, []);
    array_last_rel_error := Array(0 .. 2, []);
    array_est_rel_error := Array(0 .. 2, []);
    array_max_est_error := Array(0 .. 2, []);
    array_type_pole := Array(0 .. 2, []);
    array_type_real_pole := Array(0 .. 2, []);
    array_type_complex_pole := Array(0 .. 2, []);
    array_est_digits := Array(0 .. 2, []);
    array_y := Array(0 .. 40, []);
    array_x := Array(0 .. 40, []);
    array_tmp0 := Array(0 .. 40, []);
    array_tmp1 := Array(0 .. 40, []);
    array_tmp2 := Array(0 .. 40, []);
    array_tmp3_g := Array(0 .. 40, []);
    array_tmp3 := Array(0 .. 40, []);
    array_tmp4 := Array(0 .. 40, []);
    array_tmp5 := Array(0 .. 40, []);
    array_tmp6 := Array(0 .. 40, []);
    array_tmp7 := Array(0 .. 40, []);
    array_m1 := Array(0 .. 40, []);
    array_y_higher := Array(0 .. 2, 0 .. 41, []);
    array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
    array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
    array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
    array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
    array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
    array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_fact_2 := Array(0 .. 40, 0 .. 41, []);
    term := 1;
    while term <= 40 do array_y_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do
        array_last_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
    term := 1;
    while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_y[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp3_g[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_given_rad_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_given_ord_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 4 do
            array_rad_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 4 do
            array_ord_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 40 do
        term := 1;
        while term <= 40 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y);
    zero_ats_ar(array_x);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3_g);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5);
    zero_ats_ar(array_tmp6);
    zero_ats_ar(array_tmp7);
    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_0D3);
    array_const_0D3[1] := c(0.3);
    zero_ats_ar(array_const_0D1);
    array_const_0D1[1] := c(0.1);
    zero_ats_ar(array_const_0D2);
    array_const_0D2[1] := c(0.2);
    zero_ats_ar(array_m1);
    array_m1[1] := glob__m1;
    iiif := 0;
    while iiif <= ATS_MAX_TERMS do
        jjjf := 0;
        while jjjf <= ATS_MAX_TERMS do
            array_fact_1[iiif] := 0;
            array_fact_2[iiif, jjjf] := 0;
            jjjf := jjjf + 1
        end do;
        iiif := iiif + 1
    end do;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := 5;
    glob_yes_pole := 4;
    glob_no_pole := 3;
    glob_not_given := 0;
    glob_no_sing_tests := 4;
    glob_ratio_test := 1;
    glob_three_term_test := 2;
    glob_six_term_test := 3;
    glob_log_10 := log(c(10.0));
    MAX_UNCHANGED := 10;
    glob__small := c(0.1*10^(-50));
    glob_small_float := c(0.1*10^(-50));
    glob_smallish_float := c(0.1*10^(-60));
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob__m2 := c(-2);
    glob__m1 := c(-1);
    glob__0 := c(0);
    glob__1 := c(1);
    glob__2 := c(2);
    glob__3 := c(3);
    glob__4 := c(4);
    glob__5 := c(5);
    glob__8 := c(8);
    glob__10 := c(10);
    glob__100 := c(100);
    glob__pi := c(0.);
    glob__0_5 := c(0.5);
    glob__0_8 := c(0.8);
    glob__m0_8 := c(-0.8);
    glob__0_25 := c(0.25);
    glob__0_125 := c(0.125);
    glob_prec := c(0.10*10^(-15));
    glob_check_sign := c(1.0);
    glob_desired_digits_correct := c(8.0);
    glob_max_estimated_step_error := c(0.);
    glob_ratio_of_radius := c(0.1);
    glob_percent_done := c(0.);
    glob_total_exp_sec := c(0.1);
    glob_optimal_expect_sec := c(0.1);
    glob_estimated_size_answer := c(100.0);
    glob_almost_1 := c(0.9990);
    glob_clock_sec := c(0.);
    glob_clock_start_sec := c(0.);
    glob_disp_incr := c(0.1);
    glob_h := c(0.1);
    glob_diff_rc_fm := c(0.1);
    glob_diff_rc_fmm1 := c(0.1);
    glob_diff_rc_fmm2 := c(0.1);
    glob_diff_ord_fm := c(0.1);
    glob_diff_ord_fmm1 := c(0.1);
    glob_diff_ord_fmm2 := c(0.1);
    glob_six_term_ord_save := c(0.1);
    glob_guess_error_rc := c(0.1);
    glob_guess_error_ord := c(0.1);
    glob_least_given_sing := c(0.99*10^201);
    glob_least_ratio_sing := c(0.99*10^201);
    glob_least_3_sing := c(0.99*10^101);
    glob_least_6_sing := c(0.99*10^101);
    glob_last_good_h := c(0.1);
    glob_max_h := c(0.1);
    glob_min_h := c(0.1*10^(-5));
    glob_display_interval := c(0.1);
    glob_abserr := c(0.1*10^(-10));
    glob_relerr := c(0.1*10^(-10));
    glob_min_pole_est := c(0.1*10^10);
    glob_max_rel_trunc_err := c(0.1*10^(-10));
    glob_max_trunc_err := c(0.1*10^(-10));
    glob_max_hours := c(0.);
    glob_optimal_clock_start_sec := c(0.);
    glob_optimal_start := c(0.);
    glob_upper_ratio_limit := c(1.0001);
    glob_lower_ratio_limit := c(0.9999);
    glob_max_sec := c(10000.0);
    glob_orig_start_sec := c(0.);
    glob_normmax := c(0.);
    glob_max_minutes := c(0.);
    glob_next_display := c(0.);
    glob_est_digits := 1;
    glob_subiter_method := 3;
    glob_html_log := true;
    glob_min_good_digits := 99999;
    glob_good_digits := 0;
    glob_min_apfp_est_good_digits := 99999;
    glob_apfp_est_good_digits := 0;
    glob_max_opt_iter := 10;
    glob_dump := false;
    glob_djd_debug := true;
    glob_display_flag := true;
    glob_djd_debug2 := true;
    glob_h_reason := 0;
    glob_sec_in_minute := 60;
    glob_min_in_hour := 60;
    glob_hours_in_day := 24;
    glob_days_in_year := 365;
    glob_sec_in_hour := 3600;
    glob_sec_in_day := 86400;
    glob_sec_in_year := 31536000;
    glob_not_yet_finished := true;
    glob_initial_pass := true;
    glob_not_yet_start_msg := true;
    glob_reached_optimal_h := false;
    glob_optimal_done := false;
    glob_type_given_pole := 0;
    glob_optimize := false;
    glob_look_poles := false;
    glob_dump_closed_form := false;
    glob_max_iter := 1000;
    glob_no_eqs := 0;
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_start := 0;
    glob_iter := 0;
    array_y_set_initial[1, 1] := true;
    array_y_set_initial[1, 2] := false;
    array_y_set_initial[1, 3] := false;
    array_y_set_initial[1, 4] := false;
    array_y_set_initial[1, 5] := false;
    array_y_set_initial[1, 6] := false;
    array_y_set_initial[1, 7] := false;
    array_y_set_initial[1, 8] := false;
    array_y_set_initial[1, 9] := false;
    array_y_set_initial[1, 10] := false;
    array_y_set_initial[1, 11] := false;
    array_y_set_initial[1, 12] := false;
    array_y_set_initial[1, 13] := false;
    array_y_set_initial[1, 14] := false;
    array_y_set_initial[1, 15] := false;
    array_y_set_initial[1, 16] := false;
    array_y_set_initial[1, 17] := false;
    array_y_set_initial[1, 18] := false;
    array_y_set_initial[1, 19] := false;
    array_y_set_initial[1, 20] := false;
    array_y_set_initial[1, 21] := false;
    array_y_set_initial[1, 22] := false;
    array_y_set_initial[1, 23] := false;
    array_y_set_initial[1, 24] := false;
    array_y_set_initial[1, 25] := false;
    array_y_set_initial[1, 26] := false;
    array_y_set_initial[1, 27] := false;
    array_y_set_initial[1, 28] := false;
    array_y_set_initial[1, 29] := false;
    array_y_set_initial[1, 30] := false;
    array_y_set_initial[1, 31] := false;
    array_y_set_initial[1, 32] := false;
    array_y_set_initial[1, 33] := false;
    array_y_set_initial[1, 34] := false;
    array_y_set_initial[1, 35] := false;
    array_y_set_initial[1, 36] := false;
    array_y_set_initial[1, 37] := false;
    array_y_set_initial[1, 38] := false;
    array_y_set_initial[1, 39] := false;
    array_y_set_initial[1, 40] := false;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 40;
    glob_iolevel := INFO;
    glob_orig_start_sec := elapsed_time_seconds();
    glob_display_flag := true;
    glob_no_eqs := 1;
    glob_iter := -1;
    opt_iter := -1;
    glob_max_iter := 50000;
    glob_max_hours := 0.;
    glob_max_minutes := 15.0;
    omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
    omniout_str(ALWAYS,
        "##############temp/add_full_linpostode.ode#################");
    omniout_str(ALWAYS, "diff  (  y  ,  x  ,  1  )   =   sin ( 0.3  *  x \
         +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=40;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(1.0);");
    omniout_str(ALWAYS, "x_end := c(5.0) ;");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_display_interval := c(0.1);");
    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, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
    omniout_str(ALWAYS, "glob_look_poles:=false;");
    omniout_str(ALWAYS, "glob_h:=c(0.001);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y := proc(x)");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - c\
        os(c(0.3) * c(x) + c(0.1)) / c(0.3));");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(1.0);
    x_end := c(5.0);
    array_y_init[1] := exact_soln_y(x_start);
    glob_display_interval := c(0.1);
    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  )   =   sin ( 0.3  *  \
            x  +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ; ");
        omniout_int(INFO, "Iterations                      ", 32, glob_iter,
            4, " ");
        prog_report(x_start, x_end);
        if glob_html_log then
            logstart(html_log_file);
            logitem_str(html_log_file, "2016-08-26T16:21:49-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"add_full_lin.ode.txt\">add_full_lin</a>");
            logitem_str(html_log_file, "diff  (  y  ,  x  ,  1  )   =   s\
                in ( 0.3  *  x  +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ;\
                 ");
            logitem_float(html_log_file, x_start);
            logitem_float(html_log_file, x_end);
            logitem_float(html_log_file, array_x[1]);
            logitem_float(html_log_file, glob_h);
            logitem_h_reason(html_log_file);
            logitem_integer(html_log_file, Digits);
            logitem_float(html_log_file, glob_desired_digits_correct);
            if array_est_digits[1] <> -16 then
                logitem_integer(html_log_file, array_est_digits[1])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_min_good_digits <> -16 then
                logitem_integer(html_log_file, glob_min_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_good_digits <> -16 then
                logitem_integer(html_log_file, glob_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            logitem_integer(html_log_file, ATS_MAX_TERMS);
            if glob_type_given_pole = 0 then
                logitem_str(html_log_file, "Not Given");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 4 then
                logitem_str(html_log_file, "No Solution");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 5 then
                logitem_str(html_log_file, "Some Pole");
                logitem_str(html_log_file, "????")
            elif glob_type_given_pole = 3 then
                logitem_str(html_log_file, "No Pole");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 1 then
                logitem_str(html_log_file, "Real Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            elif glob_type_given_pole = 2 then
                logitem_str(html_log_file, "Complex Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_ratio_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_3_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_3_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_6_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_6_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            logitem_integer(html_log_file, glob_iter);
            logitem_time(html_log_file, glob_clock_sec);
            if c(glob_percent_done) < glob__100 then
                logitem_time(html_log_file, glob_total_exp_sec); 0
            else logitem_str(html_log_file, "Done"); 0
            end if;
            log_revs(html_log_file, "<td> 308.maple.seems.ok </td>");
            logitem_str(html_log_file, "<a href=\"diffeq.add_full_lin.mxt\
                .txt\">add_full_lin diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.add_full_lin.mx\
                t.txt\">add_full_lin 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/add_full_linpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   sin ( 0.3  *  x  +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(1.0);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_display_interval := c(0.1);
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(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3));

end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y[1] (closed_form)                = -2.8202033133429502759950891068393           
y[1] (numeric)                    = -2.8202033133429502759950891068393           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4.0MB, alloc=40.3MB, time=0.09
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y[1] (closed_form)                = -2.8132903198565881669326461707355           
y[1] (numeric)                    = -2.8132903198565881669326461707355           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y[1] (closed_form)                = -2.806339729733044835776485786148            
y[1] (numeric)                    = -2.806339729733044835776485786148            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y[1] (closed_form)                = -2.7993515783926048291912240097545           
y[1] (numeric)                    = -2.7993515783926048291912240097545           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y[1] (closed_form)                = -2.792325901503603459873397519041            
y[1] (numeric)                    = -2.7923259015036034598733975190412           
absolute error                    = 2e-31                                        
relative error                    = 7.1624877272493367167518482517012e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y[1] (closed_form)                = -2.7852627349821057917744105346046           
y[1] (numeric)                    = -2.7852627349821057917744105346047           
absolute error                    = 1e-31                                        
relative error                    = 3.5903255640492551354372514226123e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y[1] (closed_form)                = -2.7781621149915833957573926239669           
y[1] (numeric)                    = -2.7781621149915833957573926239668           
absolute error                    = 1e-31                                        
relative error                    = 3.5995019678793278712369622641447e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y[1] (closed_form)                = -2.7710240779425888785971642932799           
y[1] (numeric)                    = -2.7710240779425888785971642932798           
absolute error                    = 1e-31                                        
relative error                    = 3.6087741278035851731659850877620e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y[1] (closed_form)                = -2.7638486604924281882525471703067           
y[1] (numeric)                    = -2.7638486604924281882525471703065           
absolute error                    = 2e-31                                        
relative error                    = 7.2362862286521320175135686834979e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=30.7MB, alloc=40.3MB, time=0.42
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y[1] (closed_form)                = -2.7566358995448306983602691159434           
y[1] (numeric)                    = -2.7566358995448306983602691159433           
absolute error                    = 1e-31                                        
relative error                    = 3.6276100161255161472942959480636e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y[1] (closed_form)                = -2.7493858322496170749197015922115           
y[1] (numeric)                    = -2.7493858322496170749197015922114           
absolute error                    = 1e-31                                        
relative error                    = 3.6371759404236643279476716553250e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y[1] (closed_form)                = -2.7420984960023649281576268821809           
y[1] (numeric)                    = -2.7420984960023649281576268821808           
absolute error                    = 1e-31                                        
relative error                    = 3.6468420133626649568156803084860e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y[1] (closed_form)                = -2.7347739284440722525821661220729           
y[1] (numeric)                    = -2.7347739284440722525821661220727           
absolute error                    = 2e-31                                        
relative error                    = 7.3132187607839453087226140600659e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y[1] (closed_form)                = -2.7274121674608186582549053884098           
y[1] (numeric)                    = -2.7274121674608186582549053884097           
absolute error                    = 1e-31                                        
relative error                    = 3.6664792066649228126968168311717e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y[1] (closed_form)                = -2.7200132511834243963301361043887           
y[1] (numeric)                    = -2.7200132511834243963301361043887           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y[1] (closed_form)                = -2.7125772179871071819299776107393           
y[1] (numeric)                    = -2.7125772179871071819299776107391           
absolute error                    = 2e-31                                        
relative error                    = 7.3730619970483950097626090551549e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y[1] (closed_form)                = -2.7051041064911368174439737085169           
y[1] (numeric)                    = -2.7051041064911368174439737085166           
absolute error                    = 3e-31                                        
relative error                    = 1.1090146189942318210833146799559e-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)                = -2.6975939555584876193615511461702           
y[1] (numeric)                    = -2.6975939555584876193615511461699           
absolute error                    = 3e-31                                        
relative error                    = 1.1121021359861791081105024240313e-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)                = -2.6900468042954886517654962126398           
y[1] (numeric)                    = -2.6900468042954886517654962126395           
absolute error                    = 3e-31                                        
relative error                    = 1.1152222315275613644627920119300e-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)                = -2.6824626920514717696343456342736           
y[1] (numeric)                    = -2.6824626920514717696343456342732           
absolute error                    = 4e-31                                        
relative error                    = 1.4911670577386158825718918844383e-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)                = -2.6748416584184174751212996783347           
y[1] (numeric)                    = -2.6748416584184174751212996783345           
absolute error                    = 2e-31                                        
relative error                    = 7.4770781055599440861507838701545e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=71.3MB, alloc=44.3MB, time=0.90
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y[1] (closed_form)                = -2.6671837432305985899969485624153           
y[1] (numeric)                    = -2.6671837432305985899969485624152           
absolute error                    = 1e-31                                        
relative error                    = 3.7492730020495715552258981963263e-30      % 
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)                = -2.6594889865642217474627577800071           
y[1] (numeric)                    = -2.659488986564221747462757780007            
absolute error                    = 1e-31                                        
relative error                    = 3.7601208542393482358080039829068e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y[1] (closed_form)                = -2.6517574287370667065618836009314           
y[1] (numeric)                    = -2.6517574287370667065618836009315           
absolute error                    = 1e-31                                        
relative error                    = 3.7710839957041725081643090485690e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y[1] (closed_form)                = -2.6439891103081234924334866146632           
y[1] (numeric)                    = -2.6439891103081234924334866146634           
absolute error                    = 2e-31                                        
relative error                    = 7.5643276751882132142404063044977e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y[1] (closed_form)                = -2.6361840720772273656762785784231           
y[1] (numeric)                    = -2.6361840720772273656762785784234           
absolute error                    = 3e-31                                        
relative error                    = 1.1380085449177672589924160242458e-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)                = -2.6283423550846916241065758341615           
y[1] (numeric)                    = -2.6283423550846916241065758341619           
absolute error                    = 4e-31                                        
relative error                    = 1.5218717577874706543512858740039e-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)                = -2.6204640006109382402156409933645           
y[1] (numeric)                    = -2.6204640006109382402156409933651           
absolute error                    = 6e-31                                        
relative error                    = 2.2896708363866676010602910181964e-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)                = -2.6125490501761263376505732804125           
y[1] (numeric)                    = -2.6125490501761263376505732804132           
absolute error                    = 7e-31                                        
relative error                    = 2.6793755315438350910344156950740e-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)                = -2.604597545539778510062456698693            
y[1] (numeric)                    = -2.6045975455397785100624566986936           
absolute error                    = 6e-31                                        
relative error                    = 2.3036188490136030017365488892200e-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)                = -2.5966095287004049856848938637889           
y[1] (numeric)                    = -2.5966095287004049856848938637894           
absolute error                    = 5e-31                                        
relative error                    = 1.9255879425592666948947483731587e-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)                = -2.5885850418951256410254417600485           
y[1] (numeric)                    = -2.5885850418951256410254417600491           
absolute error                    = 6e-31                                        
relative error                    = 2.3178686050072157467629318414890e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.32                                         
y[1] (closed_form)                = -2.5805241275992898670718236462092           
y[1] (numeric)                    = -2.5805241275992898670718236462099           
absolute error                    = 7e-31                                        
relative error                    = 2.7126272237230471713700838565424e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=111.6MB, alloc=44.3MB, time=1.38
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y[1] (closed_form)                = -2.5724268285260942914341186882642           
y[1] (numeric)                    = -2.572426828526094291434118688265            
absolute error                    = 8e-31                                        
relative error                    = 3.1099038119516522775212756431829e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y[1] (closed_form)                = -2.5642931876261983598634274594928           
y[1] (numeric)                    = -2.5642931876261983598634274594936           
absolute error                    = 8e-31                                        
relative error                    = 3.1197680665391115253853818149957e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y[1] (closed_form)                = -2.5561232480873377806067770448384           
y[1] (numeric)                    = -2.5561232480873377806067770448392           
absolute error                    = 8e-31                                        
relative error                    = 3.1297395405272944392284921484961e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y[1] (closed_form)                = -2.5479170533339358350772639462408           
y[1] (numeric)                    = -2.5479170533339358350772639462416           
absolute error                    = 8e-31                                        
relative error                    = 3.1398196379792045401406643686127e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.37                                         
y[1] (closed_form)                = -2.5396746470267125583376361339824           
y[1] (numeric)                    = -2.5396746470267125583376361339831           
absolute error                    = 7e-31                                        
relative error                    = 2.7562585657163404688150564339963e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y[1] (closed_form)                = -2.5313960730622917929146872537802           
y[1] (numeric)                    = -2.5313960730622917929146872537812           
absolute error                    = 1.0e-30                                      
relative error                    = 3.9503893153720331171717244566523e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y[1] (closed_form)                = -2.5230813755728061194809760076898           
y[1] (numeric)                    = -2.5230813755728061194809760076907           
absolute error                    = 9e-31                                        
relative error                    = 3.5670668758976361849953994410771e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y[1] (closed_form)                = -2.5147305989254996679594919066284           
y[1] (numeric)                    = -2.5147305989254996679594919066292           
absolute error                    = 8e-31                                        
relative error                    = 3.1812552817459889566467617881522e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y[1] (closed_form)                = -2.5063437877223288126259647715032           
y[1] (numeric)                    = -2.506343787722328812625964771504            
absolute error                    = 8e-31                                        
relative error                    = 3.1919005043079504315036012307505e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y[1] (closed_form)                = -2.49792098679956075480255936685             
y[1] (numeric)                    = -2.4979209867995607548025593668509           
absolute error                    = 9e-31                                        
relative error                    = 3.6029962707231867510439188368539e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y[1] (closed_form)                = -2.4894622412273699967557082141659           
y[1] (numeric)                    = -2.4894622412273699967557082141669           
absolute error                    = 1.0e-30                                      
relative error                    = 4.0169317832552215976644568251597e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y[1] (closed_form)                = -2.4809675963094327104298147806401           
y[1] (numeric)                    = -2.480967596309432710429814780641            
absolute error                    = 9e-31                                        
relative error                    = 3.6276169077693575276458001266867e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y[1] (closed_form)                = -2.4724370975825190046675057019428           
y[1] (numeric)                    = -2.4724370975825190046675057019437           
absolute error                    = 9e-31                                        
relative error                    = 3.6401330528489288871065474931307e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=152.2MB, alloc=44.3MB, time=1.86
 
TOP MAIN SOLVE Loop
x[1]                              = 1.46                                         
y[1] (closed_form)                = -2.4638707908160830945860243046089           
y[1] (numeric)                    = -2.4638707908160830945860243046098           
absolute error                    = 9e-31                                        
relative error                    = 3.6527889504380303520124512821958e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y[1] (closed_form)                = -2.4552687220118513767982382741164           
y[1] (numeric)                    = -2.4552687220118513767982382741173           
absolute error                    = 9e-31                                        
relative error                    = 3.6655865483536093987796532986078e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y[1] (closed_form)                = -2.4466309374034084141855816991013           
y[1] (numeric)                    = -2.4466309374034084141855816991021           
absolute error                    = 8e-31                                        
relative error                    = 3.2698025181069367600620913967414e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.49                                         
y[1] (closed_form)                = -2.437957483455780833949065740627            
y[1] (numeric)                    = -2.4379574834557808339490657406278           
absolute error                    = 8e-31                                        
relative error                    = 3.2814354041400584322458648049083e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y[1] (closed_form)                = -2.4292484068650191426832726587259           
y[1] (numeric)                    = -2.4292484068650191426832726587266           
absolute error                    = 7e-31                                        
relative error                    = 2.8815496925790323459107119213443e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y[1] (closed_form)                = -2.4205037545577774622369947075191           
y[1] (numeric)                    = -2.4205037545577774622369947075198           
absolute error                    = 7e-31                                        
relative error                    = 2.8919599842880185423884659382290e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.52                                         
y[1] (closed_form)                = -2.4117235736908911901428923163821           
y[1] (numeric)                    = -2.4117235736908911901428923163828           
absolute error                    = 7e-31                                        
relative error                    = 2.9024885257837533472768247717052e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y[1] (closed_form)                = -2.4029079116509525884172248394417           
y[1] (numeric)                    = -2.4029079116509525884172248394424           
absolute error                    = 7e-31                                        
relative error                    = 2.9131370228793116302419397028624e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y[1] (closed_form)                = -2.3940568160538843045493518110525           
y[1] (numeric)                    = -2.3940568160538843045493518110532           
absolute error                    = 7e-31                                        
relative error                    = 2.9239072160108865574635643889260e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.55                                         
y[1] (closed_form)                = -2.3851703347445108285193129230097           
y[1] (numeric)                    = -2.3851703347445108285193129230105           
absolute error                    = 8e-31                                        
relative error                    = 3.3540581498373052412627709916009e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.56                                         
y[1] (closed_form)                = -2.3762485157961278897003706726133           
y[1] (numeric)                    = -2.3762485157961278897003706726139           
absolute error                    = 6e-31                                        
relative error                    = 2.5249884261326035138143747932533e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.57                                         
y[1] (closed_form)                = -2.3672914075100697975219406521301           
y[1] (numeric)                    = -2.3672914075100697975219406521308           
absolute error                    = 7e-31                                        
relative error                    = 2.9569659137835669907778006671535e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=192.6MB, alloc=44.3MB, time=2.34
 
TOP MAIN SOLVE Loop
x[1]                              = 1.58                                         
y[1] (closed_form)                = -2.3582990584152747297868405928328           
y[1] (numeric)                    = -2.3582990584152747297868405928333           
absolute error                    = 5e-31                                        
relative error                    = 2.1201721563506412937175096354403e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.59                                         
y[1] (closed_form)                = -2.3492715172678479725552603740685           
y[1] (numeric)                    = -2.3492715172678479725552603740689           
absolute error                    = 4e-31                                        
relative error                    = 1.7026554702591012532720270925766e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y[1] (closed_form)                = -2.3402088330506231155262910935001           
y[1] (numeric)                    = -2.3402088330506231155262910935005           
absolute error                    = 4e-31                                        
relative error                    = 1.7092491676419001371760257760872e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.61                                         
y[1] (closed_form)                = -2.3311110549727212068662518028266           
y[1] (numeric)                    = -2.3311110549727212068662518028269           
absolute error                    = 3e-31                                        
relative error                    = 1.2869399737950735124117487127315e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.62                                         
y[1] (closed_form)                = -2.3219782324691078714514174783385           
y[1] (numeric)                    = -2.3219782324691078714514174783387           
absolute error                    = 2e-31                                        
relative error                    = 8.6133451728066897656895485105876e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.63                                         
y[1] (closed_form)                = -2.3128104152001483965110810523045           
y[1] (numeric)                    = -2.3128104152001483965110810523048           
absolute error                    = 3e-31                                        
relative error                    = 1.2971231797831483197852376310199e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.64                                         
y[1] (closed_form)                = -2.3036076530511607886751757144625           
y[1] (numeric)                    = -2.3036076530511607886751757144627           
absolute error                    = 2e-31                                        
relative error                    = 8.6820340145639463598839704449739e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.65                                         
y[1] (closed_form)                = -2.2943699961319668064489410381473           
y[1] (numeric)                    = -2.2943699961319668064489410381474           
absolute error                    = 1e-31                                        
relative error                    = 4.3584949318805611433369823116131e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.66                                         
y[1] (closed_form)                = -2.2850974947764409721553376285322           
y[1] (numeric)                    = -2.2850974947764409721553376285323           
absolute error                    = 1e-31                                        
relative error                    = 4.3761808950643196720903865596801e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.67                                         
y[1] (closed_form)                = -2.2757901995420575674040997670831           
y[1] (numeric)                    = -2.2757901995420575674040997670833           
absolute error                    = 2e-31                                        
relative error                    = 8.7881563089710420926160973998802e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.68                                         
y[1] (closed_form)                = -2.2664481612094356161644637729721           
y[1] (numeric)                    = -2.2664481612094356161644637729723           
absolute error                    = 2e-31                                        
relative error                    = 8.8243800772956926771033957693826e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.69                                         
y[1] (closed_form)                = -2.2570714307818818595367213555316           
y[1] (numeric)                    = -2.2570714307818818595367213555318           
absolute error                    = 2e-31                                        
relative error                    = 8.8610398976481278872941131040445e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=233.1MB, alloc=44.3MB, time=2.82
 
TOP MAIN SOLVE Loop
x[1]                              = 1.7                                          
y[1] (closed_form)                = -2.2476600594849317263358219288494           
y[1] (numeric)                    = -2.2476600594849317263358219288497           
absolute error                    = 3e-31                                        
relative error                    = 1.3347214083109492329553345174912e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.71                                         
y[1] (closed_form)                = -2.2382140987658883036182855376373           
y[1] (numeric)                    = -2.2382140987658883036182855376374           
absolute error                    = 1e-31                                        
relative error                    = 4.4678478281026927952581358500715e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.72                                         
y[1] (closed_form)                = -2.2287336002933593113016885402071           
y[1] (numeric)                    = -2.2287336002933593113016885402073           
absolute error                    = 2e-31                                        
relative error                    = 8.9737059634976023149309939879600e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.73                                         
y[1] (closed_form)                = -2.2192186159567920850439473477642           
y[1] (numeric)                    = -2.2192186159567920850439473477644           
absolute error                    = 2e-31                                        
relative error                    = 9.0121810695866105483423206369371e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.74                                         
y[1] (closed_form)                = -2.2096691978660065715675511675993           
y[1] (numeric)                    = -2.2096691978660065715675511675997           
absolute error                    = 4e-31                                        
relative error                    = 1.8102257133615338333416399995418e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.75                                         
y[1] (closed_form)                = -2.2000853983507263406317826798036           
y[1] (numeric)                    = -2.2000853983507263406317826798039           
absolute error                    = 3e-31                                        
relative error                    = 1.3635834328289812014186947401253e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.76                                         
y[1] (closed_form)                = -2.1904672699601076178738157318529           
y[1] (numeric)                    = -2.1904672699601076178738157318532           
absolute error                    = 3e-31                                        
relative error                    = 1.3695707948444422278433753581505e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.77                                         
y[1] (closed_form)                = -2.180814865462266342757391302154            
y[1] (numeric)                    = -2.1808148654622663427573913021544           
absolute error                    = 4e-31                                        
relative error                    = 1.8341767856356398255446159062029e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.78                                         
y[1] (closed_form)                = -2.1711282378438032558855470021118           
y[1] (numeric)                    = -2.1711282378438032558855470021124           
absolute error                    = 6e-31                                        
relative error                    = 2.7635401241700657064665820156919e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.79                                         
y[1] (closed_form)                = -2.1614074403093270199516110964921           
y[1] (numeric)                    = -2.1614074403093270199516110964926           
absolute error                    = 5e-31                                        
relative error                    = 2.3133074804648731526694619805061e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y[1] (closed_form)                = -2.1516525262809753786203692642011           
y[1] (numeric)                    = -2.1516525262809753786203692642017           
absolute error                    = 6e-31                                        
relative error                    = 2.7885543444929290070940681464971e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.81                                         
y[1] (closed_form)                = -2.1418635493979343576489709368039           
y[1] (numeric)                    = -2.1418635493979343576489709368046           
absolute error                    = 7e-31                                        
relative error                    = 3.2681820473426797536441907152821e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=273.6MB, alloc=44.3MB, time=3.30
 
TOP MAIN SOLVE Loop
x[1]                              = 1.82                                         
y[1] (closed_form)                = -2.1320405635159555125747618812348           
y[1] (numeric)                    = -2.1320405635159555125747618812354           
absolute error                    = 6e-31                                        
relative error                    = 2.8142053686377238154515714504372e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.83                                         
y[1] (closed_form)                = -2.1221836227068712273148105776266           
y[1] (numeric)                    = -2.1221836227068712273148105776272           
absolute error                    = 6e-31                                        
relative error                    = 2.8272765541121867880650009390927e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.84                                         
y[1] (closed_form)                = -2.112292781258108068039437724791            
y[1] (numeric)                    = -2.1122927812581080680394377247916           
absolute error                    = 6e-31                                        
relative error                    = 2.8405153174013712065936856676513e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.85                                         
y[1] (closed_form)                = -2.1023680936721981966995607267213           
y[1] (numeric)                    = -2.102368093672198196699560726722            
absolute error                    = 7e-31                                        
relative error                    = 3.3295786884651236998412986060626e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.86                                         
y[1] (closed_form)                = -2.092409614666288848605128116062            
y[1] (numeric)                    = -2.0924096146662888486051281160627           
absolute error                    = 7e-31                                        
relative error                    = 3.3454252699543276179898259384318e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.87                                         
y[1] (closed_form)                = -2.0824173991716498784693423976073           
y[1] (numeric)                    = -2.0824173991716498784693423976081           
absolute error                    = 8e-31                                        
relative error                    = 3.8416889924096214062298458720452e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.88                                         
y[1] (closed_form)                = -2.0723915023331793793507535897631           
y[1] (numeric)                    = -2.0723915023331793793507535897639           
absolute error                    = 8e-31                                        
relative error                    = 3.8602744659941363479382342630038e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.89                                         
y[1] (closed_form)                = -2.0623319795089073789426496480555           
y[1] (numeric)                    = -2.0623319795089073789426496480564           
absolute error                    = 9e-31                                        
relative error                    = 4.3639918739674124665707965827361e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y[1] (closed_form)                = -2.0522388862694976176764738161271           
y[1] (numeric)                    = -2.052238886269497617676473816128            
absolute error                    = 9e-31                                        
relative error                    = 4.3854543738618792031871436880383e-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)                = -2.0421122783977474131232626104643           
y[1] (numeric)                    = -2.0421122783977474131232626104653           
absolute error                    = 1.0e-30                                      
relative error                    = 4.8968903942177240625511515592697e-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)                = -2.0319522118880856151943214500028           
y[1] (numeric)                    = -2.0319522118880856151943214500036           
absolute error                    = 8e-31                                        
relative error                    = 3.9371004658453149569214518796987e-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)                = -2.0217587429460686566595377357267           
y[1] (numeric)                    = -2.0217587429460686566595377357273           
absolute error                    = 6e-31                                        
relative error                    = 2.9677131462564684240501197634906e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.94                                         
y[1] (closed_form)                = -2.0115319279878747035188733137868           
y[1] (numeric)                    = -2.0115319279878747035188733137874           
absolute error                    = 6e-31                                        
relative error                    = 2.9828012752458619437864765734084e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=314.2MB, alloc=44.3MB, time=3.78
 
TOP MAIN SOLVE Loop
x[1]                              = 1.95                                         
y[1] (closed_form)                = -2.0012718236397959097796795642219           
y[1] (numeric)                    = -2.0012718236397959097796795642226           
absolute error                    = 7e-31                                        
relative error                    = 3.4977757230743449082430682747581e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.96                                         
y[1] (closed_form)                = -1.9909784867377287812095386921676           
y[1] (numeric)                    = -1.9909784867377287812095386921683           
absolute error                    = 7e-31                                        
relative error                    = 3.5158591851334798845471382089996e-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)                = -1.9806519743266626526513540059379           
y[1] (numeric)                    = -1.9806519743266626526513540059386           
absolute error                    = 7e-31                                        
relative error                    = 3.5341897974679281973571875014223e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.98                                         
y[1] (closed_form)                = -1.9702923436601662835043898933892           
y[1] (numeric)                    = -1.97029234366016628350438989339             
absolute error                    = 8e-31                                        
relative error                    = 4.0603111643516748259314393579947e-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)                = -1.9598996521998725759918987017286           
y[1] (numeric)                    = -1.9598996521998725759918987017294           
absolute error                    = 8e-31                                        
relative error                    = 4.0818416346063782033368311751950e-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)                = -1.9494739576149614208528666339729           
y[1] (numeric)                    = -1.9494739576149614208528666339736           
absolute error                    = 7e-31                                        
relative error                    = 3.5907122394002057958164715479346e-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)                = -1.939015317781640675112263945555            
y[1] (numeric)                    = -1.9390153177816406751122639455558           
absolute error                    = 8e-31                                        
relative error                    = 4.1258054676703219817155779839316e-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)                = -1.9285237907826252766009960054276           
y[1] (numeric)                    = -1.9285237907826252766009960054283           
absolute error                    = 7e-31                                        
relative error                    = 3.6297192876004344953181727577809e-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)                = -1.9179994349066144999135210261274           
y[1] (numeric)                    = -1.9179994349066144999135210261281           
absolute error                    = 7e-31                                        
relative error                    = 3.6496361117754047166504086290940e-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)                = -1.9074423086477673585078273157203           
y[1] (numeric)                    = -1.9074423086477673585078273157211           
absolute error                    = 8e-31                                        
relative error                    = 4.1940980147763400703836163913936e-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)                = -1.8968524707051761576691476107969           
y[1] (numeric)                    = -1.8968524707051761576691476107977           
absolute error                    = 8e-31                                        
relative error                    = 4.2175130241024545102043934869873e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.06                                         
y[1] (closed_form)                = -1.8862299799823382030754302635724           
y[1] (numeric)                    = -1.8862299799823382030754302635733           
absolute error                    = 9e-31                                        
relative error                    = 4.7714224116426523417233424060388e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=354.7MB, alloc=44.3MB, time=4.26
 
TOP MAIN SOLVE Loop
x[1]                              = 2.07                                         
y[1] (closed_form)                = -1.8755748955866256697191866278861           
y[1] (numeric)                    = -1.8755748955866256697191866278867           
absolute error                    = 6e-31                                        
relative error                    = 3.1990191456062186475705902341143e-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)                = -1.8648872768287536359568907690869           
y[1] (numeric)                    = -1.8648872768287536359568907690874           
absolute error                    = 5e-31                                        
relative error                    = 2.6811271984773872658450981737286e-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)                = -1.8541671832222462874736214624423           
y[1] (numeric)                    = -1.854167183222246287473621462443            
absolute error                    = 7e-31                                        
relative error                    = 3.7752798471144972636509130562919e-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)                = -1.8434146744829012959671071951678           
y[1] (numeric)                    = -1.8434146744829012959671071951685           
absolute error                    = 7e-31                                        
relative error                    = 3.7973007901564954816327496386639e-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)                = -1.8326298105282523773717624002295           
y[1] (numeric)                    = -1.8326298105282523773717624002301           
absolute error                    = 6e-31                                        
relative error                    = 3.2739836302621915572997059149271e-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)                = -1.8218126514770300344596872778642           
y[1] (numeric)                    = -1.821812651477030034459687277865            
absolute error                    = 8e-31                                        
relative error                    = 4.3912308949627834014066576095556e-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)                = -1.8109632576486204886719441558311           
y[1] (numeric)                    = -1.8109632576486204886719441558319           
absolute error                    = 8e-31                                        
relative error                    = 4.4175385481797734718769529449010e-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)                = -1.8000816895625228060497202546981           
y[1] (numeric)                    = -1.8000816895625228060497202546988           
absolute error                    = 7e-31                                        
relative error                    = 3.8887124071026037667984306838119e-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)                = -1.7891680079378042221512398133014           
y[1] (numeric)                    = -1.7891680079378042221512398133022           
absolute error                    = 8e-31                                        
relative error                    = 4.4713520275945484139194791377603e-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)                = -1.7782222736925536708564976456109           
y[1] (numeric)                    = -1.7782222736925536708564976456119           
absolute error                    = 1.0e-30                                      
relative error                    = 5.6235939387006876020310025670908e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.17                                         
y[1] (closed_form)                = -1.7672445479433335219780511977215           
y[1] (numeric)                    = -1.7672445479433335219780511977225           
absolute error                    = 1.0e-30                                      
relative error                    = 5.6585264397265798010731124000197e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.18                                         
y[1] (closed_form)                = -1.7562348920046295326122289070712           
y[1] (numeric)                    = -1.7562348920046295326122289070722           
absolute error                    = 1.0e-30                                      
relative error                    = 5.6939991600927829904397244235646e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=395.3MB, alloc=44.3MB, time=4.74
 
TOP MAIN SOLVE Loop
x[1]                              = 2.19                                         
y[1] (closed_form)                = -1.745193367388299017181188990184            
y[1] (numeric)                    = -1.7451933673882990171811889901852           
absolute error                    = 1.2e-30                                      
relative error                    = 6.8760288826665273148216809462150e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.2                                          
y[1] (closed_form)                = -1.7341200358030172411322945555567           
y[1] (numeric)                    = -1.7341200358030172411322945555579           
absolute error                    = 1.2e-30                                      
relative error                    = 6.9199361937152014560003094040807e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.21                                         
y[1] (closed_form)                = -1.7230149591537220432772580104725           
y[1] (numeric)                    = -1.7230149591537220432772580104736           
absolute error                    = 1.1e-30                                      
relative error                    = 6.3841581534514200140767792521628e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.22                                         
y[1] (closed_form)                = -1.7118781995410566917694499606439           
y[1] (numeric)                    = -1.7118781995410566917694499606452           
absolute error                    = 1.3e-30                                      
relative error                    = 7.5939982198997654539544380986510e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.23                                         
y[1] (closed_form)                = -1.7007098192608109787336650461838           
y[1] (numeric)                    = -1.700709819260810978733665046185            
absolute error                    = 1.2e-30                                      
relative error                    = 7.0558774131236727492889568876767e-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)                = -1.6895098808033605585784892734012           
y[1] (numeric)                    = -1.6895098808033605585784892734024           
absolute error                    = 1.2e-30                                      
relative error                    = 7.1026515656090805878352766221637e-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)                = -1.6782784468531045350372202466516           
y[1] (numeric)                    = -1.6782784468531045350372202466528           
absolute error                    = 1.2e-30                                      
relative error                    = 7.1501841798069218901565562335416e-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)                = -1.6670155802879013019990531356729           
y[1] (numeric)                    = -1.667015580287901301999053135674            
absolute error                    = 1.1e-30                                      
relative error                    = 6.5986185912553073536255967056008e-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)                = -1.65572134417850264320796108966             
y[1] (numeric)                    = -1.6557213441785026432079610896611           
absolute error                    = 1.1e-30                                      
relative error                    = 6.6436300037297184735926970450073e-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)                = -1.6443958017879860959223689883283           
y[1] (numeric)                    = -1.6443958017879860959223689883296           
absolute error                    = 1.3e-30                                      
relative error                    = 7.9056392541654673006182922361905e-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)                = -1.6330390165711855836443437613588           
y[1] (numeric)                    = -1.63303901657118558364434376136             
absolute error                    = 1.2e-30                                      
relative error                    = 7.3482628879228064772640684872836e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.3                                          
y[1] (closed_form)                = -1.6216510521741203230426028702832           
y[1] (numeric)                    = -1.6216510521741203230426028702844           
absolute error                    = 1.2e-30                                      
relative error                    = 7.3998657010161351245293636730745e-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)                = -1.6102319724334220102091747908561           
y[1] (numeric)                    = -1.6102319724334220102091747908572           
absolute error                    = 1.1e-30                                      
relative error                    = 6.8313138655274186867488790823635e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=435.9MB, alloc=44.3MB, time=5.22
 
TOP MAIN SOLVE Loop
x[1]                              = 2.32                                         
y[1] (closed_form)                = -1.5987818413757602914050313194782           
y[1] (numeric)                    = -1.5987818413757602914050313194793           
absolute error                    = 1.1e-30                                      
relative error                    = 6.8802382634859308895393439437724e-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)                = -1.5873007232172665234654511149086           
y[1] (numeric)                    = -1.5873007232172665234654511149098           
absolute error                    = 1.2e-30                                      
relative error                    = 7.5600041154630433495045045047831e-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)                = -1.5757886823629558290512669373775           
y[1] (numeric)                    = -1.5757886823629558290512669373787           
absolute error                    = 1.2e-30                                      
relative error                    = 7.6152342850981374967335711701145e-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)                = -1.5642457834061474519474954227494           
y[1] (numeric)                    = -1.5642457834061474519474954227505           
absolute error                    = 1.1e-30                                      
relative error                    = 7.0321429769479602606556049751600e-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)                = -1.5526720911278834176261477914676           
y[1] (numeric)                    = -1.5526720911278834176261477914685           
absolute error                    = 9e-31                                        
relative error                    = 5.7964589248604772033345294237358e-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)                = -1.5410676704963455043052725029433           
y[1] (numeric)                    = -1.5410676704963455043052725029442           
absolute error                    = 9e-31                                        
relative error                    = 5.8401069416382534161240553823076e-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)                = -1.5294325866662705297514863885618           
y[1] (numeric)                    = -1.5294325866662705297514863885627           
absolute error                    = 9e-31                                        
relative error                    = 5.8845352704413397191876898868948e-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)                = -1.5177669049783639590884090937133           
y[1] (numeric)                    = -1.5177669049783639590884090937141           
absolute error                    = 8e-31                                        
relative error                    = 5.2709015948098047654730452104954e-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)                = -1.5060706909587118388885265947898           
y[1] (numeric)                    = -1.5060706909587118388885265947906           
absolute error                    = 8e-31                                        
relative error                    = 5.3118356581970798915529194193903e-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)                = -1.4943440103181910628410729949361           
y[1] (numeric)                    = -1.494344010318191062841072994937            
absolute error                    = 9e-31                                        
relative error                    = 6.0227095888607521066968211191999e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.42                                         
y[1] (closed_form)                = -1.4825869289518779743035356069107           
y[1] (numeric)                    = -1.4825869289518779743035356069116           
absolute error                    = 9e-31                                        
relative error                    = 6.0704703543842745765791824082066e-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)                = -1.4707995129384553110593563675796           
y[1] (numeric)                    = -1.4707995129384553110593563675806           
absolute error                    = 1.0e-30                                      
relative error                    = 6.7990231925093408481997567756202e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=476.3MB, alloc=44.3MB, time=5.69
 
TOP MAIN SOLVE Loop
x[1]                              = 2.44                                         
y[1] (closed_form)                = -1.4589818285396174976193227616103           
y[1] (numeric)                    = -1.4589818285396174976193227616113           
absolute error                    = 1.0e-30                                      
relative error                    = 6.8540949615593227446271866955679e-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)                = -1.4471339421994742904190135275694           
y[1] (numeric)                    = -1.4471339421994742904190135275703           
absolute error                    = 9e-31                                        
relative error                    = 6.2191893490667857043556347538609e-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)                = -1.4352559205439527812794883440211           
y[1] (numeric)                    = -1.4352559205439527812794883440221           
absolute error                    = 1.0e-30                                      
relative error                    = 6.9673985362903531433629107101351e-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)                = -1.4233478303801977645131863129418           
y[1] (numeric)                    = -1.4233478303801977645131863129427           
absolute error                    = 9e-31                                        
relative error                    = 6.3231206089631398670309258928898e-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)                = -1.411409738695970473071725239846            
y[1] (numeric)                    = -1.4114097386959704730717252398469           
absolute error                    = 9e-31                                        
relative error                    = 6.3766033018273481569506468416084e-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)                = -1.3994417126590456891469723218978           
y[1] (numeric)                    = -1.3994417126590456891469723218986           
absolute error                    = 8e-31                                        
relative error                    = 5.7165653471907676360635443503877e-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)                = -1.3874438196166072346513867648716           
y[1] (numeric)                    = -1.3874438196166072346513867648723           
absolute error                    = 7e-31                                        
relative error                    = 5.0452493290390036060224039024395e-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)                = -1.3754161270946418470182159254384           
y[1] (numeric)                    = -1.3754161270946418470182159254394           
absolute error                    = 1.0e-30                                      
relative error                    = 7.2705269358179511166939365645519e-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)                = -1.3633587027973314457766586856783           
y[1] (numeric)                    = -1.3633587027973314457766586856793           
absolute error                    = 1.0e-30                                      
relative error                    = 7.3348268357271334705195214827103e-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)                = -1.3512716146064437953715927811452           
y[1] (numeric)                    = -1.3512716146064437953715927811463           
absolute error                    = 1.1e-30                                      
relative error                    = 8.1404803305986239803924217752774e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.54                                         
y[1] (closed_form)                = -1.3391549305807215697118965919177           
y[1] (numeric)                    = -1.3391549305807215697118965919187           
absolute error                    = 1.0e-30                                      
relative error                    = 7.4673958715617185143817098687206e-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)                = -1.3270087189552698239457803379228           
y[1] (numeric)                    = -1.3270087189552698239457803379238           
absolute error                    = 1.0e-30                                      
relative error                    = 7.5357455133172152303774538773897e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=516.8MB, alloc=44.3MB, time=6.18
 
TOP MAIN SOLVE Loop
x[1]                              = 2.56                                         
y[1] (closed_form)                = -1.3148330481409418789758765659908           
y[1] (numeric)                    = -1.3148330481409418789758765659919           
absolute error                    = 1.1e-30                                      
relative error                    = 8.3660811656301392272666670644805e-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)                = -1.3026279867237236242411251475458           
y[1] (numeric)                    = -1.302627986723723624241125147547            
absolute error                    = 1.2e-30                                      
relative error                    = 9.2121466161505851939518220528079e-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)                = -1.2903936034641162443067235940147           
y[1] (numeric)                    = -1.290393603464116244306723594016            
absolute error                    = 1.3e-30                                      
relative error                    = 1.0074445475474265972821952554343e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.59                                         
y[1] (closed_form)                = -1.2781299672965173748175992138048           
y[1] (numeric)                    = -1.2781299672965173748175992138061           
absolute error                    = 1.3e-30                                      
relative error                    = 1.0171109615321373086844199672227e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.6                                          
y[1] (closed_form)                = -1.265837147328600693384995352407            
y[1] (numeric)                    = -1.2658371473286006933849953524084           
absolute error                    = 1.4e-30                                      
relative error                    = 1.1059874510354938704564917607854e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.61                                         
y[1] (closed_form)                = -1.253515212840693950989849548586            
y[1] (numeric)                    = -1.2535152128406939509898495485874           
absolute error                    = 1.4e-30                                      
relative error                    = 1.1168592017541971600563986484297e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.62                                         
y[1] (closed_form)                = -1.2411642332851554495006767779696           
y[1] (numeric)                    = -1.2411642332851554495006767779709           
absolute error                    = 1.3e-30                                      
relative error                    = 1.0474036917411937131392277312904e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.63                                         
y[1] (closed_form)                = -1.2287842782857489709176559143099           
y[1] (numeric)                    = -1.2287842782857489709176559143113           
absolute error                    = 1.4e-30                                      
relative error                    = 1.1393374937650654768783844485768e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.64                                         
y[1] (closed_form)                = -1.2163754176370171639685519924143           
y[1] (numeric)                    = -1.2163754176370171639685519924156           
absolute error                    = 1.3e-30                                      
relative error                    = 1.0687489907724668764033982507545e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.65                                         
y[1] (closed_form)                = -1.2039377213036533936959906798049           
y[1] (numeric)                    = -1.2039377213036533936959906798063           
absolute error                    = 1.4e-30                                      
relative error                    = 1.1628508478694774558709694230665e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.66                                         
y[1] (closed_form)                = -1.191471259419872059689434431623            
y[1] (numeric)                    = -1.1914712594198720596894344316244           
absolute error                    = 1.4e-30                                      
relative error                    = 1.1750178520308250543339059998310e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.67                                         
y[1] (closed_form)                = -1.1789761022887773886289919906428           
y[1] (numeric)                    = -1.1789761022887773886289919906442           
absolute error                    = 1.4e-30                                      
relative error                    = 1.1874710583888367982254202097503e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=557.4MB, alloc=44.3MB, time=6.66
 
TOP MAIN SOLVE Loop
x[1]                              = 2.68                                         
y[1] (closed_form)                = -1.1664523203817307068219240774588           
y[1] (numeric)                    = -1.1664523203817307068219240774603           
absolute error                    = 1.5e-30                                      
relative error                    = 1.2859505474763967965478390193656e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.69                                         
y[1] (closed_form)                = -1.1538999843377161984263881713874           
y[1] (numeric)                    = -1.1538999843377161984263881713889           
absolute error                    = 1.5e-30                                      
relative error                    = 1.2999393538088387938194332965441e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.7                                          
y[1] (closed_form)                = -1.1413191649627051550705940872489           
y[1] (numeric)                    = -1.1413191649627051550705940872505           
absolute error                    = 1.6e-30                                      
relative error                    = 1.4018865617246365454032644325137e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.71                                         
y[1] (closed_form)                = -1.1287099332290187225891194843154           
y[1] (numeric)                    = -1.1287099332290187225891194843169           
absolute error                    = 1.5e-30                                      
relative error                    = 1.3289508277018462094600616558698e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.72                                         
y[1] (closed_form)                = -1.1160723602746891506116603791272           
y[1] (numeric)                    = -1.1160723602746891506116603791288           
absolute error                    = 1.6e-30                                      
relative error                    = 1.4335988032229433245930370053907e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.73                                         
y[1] (closed_form)                = -1.1034065174028195507529660518597           
y[1] (numeric)                    = -1.1034065174028195507529660518613           
absolute error                    = 1.6e-30                                      
relative error                    = 1.4500548753020366169938847673336e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.74                                         
y[1] (closed_form)                = -1.090712476080942169166130315194            
y[1] (numeric)                    = -1.0907124760809421691661303151956           
absolute error                    = 1.6e-30                                      
relative error                    = 1.4669310520303092403900523443728e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.75                                         
y[1] (closed_form)                = -1.0779903079403751792347818344126           
y[1] (numeric)                    = -1.0779903079403751792347818344141           
absolute error                    = 1.5e-30                                      
relative error                    = 1.3914781876526543293722267149748e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.76                                         
y[1] (closed_form)                = -1.0652400847755780001930349273582           
y[1] (numeric)                    = -1.0652400847755780001930349273597           
absolute error                    = 1.5e-30                                      
relative error                    = 1.4081332663293609380314945035685e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.77                                         
y[1] (closed_form)                = -1.0524618785435051474753289131013           
y[1] (numeric)                    = -1.0524618785435051474753289131027           
absolute error                    = 1.4e-30                                      
relative error                    = 1.3302144510330868237086383615457e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.78                                         
y[1] (closed_form)                = -1.0396557613629586206114984992521           
y[1] (numeric)                    = -1.0396557613629586206114984992535           
absolute error                    = 1.4e-30                                      
relative error                    = 1.3465995688463655596243885470280e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.79                                         
y[1] (closed_form)                = -1.0268218055139388344955797809049           
y[1] (numeric)                    = -1.0268218055139388344955797809064           
absolute error                    = 1.5e-30                                      
relative error                    = 1.4608182178690963693534407120887e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.8                                          
y[1] (closed_form)                = -1.0139600834369940998699660507467           
y[1] (numeric)                    = -1.0139600834369940998699660507482           
absolute error                    = 1.5e-30                                      
relative error                    = 1.4793481760302526380827791041339e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=597.9MB, alloc=44.3MB, time=7.14
 
TOP MAIN SOLVE Loop
x[1]                              = 2.81                                         
y[1] (closed_form)                = -1.0010706677325686588795846719229           
y[1] (numeric)                    = -1.0010706677325686588795846719245           
absolute error                    = 1.6e-30                                      
relative error                    = 1.5982887637932794846396672619511e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.82                                         
y[1] (closed_form)                = -0.9881536311603492815637706253097           
y[1] (numeric)                    = -0.98815363116034928156377062531124          
absolute error                    = 1.54e-30                                     
relative error                    = 1.5584621170613314471389747970186e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.83                                         
y[1] (closed_form)                = -0.9752090466386104291664638938584           
y[1] (numeric)                    = -0.97520904663861042916646389385998          
absolute error                    = 1.58e-30                                     
relative error                    = 1.6201654460097629664553274508551e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.84                                         
y[1] (closed_form)                = -0.9622369872435579901582564720901           
y[1] (numeric)                    = -0.96223698724355799015825647209169          
absolute error                    = 1.59e-30                                     
relative error                    = 1.6523995866701649431942703990006e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.85                                         
y[1] (closed_form)                = -0.9492375262086715948766603725351           
y[1] (numeric)                    = -0.94923752620867159487666037253664          
absolute error                    = 1.54e-30                                     
relative error                    = 1.6223547399678556839473263038112e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.86                                         
y[1] (closed_form)                = -0.9362107369240455147037604273318           
y[1] (numeric)                    = -0.9362107369240455147037604273334           
absolute error                    = 1.60e-30                                     
relative error                    = 1.7090169305864385758750939589089e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.87                                         
y[1] (closed_form)                = -0.9231566929357281517131548371806           
y[1] (numeric)                    = -0.92315669293572815171315483718219          
absolute error                    = 1.59e-30                                     
relative error                    = 1.7223511589821715048614981555475e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.88                                         
y[1] (closed_form)                = -0.9100754679450601247307721867428           
y[1] (numeric)                    = -0.91007546794506012473077218674438          
absolute error                    = 1.58e-30                                     
relative error                    = 1.7361197567138269492242810230488e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.89                                         
y[1] (closed_form)                = -0.8969671358080109577667859112155           
y[1] (numeric)                    = -0.89696713580801095776678591121711          
absolute error                    = 1.61e-30                                     
relative error                    = 1.7949375576059102599642884254687e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.9                                          
y[1] (closed_form)                = -0.8838317705345143767884258494995           
y[1] (numeric)                    = -0.88383177053451437678842584950111          
absolute error                    = 1.61e-30                                     
relative error                    = 1.8216136301892851460975115370720e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.91                                         
y[1] (closed_form)                = -0.8706694462878022208160114419108           
y[1] (numeric)                    = -0.87066944628780222081601144191239          
absolute error                    = 1.59e-30                                     
relative error                    = 1.8261809998951324778866496651538e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.92                                         
y[1] (closed_form)                = -0.8574802373837369733370022120385           
y[1] (numeric)                    = -0.85748023738373697333700221204008          
absolute error                    = 1.58e-30                                     
relative error                    = 1.8426080638554975332098967941086e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=638.5MB, alloc=44.3MB, time=7.62
 
TOP MAIN SOLVE Loop
x[1]                              = 2.93                                         
y[1] (closed_form)                = -0.8442642182901429200452783008831           
y[1] (numeric)                    = -0.84426421829014292004527830088466          
absolute error                    = 1.56e-30                                     
relative error                    = 1.8477627811343352598779680797454e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.94                                         
y[1] (closed_form)                = -0.8310214636261359389252268850663           
y[1] (numeric)                    = -0.83102146362613593892522688506786          
absolute error                    = 1.56e-30                                     
relative error                    = 1.8772078319048333792703470408459e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.95                                         
y[1] (closed_form)                = -0.8177520481614519287125191984192           
y[1] (numeric)                    = -0.81775204816145192871251919842078          
absolute error                    = 1.58e-30                                     
relative error                    = 1.9321260075744310817812695030774e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.96                                         
y[1] (closed_form)                = -0.8044560468157738817757174768489           
y[1] (numeric)                    = -0.80445604681577388177571747685047          
absolute error                    = 1.57e-30                                     
relative error                    = 1.9516293105315436731274383141897e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.97                                         
y[1] (closed_form)                = -0.7911335346580576074750513497645           
y[1] (numeric)                    = -0.79113353465805760747505134976604          
absolute error                    = 1.54e-30                                     
relative error                    = 1.9465740390661308323192564923688e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.98                                         
y[1] (closed_form)                = -0.777784586905856112066848897709            
y[1] (numeric)                    = -0.77778458690585611206684889771058          
absolute error                    = 1.58e-30                                     
relative error                    = 2.0314107872534184191816340008683e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.99                                         
y[1] (closed_form)                = -0.7644092789246426412341986758835           
y[1] (numeric)                    = -0.76440927892464264123419867588508          
absolute error                    = 1.58e-30                                     
relative error                    = 2.0669555479791085984214291029092e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3                                            
y[1] (closed_form)                = -0.7510076862271323913364553581433           
y[1] (numeric)                    = -0.7510076862271323913364553581448           
absolute error                    = 1.50e-30                                     
relative error                    = 1.9973164423064835853135423297702e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.01                                         
y[1] (closed_form)                = -0.7375798844726028954821831774678           
y[1] (numeric)                    = -0.73757988447260289548218317746934          
absolute error                    = 1.54e-30                                     
relative error                    = 2.0879094351944771251686148437678e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.02                                         
y[1] (closed_form)                = -0.7241259494662130905420579190215           
y[1] (numeric)                    = -0.72412594946621309054205791902305          
absolute error                    = 1.55e-30                                     
relative error                    = 2.1405116073282238753280209205179e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.03                                         
y[1] (closed_form)                = -0.7106459571583210712301197533899           
y[1] (numeric)                    = -0.71064595715832107123011975339142          
absolute error                    = 1.52e-30                                     
relative error                    = 2.1388991025546173660007344678580e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.04                                         
y[1] (closed_form)                = -0.6971399836438005373935855735579           
y[1] (numeric)                    = -0.69713998364380053739358557355946          
absolute error                    = 1.56e-30                                     
relative error                    = 2.2377141414930987155466552279198e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=679.0MB, alloc=44.3MB, time=8.10
 
TOP MAIN SOLVE Loop
x[1]                              = 3.05                                         
y[1] (closed_form)                = -0.6836081051613559406631906133399           
y[1] (numeric)                    = -0.68360810516135594066319061334142          
absolute error                    = 1.52e-30                                     
relative error                    = 2.2234961647232454693908055730176e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.06                                         
y[1] (closed_form)                = -0.6700503980928363366277348714274           
y[1] (numeric)                    = -0.67005039809283633662773487142894          
absolute error                    = 1.54e-30                                     
relative error                    = 2.2983345795828197348323727813950e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.07                                         
y[1] (closed_form)                = -0.6564669389625479487081601386415           
y[1] (numeric)                    = -0.65646693896254794870816013864302          
absolute error                    = 1.52e-30                                     
relative error                    = 2.3154250576611557555100834619306e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.08                                         
y[1] (closed_form)                = -0.6428578044365654499180781215028           
y[1] (numeric)                    = -0.64285780443656544991807812150434          
absolute error                    = 1.54e-30                                     
relative error                    = 2.3955530902354640892851511888845e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.09                                         
y[1] (closed_form)                = -0.6292230713220419687092091685204           
y[1] (numeric)                    = -0.62922307132204196870920916852195          
absolute error                    = 1.55e-30                                     
relative error                    = 2.4633553196696060167560143238074e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.1                                          
y[1] (closed_form)                = -0.6155628165665178251116743327912           
y[1] (numeric)                    = -0.61556281656651782511167433279268          
absolute error                    = 1.48e-30                                     
relative error                    = 2.4043037691183722471814453583609e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.11                                         
y[1] (closed_form)                = -0.6018771172572280033905108422517           
y[1] (numeric)                    = -0.60187711725722800339051084225319          
absolute error                    = 1.49e-30                                     
relative error                    = 2.4755883838714030106580999820701e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.12                                         
y[1] (closed_form)                = -0.5881660506204083674511523943855           
y[1] (numeric)                    = -0.58816605062040836745115239438704          
absolute error                    = 1.54e-30                                     
relative error                    = 2.6183082113895891765392411877135e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.13                                         
y[1] (closed_form)                = -0.5744296940206006252379309430181           
y[1] (numeric)                    = -0.57442969402060062523793094301964          
absolute error                    = 1.54e-30                                     
relative error                    = 2.6809199037415558356739655426996e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.14                                         
y[1] (closed_form)                = -0.5606681249599560483809156991947           
y[1] (numeric)                    = -0.5606681249599560483809156991962           
absolute error                    = 1.50e-30                                     
relative error                    = 2.6753794860500278425888361978619e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.15                                         
y[1] (closed_form)                = -0.5468814210775379533576078246989           
y[1] (numeric)                    = -0.54688142107753795335760782470042          
absolute error                    = 1.52e-30                                     
relative error                    = 2.7793959374320952246082346334101e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.16                                         
y[1] (closed_form)                = -0.5330696601486229504471556547098           
y[1] (numeric)                    = -0.5330696601486229504471556547113           
absolute error                    = 1.50e-30                                     
relative error                    = 2.8138911518276826986893693506759e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=719.8MB, alloc=44.3MB, time=8.58
 
TOP MAIN SOLVE Loop
x[1]                              = 3.17                                         
y[1] (closed_form)                = -0.5192329200840009667658451450909           
y[1] (numeric)                    = -0.51923292008400096676584514509243          
absolute error                    = 1.53e-30                                     
relative error                    = 2.9466544604923705080058310418166e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.18                                         
y[1] (closed_form)                = -0.5053712789292740496836535000557           
y[1] (numeric)                    = -0.50537127892927404968365350005723          
absolute error                    = 1.53e-30                                     
relative error                    = 3.0274771515342113428715106211537e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.19                                         
y[1] (closed_form)                = -0.49148481486415395693263049815             
y[1] (numeric)                    = -0.4914848148641539569326304981515           
absolute error                    = 1.50e-30                                     
relative error                    = 3.0519762862146593522278140854736e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.2                                          
y[1] (closed_form)                = -0.4775736062017585397287917998547           
y[1] (numeric)                    = -0.4775736062017585397287917998562           
absolute error                    = 1.50e-30                                     
relative error                    = 3.1408770931245752811213215926024e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.21                                         
y[1] (closed_form)                = -0.4636377313879069252400713903567           
y[1] (numeric)                    = -0.46363773138790692524007139035814          
absolute error                    = 1.44e-30                                     
relative error                    = 3.1058731904526775464396602351599e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.22                                         
y[1] (closed_form)                = -0.4496772690004135047436861883984           
y[1] (numeric)                    = -0.44967726900041350474368618839988          
absolute error                    = 1.48e-30                                     
relative error                    = 3.2912493070639046529142552565430e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.23                                         
y[1] (closed_form)                = -0.4356922977483807338270146393469           
y[1] (numeric)                    = -0.43569229774838073382701463934835          
absolute error                    = 1.45e-30                                     
relative error                    = 3.3280367991205531413626335733535e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.24                                         
y[1] (closed_form)                = -0.4216828964714907509967827109768           
y[1] (numeric)                    = -0.42168289647149075099678271097826          
absolute error                    = 1.46e-30                                     
relative error                    = 3.4623173294834073662136229836649e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.25                                         
y[1] (closed_form)                = -0.4076491441392958210719850277215           
y[1] (numeric)                    = -0.40764914413929582107198502772298          
absolute error                    = 1.48e-30                                     
relative error                    = 3.6305730584197580085329259107307e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.26                                         
y[1] (closed_form)                = -0.3935911198505076097465458175956           
y[1] (numeric)                    = -0.3935911198505076097465458175971           
absolute error                    = 1.50e-30                                     
relative error                    = 3.8110615924712038901224595100731e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.27                                         
y[1] (closed_form)                = -0.3795089028322852957182438104454           
y[1] (numeric)                    = -0.37950890283228529571824381044695          
absolute error                    = 1.55e-30                                     
relative error                    = 4.0842256622501019407290049288670e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.28                                         
y[1] (closed_form)                = -0.3654025724395225267908871219617           
y[1] (numeric)                    = -0.36540257243952252679088712196327          
absolute error                    = 1.57e-30                                     
relative error                    = 4.2966309446544725211117286781825e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=760.4MB, alloc=44.3MB, time=9.07
 
TOP MAIN SOLVE Loop
x[1]                              = 3.29                                         
y[1] (closed_form)                = -0.3512722081541332263671283908357           
y[1] (numeric)                    = -0.3512722081541332263671283908372           
absolute error                    = 1.50e-30                                     
relative error                    = 4.2701926459887240218690260067638e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.3                                          
y[1] (closed_form)                = -0.3371178895843362567596569129171           
y[1] (numeric)                    = -0.33711788958433625675965691291869          
absolute error                    = 1.59e-30                                     
relative error                    = 4.7164509779070391912052386314159e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.31                                         
y[1] (closed_form)                = -0.3229396964639389457587931431252           
y[1] (numeric)                    = -0.32293969646393894575879314312678          
absolute error                    = 1.58e-30                                     
relative error                    = 4.8925542982184312108130831665997e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.32                                         
y[1] (closed_form)                = -0.3087377086516194829047416205657           
y[1] (numeric)                    = -0.30873770865161948290474162056722          
absolute error                    = 1.52e-30                                     
relative error                    = 4.9232729187453171301260630034497e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.33                                         
y[1] (closed_form)                = -0.2945120061302081919229310227556           
y[1] (numeric)                    = -0.29451200613020819192293102275715          
absolute error                    = 1.55e-30                                     
relative error                    = 5.2629433358812600123407602856870e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.34                                         
y[1] (closed_form)                = -0.2802626690059676857909845794854           
y[1] (numeric)                    = -0.28026266900596768579098457948699          
absolute error                    = 1.59e-30                                     
relative error                    = 5.6732493329896313467520893190589e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.35                                         
y[1] (closed_form)                = -0.2659897775078719109159203846322           
y[1] (numeric)                    = -0.26598977750787191091592038463376          
absolute error                    = 1.56e-30                                     
relative error                    = 5.8648870442166978828951068858475e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.36                                         
y[1] (closed_form)                = -0.2516934119868840869101791446714           
y[1] (numeric)                    = -0.25169341198688408691017914467293          
absolute error                    = 1.53e-30                                     
relative error                    = 6.0788241850355993016584320055047e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.37                                         
y[1] (closed_form)                = -0.2373736529152335484650165057321           
y[1] (numeric)                    = -0.23737365291523354846501650573368          
absolute error                    = 1.58e-30                                     
relative error                    = 6.6561725810581856382382702216632e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.38                                         
y[1] (closed_form)                = -0.2230305808856914958296782173495           
y[1] (numeric)                    = -0.22303058088569149582967821735106          
absolute error                    = 1.56e-30                                     
relative error                    = 6.9945565034399354016972910192087e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.39                                         
y[1] (closed_form)                = -0.208664276610845660414598931654            
y[1] (numeric)                    = -0.20866427661084566041459893165556          
absolute error                    = 1.56e-30                                     
relative error                    = 7.4761239697457465903710627546164e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.4                                          
y[1] (closed_form)                = -0.1942748209223738920466293132038           
y[1] (numeric)                    = -0.1942748209223738920466293132053           
absolute error                    = 1.50e-30                                     
relative error                    = 7.7210211435446532764997623902514e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=801.0MB, alloc=44.3MB, time=9.55
 
TOP MAIN SOLVE Loop
x[1]                              = 3.41                                         
y[1] (closed_form)                = -0.1798622947703166744140012591308           
y[1] (numeric)                    = -0.17986229477031667441400125913236          
absolute error                    = 1.56e-30                                     
relative error                    = 8.6733019946849496496801378580198e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.42                                         
y[1] (closed_form)                = -0.1654267792223485752483873143951           
y[1] (numeric)                    = -0.16542677922234857524838731439662          
absolute error                    = 1.52e-30                                     
relative error                    = 9.1883551571597868198192355066898e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.43                                         
y[1] (closed_form)                = -0.1509683554630486378009977259016           
y[1] (numeric)                    = -0.15096835546304863780099772590317          
absolute error                    = 1.57e-30                                     
relative error                    = 1.0399530386248903757859462549943e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.44                                         
y[1] (closed_form)                = -0.1364871047931697201791869257517           
y[1] (numeric)                    = -0.13648710479316972017918692575323          
absolute error                    = 1.53e-30                                     
relative error                    = 1.1209850207596801582000336233033e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.45                                         
y[1] (closed_form)                = -0.1219831086289067891195104822109           
y[1] (numeric)                    = -0.12198310862890678911951048221246          
absolute error                    = 1.56e-30                                     
relative error                    = 1.2788655884691243400721495182973e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.46                                         
y[1] (closed_form)                = -0.1074564485011641747825836218671           
y[1] (numeric)                    = -0.10745644850116417478258362186864          
absolute error                    = 1.54e-30                                     
relative error                    = 1.4331387473533668480620567872309e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.47                                         
y[1] (closed_form)                = -0.0929072060548217931644432232215           
y[1] (numeric)                    = -0.092907206054821793164443223223081         
absolute error                    = 1.581e-30                                    
relative error                    = 1.7016979275720536487372485415688e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.48                                         
y[1] (closed_form)                = -0.0783354630480003427284066264593           
y[1] (numeric)                    = -0.078335463048000342728406626460842         
absolute error                    = 1.542e-30                                    
relative error                    = 1.9684571201872309554721161201151e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.49                                         
y[1] (closed_form)                = -0.0637413013513254818706526127476           
y[1] (numeric)                    = -0.063741301351325481870652612749171         
absolute error                    = 1.571e-30                                    
relative error                    = 2.4646500254851347033835849661572e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.5                                          
y[1] (closed_form)                = -0.0491248029471909938419223960331           
y[1] (numeric)                    = -0.04912480294719099384192239603462          
absolute error                    = 1.520e-30                                    
relative error                    = 3.0941599941560989910833188424826e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.51                                         
y[1] (closed_form)                = -0.0344860499290209457568513583932           
y[1] (numeric)                    = -0.034486049929020945756851358394761         
absolute error                    = 1.561e-30                                    
relative error                    = 4.5264679579506616361472037783460e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.52                                         
y[1] (closed_form)                = -0.019825124500530848331495464532            
y[1] (numeric)                    = -0.019825124500530848331495464533605         
absolute error                    = 1.605e-30                                    
relative error                    = 8.0957877462864036280197098131307e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=841.6MB, alloc=44.3MB, time=10.03
 
TOP MAIN SOLVE Loop
x[1]                              = 3.53                                         
y[1] (closed_form)                = -0.0051421089749878229986097305112           
y[1] (numeric)                    = -0.0051421089749878229986097305127593        
absolute error                    = 1.5593e-30                                   
relative error                    = 3.0324133688817681468543254812895e-26      % 
Desired digits                    = 8                                   
Estimated correct digits          = 9                                   
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.54                                         
y[1] (closed_form)                = 0.0095629142255302169408302846599            
y[1] (numeric)                    = 0.0095629142255302169408302846583838         
absolute error                    = 1.5162e-30                                   
relative error                    = 1.5854999472359421971381303470548e-26      % 
Desired digits                    = 8                                   
Estimated correct digits          = 9                                   
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.55                                         
y[1] (closed_form)                = 0.0242898625708763644624993287941            
y[1] (numeric)                    = 0.024289862570876364462499328792582          
absolute error                    = 1.518e-30                                    
relative error                    = 6.2495207437694095653546596364094e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.56                                         
y[1] (closed_form)                = 0.0390386534235774895838073509547            
y[1] (numeric)                    = 0.039038653423577489583807350953115          
absolute error                    = 1.585e-30                                    
relative error                    = 4.0600785657292559150382727996106e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.57                                         
y[1] (closed_form)                = 0.0538092040395779760642665684793            
y[1] (numeric)                    = 0.053809204039577976064266568477718          
absolute error                    = 1.582e-30                                    
relative error                    = 2.9400174714281233167339218674818e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.58                                         
y[1] (closed_form)                = 0.0686014315689844173475154235172            
y[1] (numeric)                    = 0.068601431568984417347515423515692          
absolute error                    = 1.508e-30                                    
relative error                    = 2.1982048559490791209200015551243e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.59                                         
y[1] (closed_form)                = 0.0834152530568112650427409775602            
y[1] (numeric)                    = 0.083415253056811265042740977558664          
absolute error                    = 1.536e-30                                    
relative error                    = 1.8413898462357755289489717407777e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.6                                          
y[1] (closed_form)                = 0.0982505854437274232346684442908            
y[1] (numeric)                    = 0.098250585443727423234668444289229          
absolute error                    = 1.571e-30                                    
relative error                    = 1.5989726604731359263211817821546e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.61                                         
y[1] (closed_form)                = 0.1131073455668037819027741103533            
y[1] (numeric)                    = 0.11310734556680378190277411035171           
absolute error                    = 1.59e-30                                     
relative error                    = 1.4057442441356823116645402590774e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.62                                         
y[1] (closed_form)                = 0.1279854501602616827219259169794            
y[1] (numeric)                    = 0.12798545016026168272192591697784           
absolute error                    = 1.56e-30                                     
relative error                    = 1.2188885518209989466355379492192e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.63                                         
y[1] (closed_form)                = 0.1428848158562223105082645488464            
y[1] (numeric)                    = 0.1428848158562223105082645488448            
absolute error                    = 1.60e-30                                     
relative error                    = 1.1197830857059005121630303260948e-27      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.64                                         
y[1] (closed_form)                = 0.157805359185457003565807075628             
y[1] (numeric)                    = 0.15780535918545700356580707562643           
absolute error                    = 1.57e-30                                     
relative error                    = 9.9489650294759302632579955911773e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=882.3MB, alloc=44.3MB, time=10.51
 
TOP MAIN SOLVE Loop
x[1]                              = 3.65                                         
y[1] (closed_form)                = 0.1727469965781384761809850913999            
y[1] (numeric)                    = 0.17274699657813847618098509139838           
absolute error                    = 1.52e-30                                     
relative error                    = 8.7989952364379308921935059773770e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.66                                         
y[1] (closed_form)                = 0.1877096443645929465041199718056            
y[1] (numeric)                    = 0.18770964436459294650411997180403           
absolute error                    = 1.57e-30                                     
relative error                    = 8.3639815381598152010572851538265e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.67                                         
y[1] (closed_form)                = 0.2026932187760531630486893925673            
y[1] (numeric)                    = 0.20269321877605316304868939256572           
absolute error                    = 1.58e-30                                     
relative error                    = 7.7950313756952699069976239748196e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.68                                         
y[1] (closed_form)                = 0.2176976359454123230311516988714            
y[1] (numeric)                    = 0.21769763594541232303115169886982           
absolute error                    = 1.58e-30                                     
relative error                    = 7.2577728882466365502327849662494e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.69                                         
y[1] (closed_form)                = 0.2327228119079788757660681561553            
y[1] (numeric)                    = 0.23272281190797887576606815615373           
absolute error                    = 1.57e-30                                     
relative error                    = 6.7462230587897632923183675564362e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.7                                          
y[1] (closed_form)                = 0.2477686626022322043232976211174            
y[1] (numeric)                    = 0.24776866260223220432329762111582           
absolute error                    = 1.58e-30                                     
relative error                    = 6.3769162064555835402674655313210e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.71                                         
y[1] (closed_form)                = 0.2628351038705791786461338190476            
y[1] (numeric)                    = 0.26283510387057917864613381904601           
absolute error                    = 1.59e-30                                     
relative error                    = 6.0494202508920609690901933486061e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.72                                         
y[1] (closed_form)                = 0.277922051460111573321412270975             
y[1] (numeric)                    = 0.27792205146011157332141227097344           
absolute error                    = 1.56e-30                                     
relative error                    = 5.6130846465916257651339212991811e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.73                                         
y[1] (closed_form)                = 0.2930294210233643431848320522389            
y[1] (numeric)                    = 0.29302942102336434318483205223736           
absolute error                    = 1.54e-30                                     
relative error                    = 5.2554449809912090017579437241321e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.74                                         
y[1] (closed_form)                = 0.3081571281190747499370170529458            
y[1] (numeric)                    = 0.30815712811907474993701705294421           
absolute error                    = 1.59e-30                                     
relative error                    = 5.1597054064756515026166679119300e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.75                                         
y[1] (closed_form)                = 0.3233050882129423329381823198641            
y[1] (numeric)                    = 0.32330508821294233293818231986257           
absolute error                    = 1.53e-30                                     
relative error                    = 4.7323721641902450697763668591879e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.76                                         
y[1] (closed_form)                = 0.3384732166783897173416734575619            
y[1] (numeric)                    = 0.33847321667838971734167345756034           
absolute error                    = 1.56e-30                                     
relative error                    = 4.6089318833232228408446124884197e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=923.0MB, alloc=44.3MB, time=11.00
 
TOP MAIN SOLVE Loop
x[1]                              = 3.77                                         
y[1] (closed_form)                = 0.3536614287973242527191110223845            
y[1] (numeric)                    = 0.35366142879732425271911102238296           
absolute error                    = 1.54e-30                                     
relative error                    = 4.3544471480449196220522534886027e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.78                                         
y[1] (closed_form)                = 0.3688696397609004753223974240336            
y[1] (numeric)                    = 0.36886963976090047532239742403206           
absolute error                    = 1.54e-30                                     
relative error                    = 4.1749166480554501208575146620095e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.79                                         
y[1] (closed_form)                = 0.3840977646702833871204311233029            
y[1] (numeric)                    = 0.38409776467028338712043112330134           
absolute error                    = 1.56e-30                                     
relative error                    = 4.0614659690590305898910384293748e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.8                                          
y[1] (closed_form)                = 0.3993457185374125447410219476754            
y[1] (numeric)                    = 0.39934571853741254474102194767388           
absolute error                    = 1.52e-30                                     
relative error                    = 3.8062258575525441743527314429165e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.81                                         
y[1] (closed_form)                = 0.4146134162857669514412122051432            
y[1] (numeric)                    = 0.4146134162857669514412122051417            
absolute error                    = 1.50e-30                                     
relative error                    = 3.6178279358093524401171519122193e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.82                                         
y[1] (closed_form)                = 0.4299007727511307452219810263784            
y[1] (numeric)                    = 0.4299007727511307452219810263769            
absolute error                    = 1.50e-30                                     
relative error                    = 3.4891772592098803792752744583080e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.83                                         
y[1] (closed_form)                = 0.44520770268235967619614407131              
y[1] (numeric)                    = 0.44520770268235967619614407130847           
absolute error                    = 1.53e-30                                     
relative error                    = 3.4365982232153835227012915744113e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.84                                         
y[1] (closed_form)                = 0.4605341207421483663111574627297            
y[1] (numeric)                    = 0.46053412074214836631115746272822           
absolute error                    = 1.48e-30                                     
relative error                    = 3.2136598209378875424282134338618e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.85                                         
y[1] (closed_form)                = 0.4758799415077983445214936206933            
y[1] (numeric)                    = 0.47587994150779834452149362069177           
absolute error                    = 1.53e-30                                     
relative error                    = 3.2150966379299001589616838348751e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.86                                         
y[1] (closed_form)                = 0.4912450794719868504982776305697            
y[1] (numeric)                    = 0.49124507947198685049827763056819           
absolute error                    = 1.51e-30                                     
relative error                    = 3.0738221370543161625031733382757e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.87                                         
y[1] (closed_form)                = 0.5066294490435363999569559474358            
y[1] (numeric)                    = 0.5066294490435363999569559474343            
absolute error                    = 1.50e-30                                     
relative error                    = 2.9607437996978732157480168987832e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.88                                         
y[1] (closed_form)                = 0.5220329645481851046769146823613            
y[1] (numeric)                    = 0.52203296454818510467691468235974           
absolute error                    = 1.56e-30                                     
relative error                    = 2.9883170334849757001001021803037e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=963.6MB, alloc=44.3MB, time=11.48
 
TOP MAIN SOLVE Loop
x[1]                              = 3.89                                         
y[1] (closed_form)                = 0.53745554022935774028017249367837           
y[1] (numeric)                    = 0.53745554022935774028017249367686           
absolute error                    = 1.51e-30                                     
relative error                    = 2.8095347186403762173406066106297e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.9                                          
y[1] (closed_form)                = 0.5528970902489375548295432797068            
y[1] (numeric)                    = 0.55289709024893755482954327970529           
absolute error                    = 1.51e-30                                     
relative error                    = 2.7310688130410207216144784188012e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.91                                         
y[1] (closed_form)                = 0.5683575286880388112999964991749            
y[1] (numeric)                    = 0.56835752868803881129999649917341           
absolute error                    = 1.49e-30                                     
relative error                    = 2.6215892722304979013451288395302e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.92                                         
y[1] (closed_form)                = 0.5838367695477800569703380917555            
y[1] (numeric)                    = 0.58383676954778005697033809175399           
absolute error                    = 1.51e-30                                     
relative error                    = 2.5863393310592517578962844692114e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.93                                         
y[1] (closed_form)                = 0.59933472675005811277579269315417           
y[1] (numeric)                    = 0.59933472675005811277579269315265           
absolute error                    = 1.52e-30                                     
relative error                    = 2.5361453828019028893222589476205e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.94                                         
y[1] (closed_form)                = 0.61485131413832277565558819593707           
y[1] (numeric)                    = 0.61485131413832277565558819593557           
absolute error                    = 1.50e-30                                     
relative error                    = 2.4396142051060913754848444481513e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.95                                         
y[1] (closed_form)                = 0.63038644547835222692322675707617           
y[1] (numeric)                    = 0.63038644547835222692322675707468           
absolute error                    = 1.49e-30                                     
relative error                    = 2.3636295016929695628904762399571e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.96                                         
y[1] (closed_form)                = 0.64594003445902913968077215377803           
y[1] (numeric)                    = 0.64594003445902913968077215377653           
absolute error                    = 1.50e-30                                     
relative error                    = 2.3221969842080478884974888217504e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.97                                         
y[1] (closed_form)                = 0.6615119946931174782921919977331            
y[1] (numeric)                    = 0.6615119946931174782921919977316            
absolute error                    = 1.50e-30                                     
relative error                    = 2.2675325799585329003630332620354e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.98                                         
y[1] (closed_form)                = 0.67710223971803998292456479110097           
y[1] (numeric)                    = 0.67710223971803998292456479109945           
absolute error                    = 1.52e-30                                     
relative error                    = 2.2448603930670217170765018266465e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.99                                         
y[1] (closed_form)                = 0.6927106829966563321597962013865            
y[1] (numeric)                    = 0.69271068299665633215979620138499           
absolute error                    = 1.51e-30                                     
relative error                    = 2.1798422300458280478999374198969e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4                                            
y[1] (closed_form)                = 0.7083372379180419766733863023571            
y[1] (numeric)                    = 0.70833723791804197667338630235557           
absolute error                    = 1.53e-30                                     
relative error                    = 2.1599880933790866922379295169635e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.01                                         
y[1] (closed_form)                = 0.72398181779826763697074992922103           
y[1] (numeric)                    = 0.72398181779826763697074992921952           
memory used=1004.4MB, alloc=44.3MB, time=11.96
absolute error                    = 1.51e-30                                     
relative error                    = 2.0856877381149242009708251244929e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.02                                         
y[1] (closed_form)                = 0.73964433588117945816561578279243           
y[1] (numeric)                    = 0.73964433588117945816561578279091           
absolute error                    = 1.52e-30                                     
relative error                    = 2.0550417629969942415290678977084e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.03                                         
y[1] (closed_form)                = 0.75532470533917981477911654309347           
y[1] (numeric)                    = 0.75532470533917981477911654309196           
absolute error                    = 1.51e-30                                     
relative error                    = 1.9991402231732007089409740330404e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.04                                         
y[1] (closed_form)                = 0.77102283927400875853233207101433           
y[1] (numeric)                    = 0.77102283927400875853233207101283           
absolute error                    = 1.50e-30                                     
relative error                    = 1.9454676613891133013998430729799e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.05                                         
y[1] (closed_form)                = 0.78673865071752610209926083991243           
y[1] (numeric)                    = 0.7867386507175261020992608399109            
absolute error                    = 1.53e-30                                     
relative error                    = 1.9447373007600430269678608412400e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.06                                         
y[1] (closed_form)                = 0.80247205263249413178147109947207           
y[1] (numeric)                    = 0.80247205263249413178147109947057           
absolute error                    = 1.50e-30                                     
relative error                    = 1.8692239749400354255143480081898e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.07                                         
y[1] (closed_form)                = 0.8182229579133609420600229832733            
y[1] (numeric)                    = 0.8182229579133609420600229832718            
absolute error                    = 1.50e-30                                     
relative error                    = 1.8332411544957288849408033995331e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.08                                         
y[1] (closed_form)                = 0.83399127938704438497465588027703           
y[1] (numeric)                    = 0.83399127938704438497465588027553           
absolute error                    = 1.50e-30                                     
relative error                    = 1.7985799576974589999822340960815e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.09                                         
y[1] (closed_form)                = 0.8497769298137166272747019491973            
y[1] (numeric)                    = 0.84977692981371662727470194919579           
absolute error                    = 1.51e-30                                     
relative error                    = 1.7769369195878426618394136275614e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.1                                          
y[1] (closed_form)                = 0.86557982188758930828071671329807           
y[1] (numeric)                    = 0.86557982188758930828071671329655           
absolute error                    = 1.52e-30                                     
relative error                    = 1.7560483291827459066807175947193e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.11                                         
y[1] (closed_form)                = 0.88139986823769929139041128075303           
y[1] (numeric)                    = 0.88139986823769929139041128075151           
absolute error                    = 1.52e-30                                     
relative error                    = 1.7245294159609297557146527453125e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.12                                         
y[1] (closed_form)                = 0.8972369814286950021571279409998            
y[1] (numeric)                    = 0.89723698142869500215712794099831           
absolute error                    = 1.49e-30                                     
relative error                    = 1.6606537969795139517567706682163e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.13                                         
y[1] (closed_form)                = 0.91309107396162334586382173858843           
y[1] (numeric)                    = 0.91309107396162334586382173858692           
absolute error                    = 1.51e-30                                     
relative error                    = 1.6537233174874562050446124746066e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1045.0MB, alloc=44.3MB, time=12.44
 
TOP MAIN SOLVE Loop
x[1]                              = 4.14                                         
y[1] (closed_form)                = 0.92896205827471719751029517038183           
y[1] (numeric)                    = 0.92896205827471719751029517038033           
absolute error                    = 1.50e-30                                     
relative error                    = 1.6147053441405597999706557434411e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.15                                         
y[1] (closed_form)                = 0.9448498467441834571262814365523            
y[1] (numeric)                    = 0.94484984674418345712628143655079           
absolute error                    = 1.51e-30                                     
relative error                    = 1.5981375296860581678022245292560e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.16                                         
y[1] (closed_form)                = 0.9607543516849916633178837469959            
y[1] (numeric)                    = 0.96075435168499166331788374699439           
absolute error                    = 1.51e-30                                     
relative error                    = 1.5716816659239997149411784934006e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.17                                         
y[1] (closed_form)                = 0.97667548535166315794985408835147           
y[1] (numeric)                    = 0.97667548535166315794985408834994           
absolute error                    = 1.53e-30                                     
relative error                    = 1.5665387561653664665864432669707e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.18                                         
y[1] (closed_form)                = 0.99261315993906079486123463797473           
y[1] (numeric)                    = 0.99261315993906079486123463797322           
absolute error                    = 1.51e-30                                     
relative error                    = 1.5212371354140650138667368560632e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.19                                         
y[1] (closed_form)                = 1.0085672875831791855069887146277            
y[1] (numeric)                    = 1.0085672875831791855069887146262            
absolute error                    = 1.5e-30                                      
relative error                    = 1.4872582310243639264423679362976e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.2                                          
y[1] (closed_form)                = 1.0245377803619354744134158253605            
y[1] (numeric)                    = 1.024537780361935474413415825359             
absolute error                    = 1.5e-30                                      
relative error                    = 1.4640748528278765606525418154276e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.21                                         
y[1] (closed_form)                = 1.0405245502959606373303770475836            
y[1] (numeric)                    = 1.0405245502959606373303770475823            
absolute error                    = 1.3e-30                                      
relative error                    = 1.2493698487270057235164692894589e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.22                                         
y[1] (closed_form)                = 1.0565275093493912949586527175629            
y[1] (numeric)                    = 1.0565275093493912949586527175618            
absolute error                    = 1.1e-30                                      
relative error                    = 1.0411465771273471395960664802386e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.23                                         
y[1] (closed_form)                = 1.0725465694306620351261142238585            
y[1] (numeric)                    = 1.0725465694306620351261142238573            
absolute error                    = 1.2e-30                                      
relative error                    = 1.1188325376277077087735634056593e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.24                                         
y[1] (closed_form)                = 1.0885816423932982362818156683359            
y[1] (numeric)                    = 1.0885816423932982362818156683347            
absolute error                    = 1.2e-30                                      
relative error                    = 1.1023518616038235164995002308575e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.25                                         
y[1] (closed_form)                = 1.1046326400367093851725992994799            
y[1] (numeric)                    = 1.1046326400367093851725992994787            
absolute error                    = 1.2e-30                                      
relative error                    = 1.0863340050861808198798099446205e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1085.7MB, alloc=44.3MB, time=12.92
 
TOP MAIN SOLVE Loop
x[1]                              = 4.26                                         
y[1] (closed_form)                = 1.1206994741069828815623609834563            
y[1] (numeric)                    = 1.120699474106982881562360983455             
absolute error                    = 1.3e-30                                      
relative error                    = 1.1599898367364638779895424767495e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.27                                         
y[1] (closed_form)                = 1.1367820562976783228497385977115            
y[1] (numeric)                    = 1.1367820562976783228497385977101            
absolute error                    = 1.4e-30                                      
relative error                    = 1.2315465328152534575195166442265e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.28                                         
y[1] (closed_form)                = 1.1528802982506222614356671493345            
y[1] (numeric)                    = 1.1528802982506222614356671493333            
absolute error                    = 1.2e-30                                      
relative error                    = 1.0408712871760208397146985728604e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.29                                         
y[1] (closed_form)                = 1.1689941115567034276879896747962            
y[1] (numeric)                    = 1.1689941115567034276879896747951            
absolute error                    = 1.1e-30                                      
relative error                    = 9.4097993234129581195126141249205e-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)                = 1.1851234077566684113461226073198            
y[1] (numeric)                    = 1.1851234077566684113461226073188            
absolute error                    = 1.0e-30                                      
relative error                    = 8.4379398251268169218491453131649e-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)                = 1.2012680983419177942046483407444            
y[1] (numeric)                    = 1.2012680983419177942046483407434            
absolute error                    = 1.0e-30                                      
relative error                    = 8.3245363910044441048757764210426e-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)                = 1.2174280947553027269106462114397            
y[1] (numeric)                    = 1.2174280947553027269106462114388            
absolute error                    = 9e-31                                        
relative error                    = 7.3926337323511145972482994586070e-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)                = 1.2336033083919219427055760991877            
y[1] (numeric)                    = 1.2336033083919219427055760991869            
absolute error                    = 8e-31                                        
relative error                    = 6.4850669137945923671031275755789e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.34                                         
y[1] (closed_form)                = 1.2497936505999192009385963499174            
y[1] (numeric)                    = 1.2497936505999192009385963499166            
absolute error                    = 8e-31                                        
relative error                    = 6.4010566833651964781169192069301e-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)                = 1.265999032681281153174329783176             
y[1] (numeric)                    = 1.265999032681281153174329783175             
absolute error                    = 1.0e-30                                      
relative error                    = 7.8989001901690460136407904531760e-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)                = 1.2822193658926356247142882000343            
y[1] (numeric)                    = 1.2822193658926356247142882000335            
absolute error                    = 8e-31                                        
relative error                    = 6.2391820095703233035955952815537e-29      % 
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)                = 1.2984545614460503043474270870072            
y[1] (numeric)                    = 1.2984545614460503043474270870065            
absolute error                    = 7e-31                                        
relative error                    = 5.3910242282212076593857619794581e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1126.3MB, alloc=44.3MB, time=13.40
 
TOP MAIN SOLVE Loop
x[1]                              = 4.38                                         
y[1] (closed_form)                = 1.3147045305098318351416281521488            
y[1] (numeric)                    = 1.3147045305098318351416281521481            
absolute error                    = 7e-31                                        
relative error                    = 5.3243902622633059167903558810382e-29      % 
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)                = 1.3309691842093252990842979638419            
y[1] (numeric)                    = 1.3309691842093252990842979638413            
absolute error                    = 6e-31                                        
relative error                    = 4.5079931760887132456293261584454e-29      % 
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)                = 1.3472484336277140883767263234136            
y[1] (numeric)                    = 1.347248433627714088376726323413             
absolute error                    = 6e-31                                        
relative error                    = 4.4535216002024934243607558949108e-29      % 
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)                = 1.3635421898068201561833681214811            
y[1] (numeric)                    = 1.3635421898068201561833681214806            
absolute error                    = 5e-31                                        
relative error                    = 3.6669199071195406245152202677391e-29      % 
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)                = 1.3798503637479046396337973361814            
y[1] (numeric)                    = 1.379850363747904639633797336181             
absolute error                    = 4e-31                                        
relative error                    = 2.8988650545667359265805093069275e-29      % 
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)                = 1.3961728664124688478717315599039            
y[1] (numeric)                    = 1.3961728664124688478717315599034            
absolute error                    = 5e-31                                        
relative error                    = 3.5812184295256594396503186060957e-29      % 
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)                = 1.4125096087230556079422400199714            
y[1] (numeric)                    = 1.4125096087230556079422400199709            
absolute error                    = 5e-31                                        
relative error                    = 3.5397989288866688781352059919319e-29      % 
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)                = 1.428860501564050961305027517482             
y[1] (numeric)                    = 1.4288605015640509613050275174813            
absolute error                    = 7e-31                                        
relative error                    = 4.8990086802299460053970830556428e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.46                                         
y[1] (closed_form)                = 1.4452254557824862037585310762041            
y[1] (numeric)                    = 1.4452254557824862037585310762033            
absolute error                    = 8e-31                                        
relative error                    = 5.5354685097686521579888959805644e-29      % 
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)                = 1.4616043821888402615564753984251            
y[1] (numeric)                    = 1.4616043821888402615564753984244            
absolute error                    = 7e-31                                        
relative error                    = 4.7892576714343726760015808084931e-29      % 
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)                = 1.4779971915578423964955074947898            
y[1] (numeric)                    = 1.477997191557842396495507494789             
absolute error                    = 8e-31                                        
relative error                    = 5.4127301768197674650244371724647e-29      % 
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)                = 1.4944037946292752327495701176758            
y[1] (numeric)                    = 1.4944037946292752327495701176748            
absolute error                    = 1.0e-30                                      
relative error                    = 6.6916318306597673307882025767270e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1167.0MB, alloc=44.3MB, time=13.88
 
TOP MAIN SOLVE Loop
x[1]                              = 4.5                                          
y[1] (closed_form)                = 1.5108241021087780982237779091733            
y[1] (numeric)                    = 1.5108241021087780982237779091723            
absolute error                    = 1.0e-30                                      
relative error                    = 6.6189042033696707523349250097060e-29      % 
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)                = 1.5272580246686506731977295013384            
y[1] (numeric)                    = 1.5272580246686506731977295013372            
absolute error                    = 1.2e-30                                      
relative error                    = 7.8572184962678353314114655600753e-29      % 
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)                = 1.5437054729486569390254232035354            
y[1] (numeric)                    = 1.5437054729486569390254232035343            
absolute error                    = 1.1e-30                                      
relative error                    = 7.1257116028673015175047353222051e-29      % 
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)                = 1.5601663575568294196562434042808            
y[1] (numeric)                    = 1.5601663575568294196562434042799            
absolute error                    = 9e-31                                        
relative error                    = 5.7686156071803214246811460047515e-29      % 
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)                = 1.5766405890702737087388494273391            
y[1] (numeric)                    = 1.5766405890702737087388494273381            
absolute error                    = 1.0e-30                                      
relative error                    = 6.3425996192936283728432049753034e-29      % 
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)                = 1.5931280780359732750672283376273            
y[1] (numeric)                    = 1.5931280780359732750672283376264            
absolute error                    = 9e-31                                        
relative error                    = 5.6492633103895225535081911768851e-29      % 
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)                = 1.6096287349715945391256681148883            
y[1] (numeric)                    = 1.6096287349715945391256681148873            
absolute error                    = 1.0e-30                                      
relative error                    = 6.2126127489743603069861738328158e-29      % 
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)                = 1.6261424703662922134869677246384            
y[1] (numeric)                    = 1.6261424703662922134869677246375            
absolute error                    = 9e-31                                        
relative error                    = 5.5345704106557957087126644253081e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.58                                         
y[1] (closed_form)                = 1.6426691946815148998158259385468            
y[1] (numeric)                    = 1.642669194681514899815825938546             
absolute error                    = 8e-31                                        
relative error                    = 4.8701223751572582528164760087200e-29      % 
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)                = 1.6592088183518109352270413115226            
y[1] (numeric)                    = 1.6592088183518109352270413115218            
absolute error                    = 8e-31                                        
relative error                    = 4.8215751456449390318652441470508e-29      % 
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)                = 1.6757612517856344807459115311739            
y[1] (numeric)                    = 1.675761251785634480745911531173             
absolute error                    = 9e-31                                        
relative error                    = 5.3706934626933905814435236078194e-29      % 
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)                = 1.692326405366151844616041437138             
y[1] (numeric)                    = 1.692326405366151844616041437137             
absolute error                    = 1.0e-30                                      
relative error                    = 5.9090255687621912323198492428770e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1207.4MB, alloc=44.3MB, time=14.36
 
TOP MAIN SOLVE Loop
x[1]                              = 4.62                                         
y[1] (closed_form)                = 1.7089041894520480331976553826928            
y[1] (numeric)                    = 1.7089041894520480331976553826918            
absolute error                    = 1.0e-30                                      
relative error                    = 5.8517031333432755180142021210055e-29      % 
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)                = 1.7254945143783335221974612980542            
y[1] (numeric)                    = 1.7254945143783335221974612980533            
absolute error                    = 9e-31                                        
relative error                    = 5.2158960373412416892661919606645e-29      % 
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)                = 1.7420972904571512409691308322871            
y[1] (numeric)                    = 1.7420972904571512409691308322862            
absolute error                    = 9e-31                                        
relative error                    = 5.1661867849173172757743766487857e-29      % 
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)                = 1.7587124279785837626215423166519            
y[1] (numeric)                    = 1.758712427978583762621542316651             
absolute error                    = 9e-31                                        
relative error                    = 5.1173801110533774127705870012555e-29      % 
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)                = 1.7753398372114606926700810237301            
y[1] (numeric)                    = 1.7753398372114606926700810237292            
absolute error                    = 9e-31                                        
relative error                    = 5.0694519501890781821933084038704e-29      % 
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)                = 1.7919794284041662489645043105002            
y[1] (numeric)                    = 1.7919794284041662489645043104993            
absolute error                    = 9e-31                                        
relative error                    = 5.0223790839021416962279367841501e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.68                                         
y[1] (closed_form)                = 1.8086311117854470256251577457384            
y[1] (numeric)                    = 1.8086311117854470256251577457375            
absolute error                    = 9e-31                                        
relative error                    = 4.9761391039631996807418996103767e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.69                                         
y[1] (closed_form)                = 1.8252947975652199337176722482062            
y[1] (numeric)                    = 1.8252947975652199337176722482052            
absolute error                    = 1.0e-30                                      
relative error                    = 5.4785670858970868336077483365164e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.7                                          
y[1] (closed_form)                = 1.841970395935380311394681616946             
y[1] (numeric)                    = 1.841970395935380311394681616945             
absolute error                    = 1.0e-30                                      
relative error                    = 5.4289689031195582146411123735643e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.71                                         
y[1] (closed_form)                = 1.8586578170706101962315746329716            
y[1] (numeric)                    = 1.8586578170706101962315746329706            
absolute error                    = 1.0e-30                                      
relative error                    = 5.3802264774915807715100287992088e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.72                                         
y[1] (closed_form)                = 1.8753569711291867524818361664182            
y[1] (numeric)                    = 1.8753569711291867524818361664173            
absolute error                    = 9e-31                                        
relative error                    = 4.7990863278583891655387641019022e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.73                                         
y[1] (closed_form)                = 1.8920677682537908459761374479675            
y[1] (numeric)                    = 1.8920677682537908459761374479668            
absolute error                    = 7e-31                                        
relative error                    = 3.6996560680595353583901970357193e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1247.7MB, alloc=44.3MB, time=14.84
 
TOP MAIN SOLVE Loop
x[1]                              = 4.74                                         
y[1] (closed_form)                = 1.9087901185723157593880068706116            
y[1] (numeric)                    = 1.9087901185723157593880068706108            
absolute error                    = 8e-31                                        
relative error                    = 4.1911365331163908049688857361285e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.75                                         
y[1] (closed_form)                = 1.9255239321986760405876493895465            
y[1] (numeric)                    = 1.9255239321986760405876493895456            
absolute error                    = 9e-31                                        
relative error                    = 4.6740525264327785828577466421718e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.76                                         
y[1] (closed_form)                = 1.942269119233616476804284795545             
y[1] (numeric)                    = 1.9422691192336164768042847955441            
absolute error                    = 9e-31                                        
relative error                    = 4.6337553899591596150094977339755e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.77                                         
y[1] (closed_form)                = 1.9590255897655211873162428613386            
y[1] (numeric)                    = 1.9590255897655211873162428613376            
absolute error                    = 1.0e-30                                      
relative error                    = 5.1045785477447058346625048043805e-29      % 
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)                = 1.975793253871222827386986611525             
y[1] (numeric)                    = 1.9757932538712228273869866115241            
absolute error                    = 9e-31                                        
relative error                    = 4.5551324676132319055164517650978e-29      % 
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)                = 1.9925720216168118961642337539192            
y[1] (numeric)                    = 1.9925720216168118961642337539183            
absolute error                    = 9e-31                                        
relative error                    = 4.5167752544759832752559659241914e-29      % 
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)                = 2.0093618030584461412584106430787            
y[1] (numeric)                    = 2.0093618030584461412584106430778            
absolute error                    = 9e-31                                        
relative error                    = 4.4790340825137192783156371421237e-29      % 
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)                = 2.0261625082431600527158030333993            
y[1] (numeric)                    = 2.0261625082431600527158030333983            
absolute error                    = 1.0e-30                                      
relative error                    = 4.9354382776881875697118309231092e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.82                                         
y[1] (closed_form)                = 2.0429740472096744391009633275058            
y[1] (numeric)                    = 2.0429740472096744391009633275049            
absolute error                    = 9e-31                                        
relative error                    = 4.4053423058860386604635122062961e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.83                                         
y[1] (closed_form)                = 2.0597963299892060784021950429099            
y[1] (numeric)                    = 2.059796329989206078402195042909             
absolute error                    = 9e-31                                        
relative error                    = 4.3693640332134986243065960597525e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.84                                         
y[1] (closed_form)                = 2.0766292666062774364732618127165            
y[1] (numeric)                    = 2.0766292666062774364732618127155            
absolute error                    = 1.0e-30                                      
relative error                    = 4.8154960352371694873384553603578e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
memory used=1288.0MB, alloc=44.3MB, time=15.32
x[1]                              = 4.85                                         
y[1] (closed_form)                = 2.0934727670795264457238604105958            
y[1] (numeric)                    = 2.0934727670795264457238604105948            
absolute error                    = 1.0e-30                                      
relative error                    = 4.7767518915234696721337437094052e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.86                                         
y[1] (closed_form)                = 2.1103267414225163367708550517684            
y[1] (numeric)                    = 2.1103267414225163367708550517675            
absolute error                    = 9e-31                                        
relative error                    = 4.2647424322232367761413925119352e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.87                                         
y[1] (closed_form)                = 2.1271910996445455157617935752569            
y[1] (numeric)                    = 2.127191099644545515761793575256             
absolute error                    = 9e-31                                        
relative error                    = 4.2309315799148950945619267045334e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.88                                         
y[1] (closed_form)                = 2.1440657517514574800818150624273            
y[1] (numeric)                    = 2.1440657517514574800818150624264            
absolute error                    = 9e-31                                        
relative error                    = 4.1976324619000257925723384422745e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.89                                         
y[1] (closed_form)                = 2.1609506077464507651547129965833            
y[1] (numeric)                    = 2.1609506077464507651547129965824            
absolute error                    = 9e-31                                        
relative error                    = 4.1648337392522163597018386928286e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.9                                          
y[1] (closed_form)                = 2.1778455776308889150486382211822            
y[1] (numeric)                    = 2.1778455776308889150486382211812            
absolute error                    = 1.0e-30                                      
relative error                    = 4.5916937833940607675871704686320e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.91                                         
y[1] (closed_form)                = 2.1947505714051104695967117126472            
y[1] (numeric)                    = 2.1947505714051104695967117126462            
absolute error                    = 1.0e-30                                      
relative error                    = 4.5563264137108109069519007430796e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.92                                         
y[1] (closed_form)                = 2.2116654990692389607426685496718            
y[1] (numeric)                    = 2.2116654990692389607426685496709            
absolute error                    = 9e-31                                        
relative error                    = 4.0693314625505417438424114273320e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.93                                         
y[1] (closed_form)                = 2.2285902706239929108215714356944            
y[1] (numeric)                    = 2.2285902706239929108215714356935            
absolute error                    = 9e-31                                        
relative error                    = 4.0384273944981595629803763040777e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.94                                         
y[1] (closed_form)                = 2.2455247960714958254856147156079            
y[1] (numeric)                    = 2.245524796071495825485614715607             
absolute error                    = 9e-31                                        
relative error                    = 4.0079717737899549560395251679116e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.95                                         
y[1] (closed_form)                = 2.2624689854160861739850880219199            
y[1] (numeric)                    = 2.2624689854160861739850880219191            
absolute error                    = 8e-31                                        
relative error                    = 3.5359600735162059698452004592317e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.96                                         
y[1] (closed_form)                = 2.2794227486651273495146824890545            
y[1] (numeric)                    = 2.2794227486651273495146824890537            
absolute error                    = 8e-31                                        
relative error                    = 3.5096605071108243626289461497223e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1328.5MB, alloc=44.3MB, time=15.79
 
TOP MAIN SOLVE Loop
x[1]                              = 4.97                                         
y[1] (closed_form)                = 2.296385995829817602335501886271             
y[1] (numeric)                    = 2.2963859958298176023355018862703            
absolute error                    = 7e-31                                        
relative error                    = 3.0482680231946343749220820570690e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.98                                         
y[1] (closed_form)                = 2.3133586369259999383833860381468            
y[1] (numeric)                    = 2.3133586369259999383833860381461            
absolute error                    = 7e-31                                        
relative error                    = 3.0259035016298326966094775754799e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.99                                         
y[1] (closed_form)                = 2.3303405819749719760744645245268            
y[1] (numeric)                    = 2.3303405819749719760744645245259            
absolute error                    = 9e-31                                        
relative error                    = 3.8620964118354184167051258789774e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
Finished!
diff  (  y  ,  x  ,  1  )   =   sin ( 0.3  *  x  +  0.1 )   +   ( 0.1  *  x  +  0.2 )   ; 
Iterations                       = 4000                                
Total Elapsed Time               = 15 Seconds
Elapsed Time(since restart)      = 15 Seconds
Time to Timeout                  = 2 Minutes 44 Seconds
Percent Done                     = 100                                        % 
> quit
memory used=1338.9MB, alloc=44.3MB, time=15.91