|\^/|     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(0.0) ) ;
> end;
                 exact_soln_y := proc(x) return c(0.) end proc

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

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

# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local min_size;
>     min_size := glob_estimated_size_answer;
>     if (float_abs(array_y[1]) < min_size) then # if number 3
>         min_size := float_abs(array_y[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     if (min_size < glob__1) then # if number 3
>         min_size := glob__1;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
    min_size := glob_estimated_size_answer;
    if float_abs(array_y[1]) < min_size then
        min_size := float_abs(array_y[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if min_size < glob__1 then
        min_size := glob__1;
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    min_size
end proc

# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     max_estimated_step_error  := glob__small;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
>     est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 3
>         max_estimated_step_error := est_tmp;
>     fi;# end if 3;
>     omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
>     max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
    max_estimated_step_error := glob__small;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
    est_tmp := float_abs(array_y[no_terms - 3]
         + array_y[no_terms - 2]*hn_div_ho
         + array_y[no_terms - 1]*hn_div_ho_2
         + array_y[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    omniout_float(ALWAYS, "max_estimated_step_error", 32,
        max_estimated_step_error, 32, "");
    max_estimated_step_error
end proc

# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
>         est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
>     fi;# end if 3;
>     if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
>         array_max_est_error[1] := c(est_tmp);
>     fi;# end if 3
>     ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    est_tmp := c(float_abs(array_y[no_terms - 3]))
         + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
    end if;
    if c(array_max_est_error[1]) <= c(est_tmp) then
        array_max_est_error[1] := c(est_tmp)
    end if
end proc

# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local ret;
>     if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 3;
>     return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
    if glob_check_sign*glob_next_display - glob_h/glob__10 <=
    glob_check_sign*array_x[1] then ret := true
    else ret := false
    end if;
    return ret
end proc

# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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)*31*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_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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)*31*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_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>     #TOP PROGRESS REPORT
>     clock_sec1   := elapsed_time_seconds();
>     total_clock_sec   :=  (clock_sec1) - (glob_orig_start_sec);
>     glob_clock_sec   :=  (clock_sec1) - (glob_clock_start_sec);
>     left_sec   :=  (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
>     expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h)  ,( clock_sec1) - (glob_orig_start_sec));
>     opt_clock_sec   := ( clock_sec1) - (glob_optimal_clock_start_sec);
>     glob_optimal_expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
>     glob_total_exp_sec   := glob_optimal_expect_sec + c(total_clock_sec);
>     percent_done   :=  comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
>     glob_percent_done := percent_done;
>     omniout_str_noeol(INFO,"Total Elapsed Time              ");
>     omniout_timestr((total_clock_sec));
>     omniout_str_noeol(INFO,"Elapsed Time(since restart)     ");
>     omniout_timestr((glob_clock_sec));
>     if (c(percent_done) < glob__100)  then # if number 3
>         omniout_str_noeol(INFO,"Expected Time Remaining         ");
>         omniout_timestr((expect_sec));
>         omniout_str_noeol(INFO,"Optimized Time Remaining        ");
>         omniout_timestr((glob_optimal_expect_sec));
>         omniout_str_noeol(INFO,"Expected Total Time             ");
>         omniout_timestr((glob_total_exp_sec));
>     fi;# end if 3;
>     omniout_str_noeol(INFO,"Time to Timeout                 ");
>     omniout_timestr((left_sec));
>     omniout_float(INFO,    "Percent Done                    ",33,percent_done,4,"%");
>     #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
    clock_sec1 := elapsed_time_seconds();
    total_clock_sec := clock_sec1 - glob_orig_start_sec;
    glob_clock_sec := clock_sec1 - glob_clock_start_sec;
    left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
    expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
        clock_sec1 - glob_orig_start_sec);
    opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
    glob_optimal_expect_sec :=
        comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
        ;
    glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
    percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
    glob_percent_done := percent_done;
    omniout_str_noeol(INFO, "Total Elapsed Time              ");
    omniout_timestr(total_clock_sec);
    omniout_str_noeol(INFO, "Elapsed Time(since restart)     ");
    omniout_timestr(glob_clock_sec);
    if c(percent_done) < glob__100 then
        omniout_str_noeol(INFO, "Expected Time Remaining         ");
        omniout_timestr(expect_sec);
        omniout_str_noeol(INFO, "Optimized Time Remaining        ");
        omniout_timestr(glob_optimal_expect_sec);
        omniout_str_noeol(INFO, "Expected Total Time             ");
        omniout_timestr(glob_total_exp_sec)
    end if;
    omniout_str_noeol(INFO, "Time to Timeout                 ");
    omniout_timestr(left_sec);
    omniout_float(INFO, "Percent Done                    ", 33,
        percent_done, 4, "%")
end proc

# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14,  rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
>     #TOP CHECK FOR POLE
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,1] :=  glob_larger_float;
>     array_ord_test_poles[1,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 3;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 4
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 5
>             found_sing := 0;
>         fi;# end if 5;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 5
>         if (rad_c  < array_rad_test_poles[1,1]) then # if number 6
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,1] := rad_c;
>             array_ord_test_poles[1,1] := tmp_ord;
>         fi;# end if 6;
>     fi;# end if 5;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,2] :=  glob_larger_float;
>     array_ord_test_poles[1,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 5;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 6
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 7
>             found_sing := 0;
>         fi;# end if 7;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 7
>         if (rad_c  < array_rad_test_poles[1,2]) then # if number 8
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 9
>                 glob_min_pole_est := rad_c;
>             fi;# end if 9;
>             array_ord_test_poles[1,2] := tmp_ord;
>         fi;# end if 8;
>     fi;# end if 7;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,3] :=  glob_larger_float;
>     array_ord_test_poles[1,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 7;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 8
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 9
>             found_sing := 0;
>         fi;# end if 9;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 9
>         if (rad_c  < array_rad_test_poles[1,3]) then # if number 10
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 11
>                 glob_min_pole_est := rad_c;
>             fi;# end if 11;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test1
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
>         h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
>         omniout_str(ALWAYS,"SETTING H FOR POLE");
>         glob_h_reason := 6;
>         if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 10;
>         term := 1;
>         ratio := c(1.0);
>         while (term <= ATS_MAX_TERMS)  do # do number 1
>             array_y[term] := array_y[term]* ratio;
>             array_y_higher[1,term] := array_y_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             ratio := ratio * h_new / float_abs(glob_h);
>             term := term + 1;
>         od;# end do number 1;
>         glob_h := h_new;
>     fi;# end if 9;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 9
>         display_poles();
>     fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 1] := glob_larger_float;
    array_ord_test_poles[1, 1] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 1] then
            array_rad_test_poles[1, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
                array_y_higher[1, last_no], last_no);
            array_rad_test_poles[1, 1] := rad_c;
            array_ord_test_poles[1, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 2] := glob_larger_float;
    array_ord_test_poles[1, 2] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 2] then
            array_rad_test_poles[1, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
                last_no);
            array_rad_test_poles[1, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 3] := glob_larger_float;
    array_ord_test_poles[1, 3] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
            array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
            array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 3] then
            array_rad_test_poles[1, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y_higher[1, last_no - 5],
                array_y_higher[1, last_no - 4],
                array_y_higher[1, last_no - 3],
                array_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
                last_no);
            array_rad_test_poles[1, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 3] := tmp_ord
        end if
    end if;
    if
    float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
    then
        h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
        omniout_str(ALWAYS, "SETTING H FOR POLE");
        glob_h_reason := 6;
        if glob_check_sign*h_new < glob_check_sign*glob_min_h then
            omniout_str(ALWAYS, "SETTING H FOR MIN H");
            h_new := glob_min_h;
            glob_h_reason := 5
        end if;
        term := 1;
        ratio := c(1.0);
        while term <= ATS_MAX_TERMS do
            array_y[term] := array_y[term]*ratio;
            array_y_higher[1, term] := array_y_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            ratio := ratio*h_new/float_abs(glob_h);
            term := term + 1
        end do;
        glob_h := h_new
    end if;
    if reached_interval() then display_poles() end if
end proc

# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
>     array_tmp1[1] := array_const_0D1[1] * array_x[1];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 1
>     array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
>     array_tmp3[1] := array_const_0D2[1] * array_x[1];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 1
>     array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
>     #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 1
>     array_tmp5[1] := expt(array_tmp2[1] , c(array_tmp4[1] )) ;
>     array_tmp5_a1[1] := ln(array_tmp2[1] ) ;
>     array_tmp5_a1[2] := array_tmp2[2] / array_tmp2[1];
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[2] := temporary;
>                 array_y_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
>     array_tmp1[2] := array_const_0D1[1] * array_x[2];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
>     array_tmp3[2] := array_const_0D2[1] * array_x[2];
>     #emit pre add LINEAR - CONST $eq_no = 1 i = 2
>     array_tmp4[2] := array_tmp3[2];
>     #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 2
>     array_tmp5_a2[1] := (array_tmp5_a1[1] * array_tmp4[2] + array_tmp5_a1[2] * array_tmp4[1]) / glob_h;
>     array_tmp5[2] := array_tmp5[1] * array_tmp5_a2[1] * glob_h;
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp6[2] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 3
>     array_tmp5_a1[3] := neg(array_tmp5_a1[2]) * array_tmp2[2] * c(1) / array_tmp2[1] / c(2);
>     array_tmp5_a2[2] := (array_tmp5_a1[2] * array_tmp4[2] + array_tmp5_a1[3] * array_tmp4[1]) * c(2) / glob_h;
>     array_tmp5[3] := ats(2,array_tmp5,array_tmp5_a2,1)*glob_h / c(2);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp6[3] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 4
>     array_tmp5_a1[4] := neg(array_tmp5_a1[3]) * array_tmp2[2] * c(2) / array_tmp2[1] / c(3);
>     array_tmp5_a2[3] := (array_tmp5_a1[3] * array_tmp4[2] + array_tmp5_a1[4] * array_tmp4[1]) * c(3) / glob_h;
>     array_tmp5[4] := ats(3,array_tmp5,array_tmp5_a2,1)*glob_h / c(3);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp6[4] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 5
>     array_tmp5_a1[5] := neg(array_tmp5_a1[4]) * array_tmp2[2] * c(3) / array_tmp2[1] / c(4);
>     array_tmp5_a2[4] := (array_tmp5_a1[4] * array_tmp4[2] + array_tmp5_a1[5] * array_tmp4[1]) * c(4) / glob_h;
>     array_tmp5[5] := ats(4,array_tmp5,array_tmp5_a2,1)*glob_h / c(4);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp6[5] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 1
>         array_tmp5_a1[kkk] := neg(array_tmp5_a1[kkk-1]) * array_tmp4[2] * c(kkk-2) / array_tmp2[1] / c(kkk - 1);
>         array_tmp5_a2[kkk-1] := (array_tmp5_a1[kkk-1] * array_tmp4[2] + array_tmp5_a1[kkk] * array_tmp4[1]) * c(kkk-1) / glob_h;
>         array_tmp5[kkk] := ats(kkk-1,array_tmp5,array_tmp5_a2,1)*glob_h/c(kkk-1);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp6[kkk] := array_tmp5[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_tmp6[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y[kkk + order_d] := c(temporary);
>                 array_y_higher[1,kkk + order_d] := c(temporary);
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
>                     if (adj3 <= order_d + 1) then # if number 3
>                         if (adj2 > 0) then # if number 4
>                             temporary := c(temporary) / c(glob_h) * c(adj2);
>                         else
>                             temporary := c(temporary);
>                         fi;# end if 4;
>                         array_y_higher[adj3,term] := c(temporary);
>                     fi;# end if 3;
>                     term  := term - 1;
>                     adj2 := adj2 - 1;
>                     adj3 := adj3 + 1;
>                 od;# end do number 1
>             fi;# end if 2
>         fi;# end if 1;
>         kkk   :=  kkk + 1;
>     od;# end do number 1;
>     #BOTTOM ATOMALL
>     #END OUTFILE4
>     #BEGIN OUTFILE5
>     #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
    array_tmp1[1] := array_const_0D1[1]*array_x[1];
    array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
    array_tmp3[1] := array_const_0D2[1]*array_x[1];
    array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
    array_tmp5[1] := expt(array_tmp2[1], c(array_tmp4[1]));
    array_tmp5_a1[1] := ln(array_tmp2[1]);
    array_tmp5_a1[2] := array_tmp2[2]/array_tmp2[1];
    array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
    if not array_y_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp6[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y[2] := temporary; array_y_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := array_const_0D1[1]*array_x[2];
    array_tmp2[2] := array_tmp1[2];
    array_tmp3[2] := array_const_0D2[1]*array_x[2];
    array_tmp4[2] := array_tmp3[2];
    array_tmp5_a2[1] := (
        array_tmp4[1]*array_tmp5_a1[2] + array_tmp4[2]*array_tmp5_a1[1])/
        glob_h;
    array_tmp5[2] := array_tmp5[1]*array_tmp5_a2[1]*glob_h;
    array_tmp6[2] := array_tmp5[2];
    if not array_y_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp6[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_tmp5_a1[3] :=
        neg(array_tmp5_a1[2])*array_tmp2[2]*c(1)/(array_tmp2[1]*c(2));
    array_tmp5_a2[2] :=
        (array_tmp4[1]*array_tmp5_a1[3] + array_tmp4[2]*array_tmp5_a1[2])*
        c(2)/glob_h;
    array_tmp5[3] := ats(2, array_tmp5, array_tmp5_a2, 1)*glob_h/c(2);
    array_tmp6[3] := array_tmp5[3];
    if not array_y_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp6[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_tmp5_a1[4] :=
        neg(array_tmp5_a1[3])*array_tmp2[2]*c(2)/(array_tmp2[1]*c(3));
    array_tmp5_a2[3] :=
        (array_tmp4[1]*array_tmp5_a1[4] + array_tmp4[2]*array_tmp5_a1[3])*
        c(3)/glob_h;
    array_tmp5[4] := ats(3, array_tmp5, array_tmp5_a2, 1)*glob_h/c(3);
    array_tmp6[4] := array_tmp5[4];
    if not array_y_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp6[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_tmp5_a1[5] :=
        neg(array_tmp5_a1[4])*array_tmp2[2]*c(3)/(array_tmp2[1]*c(4));
    array_tmp5_a2[4] :=
        (array_tmp4[1]*array_tmp5_a1[5] + array_tmp4[2]*array_tmp5_a1[4])*
        c(4)/glob_h;
    array_tmp5[5] := ats(4, array_tmp5, array_tmp5_a2, 1)*glob_h/c(4);
    array_tmp6[5] := array_tmp5[5];
    if not array_y_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp6[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_tmp5_a1[kkk] := neg(array_tmp5_a1[kkk - 1])*array_tmp4[2]*
            c(kkk - 2)/(array_tmp2[1]*c(kkk - 1));
        array_tmp5_a2[kkk - 1] := (array_tmp4[1]*array_tmp5_a1[kkk]
             + array_tmp4[2]*array_tmp5_a1[kkk - 1])*c(kkk - 1)/glob_h;
        array_tmp5[kkk] :=
            ats(kkk - 1, array_tmp5, array_tmp5_a2, 1)*glob_h/c(kkk - 1);
        array_tmp6[kkk] := array_tmp5[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_tmp6[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y[kkk + order_d] := c(temporary);
                array_y_higher[1, kkk + order_d] := c(temporary);
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
                do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then
                            temporary := c(temporary)*c(adj2)/c(glob_h)
                        else temporary := c(temporary)
                        end if;
                        array_y_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        kkk := kkk + 1
    end do
end proc

# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
>     #BEGIN OUTFIEMAIN
>     local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
>     term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
>     rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
>     x_start,x_end
>     ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
>     global
>     ALWAYS,
>     INFO,
>     DEBUGL,
>     DEBUGMASSIVE,
>     glob_iolevel,
>     glob_yes_pole,
>     glob_no_pole,
>     glob_not_given,
>     glob_no_sing_tests,
>     glob_ratio_test,
>     glob_three_term_test,
>     glob_six_term_test,
>     glob_log_10,
>     #Top Generate Globals Decl
>     MAX_UNCHANGED,
>     glob__small,
>     glob_small_float,
>     glob_smallish_float,
>     glob_large_float,
>     glob_larger_float,
>     glob__m2,
>     glob__m1,
>     glob__0,
>     glob__1,
>     glob__2,
>     glob__3,
>     glob__4,
>     glob__5,
>     glob__8,
>     glob__10,
>     glob__100,
>     glob__pi,
>     glob__0_5,
>     glob__0_8,
>     glob__m0_8,
>     glob__0_25,
>     glob__0_125,
>     glob_prec,
>     glob_check_sign,
>     glob_desired_digits_correct,
>     glob_max_estimated_step_error,
>     glob_ratio_of_radius,
>     glob_percent_done,
>     glob_total_exp_sec,
>     glob_optimal_expect_sec,
>     glob_estimated_size_answer,
>     glob_almost_1,
>     glob_clock_sec,
>     glob_clock_start_sec,
>     glob_disp_incr,
>     glob_h,
>     glob_diff_rc_fm,
>     glob_diff_rc_fmm1,
>     glob_diff_rc_fmm2,
>     glob_diff_ord_fm,
>     glob_diff_ord_fmm1,
>     glob_diff_ord_fmm2,
>     glob_six_term_ord_save,
>     glob_guess_error_rc,
>     glob_guess_error_ord,
>     glob_least_given_sing,
>     glob_least_ratio_sing,
>     glob_least_3_sing,
>     glob_least_6_sing,
>     glob_last_good_h,
>     glob_max_h,
>     glob_min_h,
>     glob_display_interval,
>     glob_abserr,
>     glob_relerr,
>     glob_min_pole_est,
>     glob_max_rel_trunc_err,
>     glob_max_trunc_err,
>     glob_max_hours,
>     glob_optimal_clock_start_sec,
>     glob_optimal_start,
>     glob_upper_ratio_limit,
>     glob_lower_ratio_limit,
>     glob_max_sec,
>     glob_orig_start_sec,
>     glob_normmax,
>     glob_max_minutes,
>     glob_next_display,
>     glob_est_digits,
>     glob_subiter_method,
>     glob_html_log,
>     glob_min_good_digits,
>     glob_good_digits,
>     glob_min_apfp_est_good_digits,
>     glob_apfp_est_good_digits,
>     glob_max_opt_iter,
>     glob_dump,
>     glob_djd_debug,
>     glob_display_flag,
>     glob_djd_debug2,
>     glob_h_reason,
>     glob_sec_in_minute,
>     glob_min_in_hour,
>     glob_hours_in_day,
>     glob_days_in_year,
>     glob_sec_in_hour,
>     glob_sec_in_day,
>     glob_sec_in_year,
>     glob_not_yet_finished,
>     glob_initial_pass,
>     glob_not_yet_start_msg,
>     glob_reached_optimal_h,
>     glob_optimal_done,
>     glob_type_given_pole,
>     glob_optimize,
>     glob_look_poles,
>     glob_dump_closed_form,
>     glob_max_iter,
>     glob_no_eqs,
>     glob_unchanged_h_cnt,
>     glob_warned,
>     glob_warned2,
>     glob_start,
>     glob_iter,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_1,
>     array_const_0D0,
>     array_const_0D1,
>     array_const_0D2,
>     array_const_0D3,
>     #END CONST
>     array_y_init,
>     array_norms,
>     array_fact_1,
>     array_1st_rel_error,
>     array_last_rel_error,
>     array_est_rel_error,
>     array_max_est_error,
>     array_type_pole,
>     array_type_real_pole,
>     array_type_complex_pole,
>     array_est_digits,
>     array_y,
>     array_x,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5_c1,
>     array_tmp5_a1,
>     array_tmp5_a2,
>     array_tmp5,
>     array_tmp6,
>     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 := 30;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=30;
>     #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..(30),[]);
>     array_norms:= Array(0..(30),[]);
>     array_fact_1:= Array(0..(30),[]);
>     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..(30),[]);
>     array_x:= Array(0..(30),[]);
>     array_tmp0:= Array(0..(30),[]);
>     array_tmp1:= Array(0..(30),[]);
>     array_tmp2:= Array(0..(30),[]);
>     array_tmp3:= Array(0..(30),[]);
>     array_tmp4:= Array(0..(30),[]);
>     array_tmp5_c1:= Array(0..(30),[]);
>     array_tmp5_a1:= Array(0..(30),[]);
>     array_tmp5_a2:= Array(0..(30),[]);
>     array_tmp5:= Array(0..(30),[]);
>     array_tmp6:= Array(0..(30),[]);
>     array_m1:= Array(0..(30),[]);
>     array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
>     array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
>     array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
>     array_y_set_initial := Array(0..(2) ,(0..30+ 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..(30) ,(0..30+ 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 <= 30) do # do number 1
>         array_y_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) 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 <= 30) do # do number 1
>         array_y[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp4[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp5_c1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp5_a1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp5_a2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp5[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp6[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <=30) do # do number 1
>         term := 1;
>         while (term <= 30) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5_c1);
>     zero_ats_ar(array_tmp5_a1);
>     zero_ats_ar(array_tmp5_a2);
>     zero_ats_ar(array_tmp5);
>     zero_ats_ar(array_tmp6);
>     zero_ats_ar(array_m1);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := c(1);
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := c(0.0);
>     zero_ats_ar(array_const_0D1);
>     array_const_0D1[1]   := c(0.1);
>     zero_ats_ar(array_const_0D2);
>     array_const_0D2[1]   := c(0.2);
>     zero_ats_ar(array_const_0D3);
>     array_const_0D3[1]   := c(0.3);
>     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;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 30;
>     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/expt_lin_linpostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =  expt (  ( 0.1  *  x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 )  )  ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=30;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(0.1);");
>     omniout_str(ALWAYS,"x_end := c(5.0) ;");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 0;");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
>     omniout_str(ALWAYS,"glob_look_poles:=false;");
>     omniout_str(ALWAYS,"glob_h:=c(0.001);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y := proc(x)");
>     omniout_str(ALWAYS,"return(c(0.0) ) ;");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(0.1);
>     x_end := c(5.0) ;
>     array_y_init[0 + 1] := exact_soln_y(x_start);
>     glob_look_poles := true;
>     glob_type_given_pole := 0;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=8;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=3;
>     glob_max_iter:=100000;
>     glob_upper_ratio_limit:=c(1.000001);
>     glob_lower_ratio_limit:=c(0.999999);
>     glob_look_poles:=false;
>     glob_h:=c(0.001);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(x_start,x_end));
>     glob__pi := arccos(glob__m1);
>     glob_prec = expt(10.0,c(-Digits));
>     if (glob_optimize)  then # if number 9
>         #BEGIN OPTIMIZE CODE
>         omniout_str(ALWAYS,"START of Optimize");
>         #Start Series -- INITIALIZE FOR OPTIMIZE
>         found_h := false;
>         glob_min_pole_est :=  glob_larger_float;
>         last_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         glob_min_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_max_h := float_abs(glob_max_h) * glob_check_sign;
>         glob_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
>         display_max := c(x_end) - c(x_start)/glob__10;
>         if ((glob_display_interval) > (display_max)) then # if number 10
>             glob_display_interval := c(display_max);
>         fi;# end if 10;
>         chk_data();
>         min_value := glob_larger_float;
>         est_answer := est_size_answer();
>         opt_iter := 1;
>         est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>         omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>         estimated_step_error  := glob_small_float;
>         while ((opt_iter <= 100) and ( not found_h)) do # do number 1
>             omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
>             array_x[1]   := c(x_start);
>             array_x[2]   :=  c(glob_h);
>             glob_next_display := c(x_start);
>             order_diff := 1;
>             #Start Series array_y
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             rows   :=  order_diff;
>             r_order   :=  1;
>             while (r_order <= rows) do # do number 2
>                 term_no   :=  1;
>                 while (term_no <= (rows - r_order + 1)) do # do number 3
>                     it  := term_no + r_order - 1;
>                     if (term_no < ATS_MAX_TERMS) then # if number 10
>                         array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 10;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             atomall();
>             if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
>                 omniout_str(ALWAYS,"SETTING H FOR MIN H");
>                 glob_h := glob_check_sign * float_abs(glob_min_h);
>                 glob_h_reason := 1;
>                 found_h := true;
>             fi;# end if 10;
>             if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
>                 omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>                 glob_h_reason := 2;
>                 glob_h := glob_display_interval;
>                 found_h := true;
>             fi;# end if 10;
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if ( not found_h) then # if number 10
>                 est_answer := est_size_answer();
>                 est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>                 omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>                 estimated_step_error := test_suggested_h();
>                 omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
>                 if (estimated_step_error < est_needed_step_err) then # if number 11
>                     omniout_str(ALWAYS,"Double H and LOOP");
>                     glob_h := glob_h*glob__2;
>                 else
>                     omniout_str(ALWAYS,"Found H for OPTIMAL");
>                     found_h := true;
>                     glob_h_reason := 3;
>                     glob_h := glob_h/glob__2;
>                 fi;# end if 11;
>             fi;# end if 10;
>             opt_iter := opt_iter + 1;
>         od;# end do number 1;
>         if (( not found_h) and (opt_iter = 1)) then # if number 10
>             omniout_str(ALWAYS,"Beginning glob_h too large.");
>             found_h := false;
>         fi;# end if 10;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
>             omniout_str(ALWAYS,"SETTING H FOR MAX H");
>             glob_h := glob_check_sign * float_abs(glob_max_h);
>             glob_h_reason := 1;
>             found_h := true;
>         fi;# end if 10;
>     else
>         found_h := true;
>         glob_h := glob_h * glob_check_sign;
>     fi;# end if 9;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 9
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 9;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 9
>         omniout_str(ALWAYS,"START of Soultion");
>         #Start Series -- INITIALIZE FOR SOLUTION
>         array_x[1]   := c(x_start);
>         array_x[2]   :=  c(glob_h);
>         glob_next_display := c(x_start);
>         glob_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         order_diff := 1;
>         #Start Series array_y
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>             term_no   :=  term_no + 1;
>         od;# end do number 1;
>         rows   :=  order_diff;
>         r_order   :=  1;
>         while (r_order <= rows) do # do number 1
>             term_no   :=  1;
>             while (term_no <= (rows - r_order + 1)) do # do number 2
>                 it  := term_no + r_order - 1;
>                 if (term_no < ATS_MAX_TERMS) then # if number 10
>                     array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 10;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         current_iter   :=  1;
>         glob_clock_start_sec   := elapsed_time_seconds();
>         glob_clock_sec   :=  elapsed_time_seconds();
>         glob_iter   :=  0;
>         omniout_str(DEBUGL," ");
>         glob_reached_optimal_h   :=  true;
>         glob_optimal_clock_start_sec := elapsed_time_seconds();
>         while ((glob_iter < glob_max_iter)  and (glob_check_sign * array_x[1] < glob_check_sign * x_end )  and  (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
>             #left paren 0001C
>             if (reached_interval()) then # if number 10
>                 omniout_str(INFO," ");
>                 omniout_str(INFO,"TOP MAIN SOLVE Loop");
>             fi;# end if 10;
>             glob_iter   :=  glob_iter + 1;
>             glob_clock_sec   := elapsed_time_seconds();
>             track_estimated_error();
>             atomall();
>             track_estimated_error();
>             display_alot(current_iter);
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if (reached_interval()) then # if number 10
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 10;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #END SUM AND ADJUST EQ =1
>             #END PART 1
>             #START PART 2  MOVE TERMS to REGULAR Array
>             term_no := ATS_MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_y[term_no] := array_y_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
>                     ord := ord + 1;
>                 od;# end do number 3;
>                 term_no   :=  term_no - 1;
>             od;# end do number 2;
>             #END PART 2 HEVE MOVED TERMS to REGULAR Array
>             ;
>         od;# end do number 1;#right paren 0001C
>         omniout_str(ALWAYS,"Finished!");
>         if (glob_iter >= glob_max_iter)  then # if number 10
>             omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
>         fi;# end if 10;
>         if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec  )) then # if number 10
>             omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
>         fi;# end if 10;
>         glob_clock_sec   := elapsed_time_seconds();
>         omniout_str(INFO,"diff  (  y  ,  x  ,  1  )   =  expt (  ( 0.1  *  x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 )  )  ; ");
>         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,"2016-08-26T16:33:39-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"expt_lin_lin.ode.txt\">expt_lin_lin</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =  expt (  ( 0.1  *  x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 )  )  ; ")
>             ;
>             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.expt_lin_lin.mxt.txt\">expt_lin_lin diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.expt_lin_lin.mxt.txt\">expt_lin_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_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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 := 30;
    Digits := 32;
    max_terms := 30;
    glob_html_log := true;
    array_y_init := Array(0 .. 30, []);
    array_norms := Array(0 .. 30, []);
    array_fact_1 := Array(0 .. 30, []);
    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 .. 30, []);
    array_x := Array(0 .. 30, []);
    array_tmp0 := Array(0 .. 30, []);
    array_tmp1 := Array(0 .. 30, []);
    array_tmp2 := Array(0 .. 30, []);
    array_tmp3 := Array(0 .. 30, []);
    array_tmp4 := Array(0 .. 30, []);
    array_tmp5_c1 := Array(0 .. 30, []);
    array_tmp5_a1 := Array(0 .. 30, []);
    array_tmp5_a2 := Array(0 .. 30, []);
    array_tmp5 := Array(0 .. 30, []);
    array_tmp6 := Array(0 .. 30, []);
    array_m1 := Array(0 .. 30, []);
    array_y_higher := Array(0 .. 2, 0 .. 31, []);
    array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
    array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
    array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
    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 .. 30, 0 .. 31, []);
    term := 1;
    while term <= 30 do array_y_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 30 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 <= 30 do array_y[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp5_c1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 30 do array_tmp5_a1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 30 do array_tmp5_a2[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 30 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 <= 30 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 <= 30 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 <= 30 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 <= 30 do
        term := 1;
        while term <= 30 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y);
    zero_ats_ar(array_x);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5_c1);
    zero_ats_ar(array_tmp5_a1);
    zero_ats_ar(array_tmp5_a2);
    zero_ats_ar(array_tmp5);
    zero_ats_ar(array_tmp6);
    zero_ats_ar(array_m1);
    zero_ats_ar(array_const_1);
    array_const_1[1] := c(1);
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := c(0.);
    zero_ats_ar(array_const_0D1);
    array_const_0D1[1] := c(0.1);
    zero_ats_ar(array_const_0D2);
    array_const_0D2[1] := c(0.2);
    zero_ats_ar(array_const_0D3);
    array_const_0D3[1] := c(0.3);
    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;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 30;
    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/expt_lin_linpostode.ode#################");
    omniout_str(ALWAYS, "diff  (  y  ,  x  ,  1  )   =  expt (  ( 0.1  * \
         x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 )  )  ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=30;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(0.1);");
    omniout_str(ALWAYS, "x_end := c(5.0) ;");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 0;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
    omniout_str(ALWAYS, "glob_look_poles:=false;");
    omniout_str(ALWAYS, "glob_h:=c(0.001);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y := proc(x)");
    omniout_str(ALWAYS, "return(c(0.0) ) ;");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(0.1);
    x_end := c(5.0);
    array_y_init[1] := exact_soln_y(x_start);
    glob_look_poles := true;
    glob_type_given_pole := 0;
    glob_desired_digits_correct := 8;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000;
    glob_upper_ratio_limit := c(1.000001);
    glob_lower_ratio_limit := c(0.999999);
    glob_look_poles := false;
    glob_h := c(0.001);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(x_start, x_end));
    glob__pi := arccos(glob__m1);
    glob_prec = expt(10.0, c(-Digits));
    if glob_optimize then
        omniout_str(ALWAYS, "START of Optimize");
        found_h := false;
        glob_min_pole_est := glob_larger_float;
        last_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        glob_min_h := float_abs(glob_min_h)*glob_check_sign;
        glob_max_h := float_abs(glob_max_h)*glob_check_sign;
        glob_h := float_abs(glob_min_h)*glob_check_sign;
        glob_display_interval :=
            c(float_abs(c(glob_display_interval))*glob_check_sign);
        display_max := c(x_end) - c(x_start)/glob__10;
        if display_max < glob_display_interval then
            glob_display_interval := c(display_max)
        end if;
        chk_data();
        min_value := glob_larger_float;
        est_answer := est_size_answer();
        opt_iter := 1;
        est_needed_step_err :=
            estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
            ;
        omniout_float(ALWAYS, "est_needed_step_err", 32,
            est_needed_step_err, 16, "");
        estimated_step_error := glob_small_float;
        while opt_iter <= 100 and not found_h do
            omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
            array_x[1] := c(x_start);
            array_x[2] := c(glob_h);
            glob_next_display := c(x_start);
            order_diff := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y[term_no] := array_y_init[term_no]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1));
                term_no := term_no + 1
            end do;
            rows := order_diff;
            r_order := 1;
            while r_order <= rows do
                term_no := 1;
                while term_no <= rows - r_order + 1 do
                    it := term_no + r_order - 1;
                    if term_no < ATS_MAX_TERMS then
                        array_y_higher[r_order, term_no] :=
                        array_y_init[it]*expt(glob_h, c(term_no - 1))/
                        c(factorial_1(term_no - 1))
                    end if;
                    term_no := term_no + 1
                end do;
                r_order := r_order + 1
            end do;
            atomall();
            if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
                omniout_str(ALWAYS, "SETTING H FOR MIN H");
                glob_h := float_abs(glob_min_h)*glob_check_sign;
                glob_h_reason := 1;
                found_h := true
            end if;
            if
            glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
            then
                omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
                glob_h_reason := 2;
                glob_h := glob_display_interval;
                found_h := true
            end if;
            if glob_look_poles then check_for_pole() end if;
            if not found_h then
                est_answer := est_size_answer();
                est_needed_step_err := estimated_needed_step_error(x_start,
                    x_end, glob_h, est_answer);
                omniout_float(ALWAYS, "est_needed_step_err", 32,
                    est_needed_step_err, 16, "");
                estimated_step_error := test_suggested_h();
                omniout_float(ALWAYS, "estimated_step_error", 32,
                    estimated_step_error, 32, "");
                if estimated_step_error < est_needed_step_err then
                    omniout_str(ALWAYS, "Double H and LOOP");
                    glob_h := glob_h*glob__2
                else
                    omniout_str(ALWAYS, "Found H for OPTIMAL");
                    found_h := true;
                    glob_h_reason := 3;
                    glob_h := glob_h/glob__2
                end if
            end if;
            opt_iter := opt_iter + 1
        end do;
        if not found_h and opt_iter = 1 then
            omniout_str(ALWAYS, "Beginning glob_h too large.");
            found_h := false
        end if;
        if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
            omniout_str(ALWAYS, "SETTING H FOR MAX H");
            glob_h := float_abs(glob_max_h)*glob_check_sign;
            glob_h_reason := 1;
            found_h := true
        end if
    else found_h := true; glob_h := glob_check_sign*glob_h
    end if;
    if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
    end if;
    if found_h then
        omniout_str(ALWAYS, "START of Soultion");
        array_x[1] := c(x_start);
        array_x[2] := c(glob_h);
        glob_next_display := c(x_start);
        glob_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y[term_no] := array_y_init[term_no]*
                expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
            term_no := term_no + 1
        end do;
        rows := order_diff;
        r_order := 1;
        while r_order <= rows do
            term_no := 1;
            while term_no <= rows - r_order + 1 do
                it := term_no + r_order - 1;
                if term_no < ATS_MAX_TERMS then
                    array_y_higher[r_order, term_no] := array_y_init[it]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1))
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        current_iter := 1;
        glob_clock_start_sec := elapsed_time_seconds();
        glob_clock_sec := elapsed_time_seconds();
        glob_iter := 0;
        omniout_str(DEBUGL, " ");
        glob_reached_optimal_h := true;
        glob_optimal_clock_start_sec := elapsed_time_seconds();
        while glob_iter < glob_max_iter and
        glob_check_sign*array_x[1] < glob_check_sign*x_end and
        glob_clock_sec - glob_orig_start_sec < glob_max_sec do
            if reached_interval() then
                omniout_str(INFO, " ");
                omniout_str(INFO, "TOP MAIN SOLVE Loop")
            end if;
            glob_iter := glob_iter + 1;
            glob_clock_sec := elapsed_time_seconds();
            track_estimated_error();
            atomall();
            track_estimated_error();
            display_alot(current_iter);
            if glob_look_poles then check_for_pole() end if;
            if reached_interval() then glob_next_display :=
                glob_next_display + glob_display_interval
            end if;
            array_x[1] := array_x[1] + glob_h;
            array_x[2] := glob_h;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            term_no := ATS_MAX_TERMS;
            while 1 <= term_no do
                array_y[term_no] := array_y_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y_higher[ord, term_no] :=
                        array_y_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do
        end do;
        omniout_str(ALWAYS, "Finished!");
        if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
            "Maximum Iterations Reached before Solution Completed!")
        end if;
        if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
        then omniout_str(ALWAYS,
            "Maximum Time Reached before Solution Completed!")
        end if;
        glob_clock_sec := elapsed_time_seconds();
        omniout_str(INFO, "diff  (  y  ,  x  ,  1  )   =  expt (  ( 0.1  \
            *  x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 )  )  ; ");
        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, "2016-08-26T16:33:39-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"expt_lin_lin.ode.txt\">expt_lin_lin</a>");
            logitem_str(html_log_file, "diff  (  y  ,  x  ,  1  )   =  ex\
                pt (  ( 0.1  *  x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 ) \
                 )  ; ");
            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.expt_lin_lin.mxt\
                .txt\">expt_lin_lin diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.expt_lin_lin.mx\
                t.txt\">expt_lin_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/expt_lin_linpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  expt (  ( 0.1  *  x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 )  )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;







glob_type_given_pole := 0;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(0.0) ) ;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0.1                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0                                            
absolute error                    = 0                                            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = -16                                 
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=4.2MB, alloc=40.3MB, time=0.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.11                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.0060640234331840161055636512832789         
absolute error                    = 0.0060640234331840161055636512832789         
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.012118484722894766365698934798558          
absolute error                    = 0.012118484722894766365698934798558          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.13                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.018163423525903902898667019986659          
absolute error                    = 0.018163423525903902898667019986659          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=20.0MB, alloc=40.3MB, time=0.28
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.024198924990009661064840743389701          
absolute error                    = 0.024198924990009661064840743389701          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.030225073520421079924487653230929          
absolute error                    = 0.030225073520421079924487653230929          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.16                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.03624195278987382591247546534259           
absolute error                    = 0.03624195278987382591247546534259           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.042249645748571623723369214400286          
absolute error                    = 0.042249645748571623723369214400286          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.18                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.048248234633957062549303635292203          
absolute error                    = 0.048248234633957062549303635292203          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.054237800980315447912151346326051          
absolute error                    = 0.054237800980315447912151346326051          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.2                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.060218425628215274410652140709507          
absolute error                    = 0.060218425628215274410652140709507          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.066190188733788802658309919008257          
absolute error                    = 0.066190188733788802658309919008257          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=62.9MB, alloc=52.3MB, time=0.79
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.07215316977785613441908320750728           
absolute error                    = 0.07215316977785613441908320750728           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.078107447574896093359188270265749          
absolute error                    = 0.078107447574896093359188270265749          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.084053100281867134832439264422273          
absolute error                    = 0.084053100281867134832439264422273          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.25                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.089990205406881426614787365325498          
absolute error                    = 0.089990205406881426614787365325498          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.095918839817735163415836293671858          
absolute error                    = 0.095918839817735163415836293671858          
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.10183907975029810123913029189165           
absolute error                    = 0.10183907975029810123913029189165           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.10775100081676522316009620203681           
absolute error                    = 0.10775100081676522316009620203681           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.1136546780137733757648428874183            
absolute error                    = 0.1136546780137733757648428874183            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=105.6MB, alloc=52.3MB, time=1.27
 
TOP MAIN SOLVE Loop
x[1]                              = 0.3                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.11955018573038564527162550366987           
absolute error                    = 0.11955018573038564527162550366987           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.1254375977559461741694719665688            
absolute error                    = 0.1254375977559461741694719665688            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.13131698728780805298768766960264           
absolute error                    = 0.13131698728780805298768766960264           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.13718842693893685749067526142258           
absolute error                    = 0.13718842693893685749067526142258           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.14305198874539233911212679794921           
absolute error                    = 0.14305198874539233911212679794921           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.14890774417369071574088747803323           
absolute error                    = 0.14890774417369071574088747803323           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.15475576412804995098960307024201           
absolute error                    = 0.15475576412804995098960307024201           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.37                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.16059611895752035276073301746844           
absolute error                    = 0.16059611895752035276073301746844           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=148.5MB, alloc=52.3MB, time=1.76
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.16642887846300276621877293533242           
absolute error                    = 0.16642887846300276621877293533242           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.17225411190415658213068403652481           
absolute error                    = 0.17225411190415658213068403652481           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.17807188800619972889855874033429           
absolute error                    = 0.17807188800619972889855874033429           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.18388227496660276543125655964828           
absolute error                    = 0.18388227496660276543125655964828           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.18968534046167914223865403662192           
absolute error                    = 0.18968534046167914223865403662192           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.43                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.19548115165307364973846570712494           
absolute error                    = 0.19548115165307364973846570712494           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.20126977519415102569810891064258           
absolute error                    = 0.20126977519415102569810891064258           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.20705127723628664795113962900829           
absolute error                    = 0.20705127723628664795113962900829           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=191.3MB, alloc=52.3MB, time=2.24
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.21282572343506119398919131507172           
absolute error                    = 0.21282572343506119398919131507172           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.47                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.21859317895636110569733354347085           
absolute error                    = 0.21859317895636110569733354347085           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.22435370848238665533592411047692           
absolute error                    = 0.22435370848238665533592411047692           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.49                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.23010737621756936783925765775455           
absolute error                    = 0.23010737621756936783925765775455           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.23585424589440051456577466594517           
absolute error                    = 0.23585424589440051456577466594517           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.51                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.24159438077917235476265459440753           
absolute error                    = 0.24159438077917235476265459440753           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.52                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.24732784367763376316680634215969           
absolute error                    = 0.24732784367763376316680634215969           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
memory used=234.1MB, alloc=52.3MB, time=2.73
x[1]                              = 0.53                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.25305469694056184532323614496761           
absolute error                    = 0.25305469694056184532323614496761           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.54                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.25877500246925110633024052529061           
absolute error                    = 0.25877500246925110633024052529061           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.55                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.26448882172092170378959693279573           
absolute error                    = 0.26448882172092170378959693279573           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.56                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.27019621571404828172065885855871           
absolute error                    = 0.27019621571404828172065885855871           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.57                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.27589724503361084906271408319113           
absolute error                    = 0.27589724503361084906271408319113           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.28159196983626913411376386009052           
absolute error                    = 0.28159196983626913411376386009052           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.59                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.28728044985546181481054311641112           
absolute error                    = 0.28728044985546181481054311641112           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.29296274440643199411949624626164           
absolute error                    = 0.29296274440643199411949624626164           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
memory used=277.1MB, alloc=52.3MB, time=3.22
x[1]                              = 0.61                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.29863891239118025995774025035434           
absolute error                    = 0.29863891239118025995774025035434           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.62                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.30430901230334663997376824572881           
absolute error                    = 0.30430901230334663997376824572881           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.63                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.3099731022330227331675148172372            
absolute error                    = 0.3099731022330227331675148172372            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.64                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.31563123987149527269689703757608           
absolute error                    = 0.31563123987149527269689703757608           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.32128348251592234728224470173565           
absolute error                    = 0.32128348251592234728224470173565           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.66                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.32692988707394348236100476617219           
absolute error                    = 0.32692988707394348236100476617219           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.67                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.3325705100682247565432686331753            
absolute error                    = 0.3325705100682247565432686331753            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.68                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.33820540764094010395517958398964           
absolute error                    = 0.33820540764094010395517958398964           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
memory used=319.8MB, alloc=52.3MB, time=3.71
x[1]                              = 0.69                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.3438346355581899287138936318273            
absolute error                    = 0.3438346355581899287138936318273            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.34945824921435813403684017987451           
absolute error                    = 0.34945824921435813403684017987451           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.71                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.35507630363640864533247545696123           
absolute error                    = 0.35507630363640864533247545696123           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.36068885348812248403300434361024           
absolute error                    = 0.36068885348812248403300434361024           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.73                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.36629595307427642689565428630636           
absolute error                    = 0.36629595307427642689565428630636           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.74                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.37189765634476426400251605781844           
absolute error                    = 0.37189765634476426400251605781844           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.75                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.37749401689866164771470787571875           
absolute error                    = 0.37749401689866164771470787571875           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.76                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.38308508798823550437013249932878           
absolute error                    = 0.38308508798823550437013249932878           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=362.7MB, alloc=52.3MB, time=4.19
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.38867092252289896054129840527808           
absolute error                    = 0.38867092252289896054129840527808           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.3942515730731127161769234291178            
absolute error                    = 0.3942515730731127161769234291178            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.79                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.39982709187423377792511487950222           
absolute error                    = 0.39982709187423377792511487950222           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.40539753083031244736401695506766           
absolute error                    = 0.40539753083031244736401695506766           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.81                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.41096294151783844073552336516268           
absolute error                    = 0.41096294151783844073552336516268           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.41652337518943699907694194827882           
absolute error                    = 0.41652337518943699907694194827882           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.83                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.4220788827775158303627097802996            
absolute error                    = 0.4220788827775158303627097802996            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.84                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.42762951489786370839208953588085           
absolute error                    = 0.42762951489786370839208953588085           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=405.5MB, alloc=52.3MB, time=4.68
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.43317532185320153667827311017614           
absolute error                    = 0.43317532185320153667827311017614           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.86                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.43871635363668666949885206154766           
absolute error                    = 0.43871635363668666949885206154766           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.44425265993537126654688331433485           
absolute error                    = 0.44425265993537126654688331433485           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.88                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.44978429013361544226579061912701           
absolute error                    = 0.44978429013361544226579061912701           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.89                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.45531129331645595595040576364116           
absolute error                    = 0.45531129331645595595040576364116           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.4608337182729311740411670688026            
absolute error                    = 0.4608337182729311740411670688026            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.46635161349936302171973557085378           
absolute error                    = 0.46635161349936302171973557085378           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.92                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.47186502720259662692321210503177           
absolute error                    = 0.47186502720259662692321210503177           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=448.3MB, alloc=52.3MB, time=5.17
 
TOP MAIN SOLVE Loop
x[1]                              = 0.93                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.47737400730319834622215425385848           
absolute error                    = 0.47737400730319834622215425385848           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.4828786014386128486463674914992            
absolute error                    = 0.4828786014386128486463674914992            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.95                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.48837885696627992048389189464284           
absolute error                    = 0.48837885696627992048389189464284           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.49387482096671164131487387101153           
absolute error                    = 0.49387482096671164131487387101153           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.97                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.49936654024653056906548042129082           
absolute error                    = 0.49936654024653056906548042129082           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.98                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.5048540613414695596702825412835            
absolute error                    = 0.5048540613414695596702825412835            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 0.99                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.51033743051933383500742042700407           
absolute error                    = 0.51033743051933383500742042700407           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.51581669378292590111239005475423           
absolute error                    = 0.51581669378292590111239005475423           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=491.2MB, alloc=52.3MB, time=5.65
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.5212918968729339072766836102596            
absolute error                    = 0.5212918968729339072766836102596            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.52676308527078402549019506437208           
absolute error                    = 0.52676308527078402549019506437208           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.53223030420145741878487542263088           
absolute error                    = 0.53223030420145741878487542263088           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.53769359863627235637538084004995           
absolute error                    = 0.53769359863627235637538084004995           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.54315301329563202306436865949551           
absolute error                    = 0.54315301329563202306436865949551           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.5486085926517385601798004121698            
absolute error                    = 0.5486085926517385601798004121698            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.55406038093127386533341156006094           
absolute error                    = 0.55406038093127386533341156006094           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.55950842211804766852787043268863           
absolute error                    = 0.55950842211804766852787043268863           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=534.1MB, alloc=52.3MB, time=6.13
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.56495275995561339258969407076058           
absolute error                    = 0.56495275995561339258969407076058           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.57039343794985229656048781968184           
absolute error                    = 0.57039343794985229656048781968184           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.57583049937152639153544573014181           
absolute error                    = 0.57583049937152639153544573014181           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.58126398725880060949034873405801           
absolute error                    = 0.58126398725880060949034873405801           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.5866939444197346968817228059815            
absolute error                    = 0.5866939444197346968817228059815            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.59212041343474529623469831935369           
absolute error                    = 0.59212041343474529623469831935369           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.59754343665903867054490169836626           
absolute error                    = 0.59754343665903867054490169836626           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.602963056225014517109993145734             
absolute error                    = 0.602963056225014517109993145734             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=576.9MB, alloc=52.3MB, time=6.63
 
TOP MAIN SOLVE Loop
x[1]                              = 1.17                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.60837931404464130936894253892942           
absolute error                    = 0.60837931404464130936894253892942           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.61379225181180359745862964037243           
absolute error                    = 0.61379225181180359745862964037243           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.61920191100462169049379837110413           
absolute error                    = 0.61920191100462169049379837110413           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.62460833288774413603383212325948           
absolute error                    = 0.62460833288774413603383212325948           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.63001155851461340481439893778809           
absolute error                    = 0.63001155851461340481439893778809           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.22                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.63541162872970518158999657013372           
absolute error                    = 0.63541162872970518158999657013372           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.64080858417074165585116333373721           
absolute error                    = 0.64080858417074165585116333373721           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.64620246527087919924406407354237           
absolute error                    = 0.64620246527087919924406407354237           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=619.9MB, alloc=52.3MB, time=7.11
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.65159331226087080972685929345668           
absolute error                    = 0.65159331226087080972685929345668           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.65698116517120369584335883424765           
absolute error                    = 0.65698116517120369584335883424765           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.27                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.66236606383421236797667821895162           
absolute error                    = 0.66236606383421236797667821895162           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.66774804788616759706077102260066           
absolute error                    = 0.66774804788616759706077102260066           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.67312715676934159497270353009962           
absolute error                    = 0.67312715676934159497270353009962           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.67850342973404976470034918154547           
absolute error                    = 0.67850342973404976470034918154547           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.31                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.68387690584066936237586965779458           
absolute error                    = 0.68387690584066936237586965779458           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.32                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.68924762396163540738205354108116           
absolute error                    = 0.68924762396163540738205354108116           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=662.8MB, alloc=52.3MB, time=7.60
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.69461562278341417097351349364468           
absolute error                    = 0.69461562278341417097351349364468           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.69998094080845456820518245451961           
absolute error                    = 0.69998094080845456820518245451961           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.7053436163571177724238524159395            
absolute error                    = 0.7053436163571177724238524159395            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.71070368756958536615208816703941           
absolute error                    = 0.71070368756958536615208816703941           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.37                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.71606119240774633687521158818808           
absolute error                    = 0.71606119240774633687521158818808           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.72141616865706322102874269243863           
absolute error                    = 0.72141616865706322102874269243863           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.726768653928417694373317292834             
absolute error                    = 0.726768653928417694373317292834             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.73211868565993590193435439846502           
absolute error                    = 0.73211868565993590193435439846502           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=705.7MB, alloc=52.3MB, time=8.08
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.73746630111879381577235477593641           
absolute error                    = 0.73746630111879381577235477593641           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.74281153740300290403446854638349           
absolute error                    = 0.74281153740300290403446854638349           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.74815443144317639001672301369729           
absolute error                    = 0.74815443144317639001672301369729           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.75349502000427637533695516167794           
absolute error                    = 0.75349502000427637533695516167794           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.75883333968734209677900215189462           
absolute error                    = 0.75883333968734209677900215189462           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.46                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.76416942693119958191707467216258           
absolute error                    = 0.76416942693119958191707467216258           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.76950331801415296426352890756784           
absolute error                    = 0.76950331801415296426352890756784           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.77483504905565771440156843442962           
absolute error                    = 0.77483504905565771440156843442962           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=748.5MB, alloc=52.3MB, time=8.56
 
TOP MAIN SOLVE Loop
x[1]                              = 1.49                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.78016465601797603936489975518359           
absolute error                    = 0.78016465601797603936489975518359           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.78549217470781469840723256013624           
absolute error                    = 0.78549217470781469840723256013624           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.79081764077794547926400069820408           
absolute error                    = 0.79081764077794547926400069820408           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.52                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.79614108972880857504506813385477           
absolute error                    = 0.79614108972880857504506813385477           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.80146255691009909800880383856286           
absolute error                    = 0.80146255691009909800880383856286           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.8067820775223369626531295447447            
absolute error                    = 0.8067820775223369626531295447447            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.55                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.81209968661842036681637335025674           
absolute error                    = 0.81209968661842036681637335025674           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.56                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.81741541910516309580844783073152           
absolute error                    = 0.81741541910516309580844783073152           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=791.4MB, alloc=52.3MB, time=9.05
 
TOP MAIN SOLVE Loop
x[1]                              = 1.57                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.82272930974481587098949883031558           
absolute error                    = 0.82272930974481587098949883031558           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.58                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.82804139315657196067726238130166           
absolute error                    = 0.82804139315657196067726238130166           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.59                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.83335170381805726779447987116908           
absolute error                    = 0.83335170381805726779447987116908           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.83866027606680510526244799276677           
absolute error                    = 0.83866027606680510526244799276677           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.61                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.84396714410171586680474634968189           
absolute error                    = 0.84396714410171586680474634968189           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.62                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.84927234198450179754505091949293           
absolute error                    = 0.84927234198450179754505091949293           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.63                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.85457590364111706556339700642714           
absolute error                    = 0.85457590364111706556339700642714           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.64                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.85987786286317333241502312320196           
absolute error                    = 0.85987786286317333241502312320196           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=834.3MB, alloc=52.3MB, time=9.54
 
TOP MAIN SOLVE Loop
x[1]                              = 1.65                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.86517825330934101751376006208471           
absolute error                    = 0.86517825330934101751376006208471           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.66                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.87047710850673644823660942920376           
absolute error                    = 0.87047710850673644823660942920376           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.67                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.87577446185229508461649407610908           
absolute error                    = 0.87577446185229508461649407610908           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.68                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.8810703466141310045549981350578            
absolute error                    = 0.8810703466141310045549981350578            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.69                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.88636479593288283260511299612426           
absolute error                    = 0.88636479593288283260511299612426           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.7                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.89165784282304629254446036865728           
absolute error                    = 0.89165784282304629254446036865728           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.71                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.89694952017429356118109323497798           
absolute error                    = 0.89694952017429356118109323497798           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.72                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.90223986075277959810572392050939           
absolute error                    = 0.90223986075277959810572392050939           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=877.2MB, alloc=52.3MB, time=10.03
 
TOP MAIN SOLVE Loop
x[1]                              = 1.73                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.90752889720243562342506411018258           
absolute error                    = 0.90752889720243562342506411018258           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.74                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.91281666204624991287987678809387           
absolute error                    = 0.91281666204624991287987678809387           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.75                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.91810318768753607716735041515061           
absolute error                    = 0.91810318768753607716735041515061           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.76                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.92338850641118898974954953486748           
absolute error                    = 0.92338850641118898974954953486748           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.77                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.92867265038492852493703387327713           
absolute error                    = 0.92867265038492852493703387327713           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.78                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.93395565166053126558835188775402           
absolute error                    = 0.93395565166053126558835188775402           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.79                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.9392375421750503373611076342105            
absolute error                    = 0.9392375421750503373611076342105            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.94451835375202352408779524117258           
absolute error                    = 0.94451835375202352408779524117258           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=920.2MB, alloc=52.3MB, time=10.51
 
TOP MAIN SOLVE Loop
x[1]                              = 1.81                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.94979811810266981652873662762924           
absolute error                    = 0.94979811810266981652873662762924           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.82                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.95507686682707454447440824573498           
absolute error                    = 0.95507686682707454447440824573498           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.83                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.96035463141536323992938338660214           
absolute error                    = 0.96035463141536323992938338660214           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.84                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.96563144324886437690924824827474           
absolute error                    = 0.96563144324886437690924824827474           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.85                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.97090733360126113121939082987941           
absolute error                    = 0.97090733360126113121939082987941           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.86                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.97618233363973230145974764378183           
absolute error                    = 0.97618233363973230145974764378183           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.87                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.98145647442608253041167720708938           
absolute error                    = 0.98145647442608253041167720708938           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.88                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.98672978691786196391138095706192           
absolute error                    = 0.98672978691786196391138095706192           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=963.1MB, alloc=52.3MB, time=11.00
 
TOP MAIN SOLVE Loop
x[1]                              = 1.89                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.99200230196947548229799758235355           
absolute error                    = 0.99200230196947548229799758235355           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 0.99727405033328163754295759880232           
absolute error                    = 0.99727405033328163754295759880232           
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.91                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0025450626606814272197186323564            
absolute error                    = 1.0025450626606814272197186323564            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.92                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0078153695031970345589407108442            
absolute error                    = 1.0078153695031970345589407108442            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.93                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0130850013135406619528520478872            
absolute error                    = 1.0130850013135406619528520478872            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.94                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0183539884466735834233608312165            
absolute error                    = 1.0183539884466735834233608312165            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.95                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0236223611608555397507629249014            
absolute error                    = 1.0236223611608555397507629249014            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.96                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.028890149618684598173068355333             
absolute error                    = 1.028890149618684598173068355333             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1005.9MB, alloc=52.3MB, time=11.48
 
TOP MAIN SOLVE Loop
x[1]                              = 1.97                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0341573838881275968094235099202            
absolute error                    = 1.0341573838881275968094235099202            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.98                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0394240939435412922342566879367            
absolute error                    = 1.0394240939435412922342566879367            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 1.99                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0446903096666843269310502588901            
absolute error                    = 1.0446903096666843269310502588901            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2                                            
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0499560608477201316854838538035            
absolute error                    = 1.0499560608477201316854838538035            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.01                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.055221377186210876336552483323             
absolute error                    = 1.055221377186210876336552483323             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.02                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0604862882921025806906057928974            
absolute error                    = 1.0604862882921025806906057928974            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.03                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0657508236867014958165559004971            
absolute error                    = 1.0657508236867014958165559004971            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.04                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0710150128036418643802487335999            
absolute error                    = 1.0710150128036418643802487335999            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1048.9MB, alloc=52.3MB, time=11.98
 
TOP MAIN SOLVE Loop
x[1]                              = 2.05                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.076278884989845167141685784272             
absolute error                    = 1.076278884989845167141685784272             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.06                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0815424695064709612299287452462            
absolute error                    = 1.0815424695064709612299287452462            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.07                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0868057955298594143266380488311            
absolute error                    = 1.0868057955298594143266380488311            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.08                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0920688921524656374298175911385            
absolute error                    = 1.0920688921524656374298175911385            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.09                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.0973317883837859174340015458729            
absolute error                    = 1.0973317883837859174340015458729            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.1                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1025945131512759493513745516278            
absolute error                    = 1.1025945131512759493513745516278            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.11                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1078570953012611666097225995466            
absolute error                    = 1.1078570953012611666097225995466            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.12                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1131195635998392664972368449626            
absolute error                    = 1.1131195635998392664972368449626            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1091.7MB, alloc=52.3MB, time=12.46
 
TOP MAIN SOLVE Loop
x[1]                              = 2.13                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1183819467337750264806135759132            
absolute error                    = 1.1183819467337750264806135759132            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.14                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1236442733113875058011968082407            
absolute error                    = 1.1236442733113875058011968082407            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.15                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1289065718634297254536902064114            
absolute error                    = 1.1289065718634297254536902064114            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.16                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1341688708439609183728254653779            
absolute error                    = 1.1341688708439609183728254653779            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.17                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1394311986312114403949263991501            
absolute error                    = 1.1394311986312114403949263991501            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.18                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1446935835284404313231712960273            
absolute error                    = 1.1446935835284404313231712960273            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.19                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1499560537647863142071580248825            
absolute error                    = 1.1499560537647863142071580248825            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.2                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1552186374961102197487520128167            
absolute error                    = 1.1552186374961102197487520128167            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1134.6MB, alloc=52.3MB, time=12.95
 
TOP MAIN SOLVE Loop
x[1]                              = 2.21                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1604813628058324215667891817628            
absolute error                    = 1.1604813628058324215667891817628            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.22                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1657442577057618668926641963208            
absolute error                    = 1.1657442577057618668926641963208            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.23                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1710073501369188861268160817669            
absolute error                    = 1.1710073501369188861268160817669            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.24                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1762706679703511635622925791351            
absolute error                    = 1.1762706679703511635622925791351            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.25                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.181534239007943050475602528039             
absolute error                    = 1.181534239007943050475602528039             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.26                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1867980909832183006966298217845            
absolute error                    = 1.1867980909832183006966298217845            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.27                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1920622515621363076981673256262            
absolute error                    = 1.1920622515621363076981673256262            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.28                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.1973267483438819211913252502602            
absolute error                    = 1.1973267483438819211913252502602            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1177.5MB, alloc=52.3MB, time=13.43
 
TOP MAIN SOLVE Loop
x[1]                              = 2.29                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2025916088616489201753727473261            
absolute error                    = 1.2025916088616489201753727473261            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.3                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2078568605834172183691869756703            
absolute error                    = 1.2078568605834172183691869756703            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.31                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2131225309127238769461195885134            
absolute error                    = 1.2131225309127238769461195885134            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.32                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2183886471894279985044613690199            
absolute error                    = 1.2183886471894279985044613690199            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.33                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.22365523669046957523151216569              
absolute error                    = 1.22365523669046957523151216569              
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.34                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.228922326630622363260271506806             
absolute error                    = 1.228922326630622363260271506806             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.35                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2341899441632408542736869248443            
absolute error                    = 1.2341899441632408542736869248443            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.36                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2394581163810014144819690588072            
absolute error                    = 1.2394581163810014144819690588072            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1220.4MB, alloc=52.3MB, time=13.92
 
TOP MAIN SOLVE Loop
x[1]                              = 2.37                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2447268703166376601834472096851            
absolute error                    = 1.2447268703166376601834472096851            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.38                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2499962329436701382185434947507            
absolute error                    = 1.2499962329436701382185434947507            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.39                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2552662311771303787394403687256            
absolute error                    = 1.2552662311771303787394403687256            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.4                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2605368918742793868446622286084            
absolute error                    = 1.2605368918742793868446622286084            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.41                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2658082418353206387678490474786            
absolute error                    = 1.2658082418353206387678490474786            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.42                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2710803078041076474632351185771            
absolute error                    = 1.2710803078041076474632351185771            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.43                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2763531164688461615965302344407            
absolute error                    = 1.2763531164688461615965302344407            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.44                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2816266944627910611288096496399            
absolute error                    = 1.2816266944627910611288096496399            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1263.3MB, alloc=52.3MB, time=14.40
 
TOP MAIN SOLVE Loop
x[1]                              = 2.45                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2869010683649380118724330281983            
absolute error                    = 1.2869010683649380118724330281983            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.46                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.2921762647007099406017155873136            
absolute error                    = 1.2921762647007099406017155873136            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.47                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.297452309942638391516855335072             
absolute error                    = 1.297452309942638391516855335072             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.48                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3027292305110398240872712768341            
absolute error                    = 1.3027292305110398240872712768341            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.49                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3080070527746869115398253579104            
absolute error                    = 1.3080070527746869115398253579104            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.5                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3132858030514748985081862676276            
absolute error                    = 1.3132858030514748985081862676276            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.51                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3185655076090830756216504399363            
absolute error                    = 1.3185655076090830756216504399363            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.52                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3238461926656314280848727936685            
absolute error                    = 1.3238461926656314280848727936685            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1306.2MB, alloc=52.3MB, time=14.89
 
TOP MAIN SOLVE Loop
x[1]                              = 2.53                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.329127884390332514583988783953             
absolute error                    = 1.329127884390332514583988783953             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.54                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3344106089041386321493456065062            
absolute error                    = 1.3344106089041386321493456065062            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.55                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3396943922803843219103228523392            
absolute error                    = 1.3396943922803843219103228523392            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.56                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.344979260545424269993333943387             
absolute error                    = 1.344979260545424269993333943387             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.57                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.350265239679266657139885056032             
absolute error                    = 1.350265239679266657139885056032             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.58                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3555523556162020099573570293905            
absolute error                    = 1.3555523556162020099573570293905            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.59                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3608406342454276060608002625118            
absolute error                    = 1.3608406342454276060608002625118            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.6                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3661301014116674847193282993007            
absolute error                    = 1.3661301014116674847193282993007            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1349.2MB, alloc=52.3MB, time=15.38
 
TOP MAIN SOLVE Loop
x[1]                              = 2.61                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3714207829157881139855012516889            
absolute error                    = 1.3714207829157881139855012516889            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.62                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3767127045154097646602470247903            
absolute error                    = 1.3767127045154097646602470247903            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.63                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.382005891925513640829221058415             
absolute error                    = 1.382005891925513640829221058415             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.64                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.387300370819044816098901472795             
absolute error                    = 1.387300370819044816098901472795             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.65                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3925961668275110240620064372034            
absolute error                    = 1.3925961668275110240620064372034            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.66                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.3978933055415773509318573927298            
absolute error                    = 1.3978933055415773509318573927298            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.67                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4031918125116568777039513114272            
absolute error                    = 1.4031918125116568777039513114272            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.68                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.408491713248497318630105995743             
absolute error                    = 1.408491713248497318630105995743             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1392.1MB, alloc=52.3MB, time=15.86
 
TOP MAIN SOLVE Loop
x[1]                              = 2.69                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4137930332237637022259656675127            
absolute error                    = 1.4137930332237637022259656675127            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.7                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.419095797870617140476263484504             
absolute error                    = 1.419095797870617140476263484504             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.71                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4244000325842897313538993881714            
absolute error                    = 1.4244000325842897313538993881714            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.72                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4297057627226556392284745250963            
absolute error                    = 1.4297057627226556392284745250963            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.73                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4350130136067983972072985048652            
absolute error                    = 1.4350130136067983972072985048652            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.74                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4403218105215744749269264302131            
absolute error                    = 1.4403218105215744749269264302131            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.75                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4456321787161731547958647473099            
absolute error                    = 1.4456321787161731547958647473099            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.76                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4509441434046727591790865691734            
absolute error                    = 1.4509441434046727591790865691734            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1435.0MB, alloc=52.3MB, time=16.35
 
TOP MAIN SOLVE Loop
x[1]                              = 2.77                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4562577297665932705122984992969            
absolute error                    = 1.4562577297665932705122984992969            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.78                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4615729629474453858383845786052            
absolute error                    = 1.4615729629474453858383845786052            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.79                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4668898680592760467700033827136            
absolute error                    = 1.4668898680592760467700033827136            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.8                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.472208470181210485400818184136             
absolute error                    = 1.472208470181210485400818184136             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.81                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4775287943599908262131861895694            
absolute error                    = 1.4775287943599908262131861895694            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.82                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4828508656105112835622118966225            
absolute error                    = 1.4828508656105112835622118966225            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.83                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4881747089163499938547742850858            
absolute error                    = 1.4881747089163499938547742850858            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.84                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4935003492302975210873624902526            
absolute error                    = 1.4935003492302975210873624902526            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1478.0MB, alloc=52.3MB, time=16.85
 
TOP MAIN SOLVE Loop
x[1]                              = 2.85                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.4988278114748820739581963141628            
absolute error                    = 1.4988278114748820739581963141628            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.86                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5041571205428914723270647806729            
absolute error                    = 1.5041571205428914723270647806729            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.87                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5094883012978919003604881123837            
absolute error                    = 1.5094883012978919003604881123837            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.88                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5148213785747434832700979608717            
absolute error                    = 1.5148213785747434832700979608717            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.89                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5201563771801127241284411591119            
absolute error                    = 1.5201563771801127241284411591119            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.9                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5254933218929818368286490983715            
absolute error                    = 1.5254933218929818368286490983715            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.91                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5308322374651550108424851486098            
absolute error                    = 1.5308322374651550108424851486098            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.92                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5361731486217616430250950715393            
absolute error                    = 1.5361731486217616430250950715393            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1520.9MB, alloc=52.3MB, time=17.34
 
TOP MAIN SOLVE Loop
x[1]                              = 2.93                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5415160800617565713142504593088            
absolute error                    = 1.5415160800617565713142504593088            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.94                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5468610564584173447769047884512            
absolute error                    = 1.5468610564584173447769047884512            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.95                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5522081024598385640663891754221            
absolute error                    = 1.5522081024598385640663891754221            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.96                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5575572426894233259694753417018            
absolute error                    = 1.5575572426894233259694753417018            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.97                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5629085017463718053437431162506            
absolute error                    = 1.5629085017463718053437431162506            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.98                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.568261904206167007372126953666             
absolute error                    = 1.568261904206167007372126953666             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 2.99                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5736174746210577226930997913454            
absolute error                    = 1.5736174746210577226930997913454            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3                                            
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5789752375205387176016038753599            
absolute error                    = 1.5789752375205387176016038753599            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1563.9MB, alloc=52.3MB, time=17.82
 
TOP MAIN SOLVE Loop
x[1]                              = 3.01                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5843352174118281911574790959451            
absolute error                    = 1.5843352174118281911574790959451            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.02                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5896974387803425306846933826509            
absolute error                    = 1.5896974387803425306846933826509            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.03                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.5950619260901683967960716332572            
absolute error                    = 1.5950619260901683967960716332572            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.04                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6004287037845321687343756049346            
absolute error                    = 1.6004287037845321687343756049346            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.05                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6057977962862667804814345698015            
absolute error                    = 1.6057977962862667804814345698015            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.06                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6111692279982759777524939681657            
absolute error                    = 1.6111692279982759777524939681657            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.07                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6165430233039960256629666449082            
absolute error                    = 1.6165430233039960256629666449082            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.08                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6219192065678548965292695932837            
absolute error                    = 1.6219192065678548965292695932837            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1606.7MB, alloc=52.3MB, time=18.31
 
TOP MAIN SOLVE Loop
x[1]                              = 3.09                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6272978021357289669443407007118            
absolute error                    = 1.6272978021357289669443407007118            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.1                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6326788343353972529516881945551            
absolute error                    = 1.6326788343353972529516881945551            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.11                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6380623274769932118293648590646            
absolute error                    = 1.6380623274769932118293648590646            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.12                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6434483058534541386870152877064            
absolute error                    = 1.6434483058534541386870152877064            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.13                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6488367937409681857750541905883            
absolute error                    = 1.6488367937409681857750541905883            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.14                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6542278153994190321050349092453            
absolute error                    = 1.6542278153994190321050349092453            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.15                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6596213950728282306842986669589            
absolute error                    = 1.6596213950728282306842986669589            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.16                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6650175569897952603759966005606            
absolute error                    = 1.6650175569897952603759966005606            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1649.7MB, alloc=52.3MB, time=18.80
 
TOP MAIN SOLVE Loop
x[1]                              = 3.17                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.670416325363935309107489190504             
absolute error                    = 1.670416325363935309107489190504             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.18                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6758177243943148148658932349805            
absolute error                    = 1.6758177243943148148658932349805            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.19                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6812217782658847906391078814319            
absolute error                    = 1.6812217782658847906391078814319            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.2                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6866285111499119591839522725752            
absolute error                    = 1.6866285111499119591839522725752            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.21                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6920379472044077232300328610288            
absolute error                    = 1.6920379472044077232300328610288            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.22                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.6974501105745549964585740958589            
absolute error                    = 1.6974501105745549964585740958589            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.23                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7028650253931329203296385897937            
absolute error                    = 1.7028650253931329203296385897937            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.24                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7082827157809394915688795297218            
absolute error                    = 1.7082827157809394915688795297218            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1692.6MB, alloc=52.3MB, time=19.29
 
TOP MAIN SOLVE Loop
x[1]                              = 3.25                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7137032058472121248661573594586            
absolute error                    = 1.7137032058472121248661573594586            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.26                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7191265196900461750829638625455            
absolute error                    = 1.7191265196900461750829638625455            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.27                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7245526813968114430135797640634            
absolute error                    = 1.7245526813968114430135797640634            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.28                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7299817150445666884961977388492            
absolute error                    = 1.7299817150445666884961977388492            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.29                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7354136447004721744248229534655            
absolute error                    = 1.7354136447004721744248229534655            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.3                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7408484944222002649705704700397            
absolute error                    = 1.7408484944222002649705704700397            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.31                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7462862882583441010819662712663            
absolute error                    = 1.7462862882583441010819662712663            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.32                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7517270502488243760979803632216            
absolute error                    = 1.7517270502488243760979803632216            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1735.4MB, alloc=52.3MB, time=19.77
 
TOP MAIN SOLVE Loop
x[1]                              = 3.33                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7571708044252942340747311642351            
absolute error                    = 1.7571708044252942340747311642351            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.34                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7626175748115423131970557205708            
absolute error                    = 1.7626175748115423131970557205708            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.35                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7680673854238939564193964550433            
absolute error                    = 1.7680673854238939564193964550433            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.36                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7735202602716106112566691170673            
absolute error                    = 1.7735202602716106112566691170673            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.37                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.778976223357287440424906025487             
absolute error                    = 1.778976223357287440424906025487             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.38                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.784435298677249164813471929085             
absolute error                    = 1.784435298677249164813471929085             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.39                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.7898975102219441600554858786262            
absolute error                    = 1.7898975102219441600554858786262            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.4                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.795362881976336827750711095635             
absolute error                    = 1.795362881976336827750711095635             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1778.4MB, alloc=52.3MB, time=20.27
 
TOP MAIN SOLVE Loop
x[1]                              = 3.41                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8008314379202982621855562743942            
absolute error                    = 1.8008314379202982621855562743942            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.42                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8063032020289952331879270412473            
absolute error                    = 1.8063032020289952331879270412473            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.43                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8117781982732775055504370231138            
absolute error                    = 1.8117781982732775055504370231138            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.44                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.817256450620063515253896365393             
absolute error                    = 1.817256450620063515253896365393             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.45                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8227379830327244225240044137521            
absolute error                    = 1.8227379830327244225240044137521            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.46                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.828222819471466561557746054939             
absolute error                    = 1.828222819471466561557746054939             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.47                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8337109838937123065620919031158            
absolute error                    = 1.8337109838937123065620919031158            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.48                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8392025002544793735561956984956            
absolute error                    = 1.8392025002544793735561956984956            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1821.3MB, alloc=52.3MB, time=20.87
 
TOP MAIN SOLVE Loop
x[1]                              = 3.49                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8446973925067585771993330961871            
absolute error                    = 1.8446973925067585771993330961871            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.5                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8501956846018900617203001607924            
absolute error                    = 1.8501956846018900617203001607924            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.51                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8556974004899380248398535862023            
absolute error                    = 1.8556974004899380248398535862023            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.52                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8612025641200639533959947044324            
absolute error                    = 1.8612025641200639533959947044324            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.53                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8667111994408983892024430316341            
absolute error                    = 1.8667111994408983892024430316341            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.54                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8722233304009112434934802389811            
absolute error                    = 1.8722233304009112434934802389811            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.55                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8777389809487806781334403532981            
absolute error                    = 1.8777389809487806781334403532981            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.56                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8832581750337605715964455076064            
absolute error                    = 1.8832581750337605715964455076064            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1864.2MB, alloc=52.3MB, time=21.35
 
TOP MAIN SOLVE Loop
x[1]                              = 3.57                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8887809366060465875515079851515            
absolute error                    = 1.8887809366060465875515079851515            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.58                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8943072896171408637198084229891            
absolute error                    = 1.8943072896171408637198084229891            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.59                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.8998372580202153385047871264702            
absolute error                    = 1.8998372580202153385047871264702            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.6                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.90537086577047373273162122217              
absolute error                    = 1.90537086577047373273162122217              
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.61                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9109081368255122036706760285682            
absolute error                    = 1.9109081368255122036706760285682            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.62                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9164490951456786883595861844146            
absolute error                    = 1.9164490951456786883595861844146            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.63                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9219937646944309530807128183418            
absolute error                    = 1.9219937646944309530807128183418            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.64                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9275421694386933656948098774466            
absolute error                    = 1.9275421694386933656948098774466            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1907.1MB, alloc=52.3MB, time=21.84
 
TOP MAIN SOLVE Loop
x[1]                              = 3.65                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9330943333492124073777885906779            
absolute error                    = 1.9330943333492124073777885906779            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.66                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9386502804009109401554672769882            
absolute error                    = 1.9386502804009109401554672769882            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.67                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9442100345732412464811080818478            
absolute error                    = 1.9442100345732412464811080818478            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.68                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.949773619850536856952346906908             
absolute error                    = 1.949773619850536856952346906908             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.69                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9553410602223631821177923518782            
absolute error                    = 1.9553410602223631821177923518782            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.7                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9609123796838669641790788714827            
absolute error                    = 1.9609123796838669641790788714827            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.71                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9664876022361245642514839042829            
absolute error                    = 1.9664876022361245642514839042829            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.72                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9720667518864891007053341725048            
absolute error                    = 1.9720667518864891007053341725048            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1950.0MB, alloc=52.3MB, time=22.33
 
TOP MAIN SOLVE Loop
x[1]                              = 3.73                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9776498526489364539713087724251            
absolute error                    = 1.9776498526489364539713087724251            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.74                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9832369285444101530553725280167            
absolute error                    = 1.9832369285444101530553725280167            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.75                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9888280036011651588734191800305            
absolute error                    = 1.9888280036011651588734191800305            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.76                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 1.9944231018551105593817474949421            
absolute error                    = 1.9944231018551105593817474949421            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.77                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0000222473501511913472118166427            
absolute error                    = 2.0000222473501511913472118166427            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.78                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0056254641385282034702598029371            
absolute error                    = 2.0056254641385282034702598029371            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.79                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0112327762811585754450722788315            
absolute error                    = 2.0112327762811585754450722788315            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.8                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0168442078479736074136318190413            
absolute error                    = 2.0168442078479736074136318190413            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=1993.0MB, alloc=52.3MB, time=22.84
 
TOP MAIN SOLVE Loop
x[1]                              = 3.81                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0224597829182563941447466873114            
absolute error                    = 2.0224597829182563941447466873114            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.82                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0280795255809782981448242730836            
absolute error                    = 2.0280795255809782981448242730836            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.83                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0337034599351344357845026535329            
absolute error                    = 2.0337034599351344357845026535329            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.84                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0393316100900781904040901561925            
absolute error                    = 2.0393316100900781904040901561925            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.85                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0449640001658547662411108928337            
absolute error                    = 2.0449640001658547662411108928337            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.86                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0506006542935337969050895657849            
absolute error                    = 2.0506006542935337969050895657849            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.87                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0562415966155410220080120937521            
absolute error                    = 2.0562415966155410220080120937521            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.88                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0618868512859890454436507342173            
absolute error                    = 2.0618868512859890454436507342173            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2035.8MB, alloc=52.3MB, time=23.32
 
TOP MAIN SOLVE Loop
x[1]                              = 3.89                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0675364424710071886951246463399            
absolute error                    = 2.0675364424710071886951246463399            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.9                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.073190394349070452437660773756             
absolute error                    = 2.073190394349070452437660773756             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.91                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0788487311113275995925073371952            
absolute error                    = 2.0788487311113275995925073371952            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.92                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0845114769619283728783151889368            
absolute error                    = 2.0845114769619283728783151889368            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.93                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0901786561183498597980231370078            
absolute error                    = 2.0901786561183498597980231370078            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.94                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.0958502928117220178923447002778            
absolute error                    = 2.0958502928117220178923447002778            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.95                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1015264112871523729853384669062            
absolute error                    = 2.1015264112871523729853384669062            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.96                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1072070358040499030432354115578            
absolute error                    = 2.1072070358040499030432354115578            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2078.8MB, alloc=52.3MB, time=23.81
 
TOP MAIN SOLVE Loop
x[1]                              = 3.97                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1128921906364481201646775438815            
absolute error                    = 2.1128921906364481201646775438815            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.98                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.118581900073327363118776719179             
absolute error                    = 2.118581900073327363118776719179             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 3.99                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1242761884189363127469141900592            
absolute error                    = 2.1242761884189363127469141900592            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4                                            
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.129975079993112742444954600228             
absolute error                    = 2.129975079993112742444954600228             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.01                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1356785991316035158445269365866            
absolute error                    = 2.1356785991316035158445269365866            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.02                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1413867701863838437152140110406            
absolute error                    = 2.1413867701863838437152140110406            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.03                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1470996175259758120138761121768            
absolute error                    = 2.1470996175259758120138761121768            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.04                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1528171655357661929128985445382            
absolute error                    = 2.1528171655357661929128985445382            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2121.7MB, alloc=52.3MB, time=24.30
 
TOP MAIN SOLVE Loop
x[1]                              = 4.05                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1585394386183235505458820735637            
absolute error                    = 2.1585394386183235505458820735637            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.06                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.164266461193714653117175246236             
absolute error                    = 2.164266461193714653117175246236             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.07                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1699982576998202029306638016627            
absolute error                    = 2.1699982576998202029306638016627            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.08                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1757348525926498958033707709523            
absolute error                    = 2.1757348525926498958033707709523            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.09                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1814762703466568212406674455499            
absolute error                    = 2.1814762703466568212406674455499            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.1                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1872225354550512146622364230366            
absolute error                    = 2.1872225354550512146622364230366            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.11                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1929736724301135728813498731278            
absolute error                    = 2.1929736724301135728813498731278            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.12                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.1987297058035071439545156534076            
absolute error                    = 2.1987297058035071439545156534076            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2164.6MB, alloc=52.3MB, time=24.79
 
TOP MAIN SOLVE Loop
x[1]                              = 4.13                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2044906601265898024340877856797            
absolute error                    = 2.2044906601265898024340877856797            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.14                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2102565599707253209730231103361            
absolute error                    = 2.2102565599707253209730231103361            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.15                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2160274299275940491485798847836            
absolute error                    = 2.2160274299275940491485798847836            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.16                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2218032946095030102903840829214            
absolute error                    = 2.2218032946095030102903840829214            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.17                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2275841786496954270179227666227            
absolute error                    = 2.2275841786496954270179227666227            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.18                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2333701067026596861131488953968            
absolute error                    = 2.2333701067026596861131488953968            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.19                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2391611034444377532754862500195            
absolute error                    = 2.2391611034444377532754862500195            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.2                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2449571935729330482290948751299            
absolute error                    = 2.2449571935729330482290948751299            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2207.5MB, alloc=52.3MB, time=25.27
 
TOP MAIN SOLVE Loop
x[1]                              = 4.21                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2507584018082177905757848692423            
absolute error                    = 2.2507584018082177905757848692423            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.22                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2565647528928398267114379097385            
absolute error                    = 2.2565647528928398267114379097385            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.23                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2623762715921289480492002007956            
absolute error                    = 2.2623762715921289480492002007956            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.24                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2681929826945027107190363411492            
absolute error                    = 2.2681929826945027107190363411492            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.25                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2740149110117717668404698524737            
absolute error                    = 2.2740149110117717668404698524737            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.26                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2798420813794447173934718710925            
absolute error                    = 2.2798420813794447173934718710925            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.27                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2856745186570324966414840230402            
absolute error                    = 2.2856745186570324966414840230402            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.28                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2915122477283522979904641644412            
absolute error                    = 2.2915122477283522979904641644412            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2250.4MB, alloc=52.3MB, time=25.76
 
TOP MAIN SOLVE Loop
x[1]                              = 4.29                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.2973552935018310510986140145185            
absolute error                    = 2.2973552935018310510986140145185            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.3                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3032036809108084599830754233387            
absolute error                    = 2.3032036809108084599830754233387            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.31                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3090574349138396118023569316699            
absolute error                    = 2.3090574349138396118023569316699            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.32                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3149165804949971659265643698751            
absolute error                    = 2.3149165804949971659265643698751            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.33                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3207811426641731328416486209679            
absolute error                    = 2.3207811426641731328416486209679            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.34                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3266511464573802523688405926695            
absolute error                    = 2.3266511464573802523688405926695            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.35                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3325266169370529806162082936735            
absolute error                    = 2.3325266169370529806162082936735            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.36                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3384075791923480950158342137955            
absolute error                    = 2.3384075791923480950158342137955            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2293.4MB, alloc=52.3MB, time=26.25
 
TOP MAIN SOLVE Loop
x[1]                              = 4.37                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3442940583394449267374636218852            
absolute error                    = 2.3442940583394449267374636218852            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.38                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3501860795218452297076067051913            
absolute error                    = 2.3501860795218452297076067051913            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.39                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.356083667910672695401980593384             
absolute error                    = 2.356083667910672695401980593384             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.4                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3619868487049721225188422800755            
absolute error                    = 2.3619868487049721225188422800755            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.41                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3678956471320082505811814392447            
absolute error                    = 2.3678956471320082505811814392447            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.42                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3738100884475642664569044208032            
absolute error                    = 2.3738100884475642664569044208032            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.43                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3797301979362399927280387066376            
absolute error                    = 2.3797301979362399927280387066376            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.44                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3856560009117497667826123427408            
absolute error                    = 2.3856560009117497667826123427408            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2336.2MB, alloc=52.3MB, time=26.74
 
TOP MAIN SOLVE Loop
x[1]                              = 4.45                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3915875227172200194462069784344            
absolute error                    = 2.3915875227172200194462069784344            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.46                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.3975247887254865619142378995162            
absolute error                    = 2.3975247887254865619142378995162            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.47                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4034678243393915896907717113488            
absolute error                    = 2.4034678243393915896907717113488            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.48                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.409416654992080412185144095242             
absolute error                    = 2.409416654992080412185144095242             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.49                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4153713061472979165637784220733            
absolute error                    = 2.4153713061472979165637784220733            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.5                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4213318032996847744014231645952            
absolute error                    = 2.4213318032996847744014231645952            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.51                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4272981719750733996235143149777            
absolute error                    = 2.4272981719750733996235143149777            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.52                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4332704377307836661795208028884            
absolute error                    = 2.4332704377307836661795208028884            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2379.2MB, alloc=52.3MB, time=27.23
 
TOP MAIN SOLVE Loop
x[1]                              = 4.53                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4392486261559183938359387417812            
absolute error                    = 2.4392486261559183938359387417812            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.54                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4452327628716586104270568292346            
absolute error                    = 2.4452327628716586104270568292346            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.55                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4512228735315585988517131142359            
absolute error                    = 2.4512228735315585988517131142359            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.56                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4572189838218407370549954425654            
absolute error                    = 2.4572189838218407370549954425654            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.57                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4632211194616901391851971211259            
absolute error                    = 2.4632211194616901391851971211259            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.58                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4692293062035491060683187198081            
absolute error                    = 2.4692293062035491060683187198081            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.59                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4752435698334113930949995669051            
absolute error                    = 2.4752435698334113930949995669051            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.6                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4812639361711163035679615964524            
absolute error                    = 2.4812639361711163035679615964524            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2422.2MB, alloc=52.3MB, time=27.72
 
TOP MAIN SOLVE Loop
x[1]                              = 4.61                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4872904310706426155118470706448            
absolute error                    = 2.4872904310706426155118470706448            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.62                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4933230804204023499017237160822            
absolute error                    = 2.4933230804204023499017237160822            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.63                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.4993619101435343882215094569569            
absolute error                    = 2.4993619101435343882215094569569            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.64                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.505406946198197947219127767694             
absolute error                    = 2.505406946198197947219127767694             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.65                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5114582145778659186813373551791            
absolute error                    = 2.5114582145778659186813373551791            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.66                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5175157413116180820078801555529            
absolute error                    = 2.5175157413116180820078801555529            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.67                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.523579552464434197321853316026             
absolute error                    = 2.523579552464434197321853316026             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.68                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5296496741374869868110278350187            
absolute error                    = 2.5296496741374869868110278350187            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2465.1MB, alloc=52.3MB, time=28.21
 
TOP MAIN SOLVE Loop
x[1]                              = 4.69                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5357261324684350119532028429067            
absolute error                    = 2.5357261324684350119532028429067            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.7                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.541808953631715454237594190437             
absolute error                    = 2.541808953631715454237594190437             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.71                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.547898163838836806953703221838             
absolute error                    = 2.547898163838836806953703221838             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.72                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5539937893386714855790905727394            
absolute error                    = 2.5539937893386714855790905727394            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.73                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.560095856417748364257984854654             
absolute error                    = 2.560095856417748364257984854654             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.74                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5662043914005452458236815496884            
absolute error                    = 2.5662043914005452458236815496884            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.75                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5723194206497812727792277983363            
absolute error                    = 2.5723194206497812727792277983363            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.76                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5784409705667092866129385508442            
absolute error                    = 2.5784409705667092866129385508442            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2508.1MB, alloc=52.3MB, time=28.70
 
TOP MAIN SOLVE Loop
x[1]                              = 4.77                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5845690675914081427878433729925            
absolute error                    = 2.5845690675914081427878433729925            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.78                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.590703738203074988707215726594             
absolute error                    = 2.590703738203074988707215726594             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.79                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.5968450089203175119218825309615            
absolute error                    = 2.5968450089203175119218825309615            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.8                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6029929063014461658090460715461            
absolute error                    = 2.6029929063014461658090460715461            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.81                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6091474569447663799168677423789            
absolute error                    = 2.6091474569447663799168677423789            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.82                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6153086874888707621340586444939            
absolute error                    = 2.6153086874888707621340586444939            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.83                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6214766246129312998091907348791            
absolute error                    = 2.6214766246129312998091907348791            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.84                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6276512950369915669103791175956            
absolute error                    = 2.6276512950369915669103791175956            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2551.0MB, alloc=52.3MB, time=29.19
 
TOP MAIN SOLVE Loop
x[1]                              = 4.85                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6338327255222589442823863436598            
absolute error                    = 2.6338327255222589442823863436598            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.86                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6400209428713968600250584565784            
absolute error                    = 2.6400209428713968600250584565784            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.87                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6462159739288170569843152669492            
absolute error                    = 2.6462159739288170569843152669492            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.88                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6524178455809718943146793057151            
absolute error                    = 2.6524178455809718943146793057151            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.89                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.658626584756646690040534496617             
absolute error                    = 2.658626584756646690040534496617             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.9                                          
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6648422184272521115119522699861            
absolute error                    = 2.6648422184272521115119522699861            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.91                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6710647736071166206200051381577            
absolute error                    = 2.6710647736071166206200051381577            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.92                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.677294277353778980606001252421             
absolute error                    = 2.677294277353778980606001252421             
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
memory used=2593.9MB, alloc=52.3MB, time=29.68
 
TOP MAIN SOLVE Loop
x[1]                              = 4.93                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6835307567682808312690138058611            
absolute error                    = 2.6835307567682808312690138058611            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.94                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6897742389954593393464420364595            
absolute error                    = 2.6897742389954593393464420364595            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.95                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.6960247512242399308131217778976            
absolute error                    = 2.6960247512242399308131217778976            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.96                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.7022823206879291118156988150444            
absolute error                    = 2.7022823206879291118156988150444            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.97                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.7085469746645073849305835956555            
absolute error                    = 2.7085469746645073849305835956555            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.98                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.7148187404769222674058170522876            
absolute error                    = 2.7148187404769222674058170522876            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
 
TOP MAIN SOLVE Loop
x[1]                              = 4.99                                         
y[1] (closed_form)                = 0                                            
y[1] (numeric)                    = 2.7210976454933814180195903754264            
absolute error                    = 2.7210976454933814180195903754264            
relative error                    = -1                                         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = -16                                 
h                                 = 0.001                                        
Finished!
diff  (  y  ,  x  ,  1  )   =  expt (  ( 0.1  *  x  +  0.2 )   ,   ( 0.2  *  x  +  0.3 )  )  ; 
Iterations                       = 4900                                
Total Elapsed Time               = 30 Seconds
Elapsed Time(since restart)      = 30 Seconds
Time to Timeout                  = 2 Minutes 29 Seconds
Percent Done                     = 100                                        % 
> quit
memory used=2634.3MB, alloc=52.3MB, time=30.12