|\^/|     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_y1 := proc(x)
> return(c(1.0) + cos(c(x)));
> end;
          exact_soln_y1 := proc(x) return c(1.0) + cos(c(x)) end proc

> exact_soln_y2 := proc(x)
> return(c(1.0) + sin(c(x)));
> end;
          exact_soln_y2 := proc(x) return c(1.0) + sin(c(x)) end proc

#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
>     local rad_given;
>     global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 1
>         rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) +  array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
>         omniout_float(ALWAYS,"Radius of convergence (given) for eq  1           ",4,rad_given,4," ");
>         omniout_float(ALWAYS,"Order of pole (given)                             ",4,array_given_ord_poles[1,1],4," ");
>         if (rad_given < glob_least_given_sing)  then # if number 2
>             glob_least_given_sing :=  rad_given;
>         fi;# end if 2;
>     elif
>     (glob_type_given_pole = 3) then # if number 2
>         omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
>     elif
>     (glob_type_given_pole = 5) then # if number 3
>         omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
>     else
>         omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
>     fi;# end if 3;
>     if (array_rad_test_poles[1,1] < glob_large_float)  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq  1      ",4,array_rad_test_poles[1,1],4," ");
>         if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
>             glob_least_ratio_sing := array_rad_test_poles[1,1];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (ratio test)                        ",4, array_ord_test_poles[1,1],4," ");
>     else
>         omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
>     fi;# end if 3;
>     if ((array_rad_test_poles[1,2] >  glob__small) and (array_rad_test_poles[1,2] < glob_large_float))  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1  ",4,array_rad_test_poles[1,2],4," ");
>         if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
>             glob_least_3_sing := array_rad_test_poles[1,2];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (three term test)                   ",4, array_ord_test_poles[1,2],4," ");
>     else
>         omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
>     fi;# end if 3;
>     if ((array_rad_test_poles[1,3] >  glob__small) and (array_rad_test_poles[1,3] < glob_large_float))  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1    ",4,array_rad_test_poles[1,3],4," ");
>         if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
>             glob_least_6_sing := array_rad_test_poles[1,3];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (six term test)                     ",4, array_ord_test_poles[1,3],4," ");
>     else
>         omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
>     fi;# end if 3
>     ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 3
>         rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) +  array_given_rad_poles[2,2] * array_given_rad_poles[2,2]);
>         omniout_float(ALWAYS,"Radius of convergence (given) for eq  2           ",4,rad_given,4," ");
>         omniout_float(ALWAYS,"Order of pole (given)                             ",4,array_given_ord_poles[2,1],4," ");
>         if (rad_given < glob_least_given_sing)  then # if number 4
>             glob_least_given_sing :=  rad_given;
>         fi;# end if 4;
>     elif
>     (glob_type_given_pole = 3) then # if number 4
>         omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
>     elif
>     (glob_type_given_pole = 5) then # if number 5
>         omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
>     else
>         omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
>     fi;# end if 5;
>     if (array_rad_test_poles[2,1] < glob_large_float)  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq  2      ",4,array_rad_test_poles[2,1],4," ");
>         if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6
>             glob_least_ratio_sing := array_rad_test_poles[2,1];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (ratio test)                        ",4, array_ord_test_poles[2,1],4," ");
>     else
>         omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
>     fi;# end if 5;
>     if ((array_rad_test_poles[2,2] >  glob__small) and (array_rad_test_poles[2,2] < glob_large_float))  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2  ",4,array_rad_test_poles[2,2],4," ");
>         if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6
>             glob_least_3_sing := array_rad_test_poles[2,2];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (three term test)                   ",4, array_ord_test_poles[2,2],4," ");
>     else
>         omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
>     fi;# end if 5;
>     if ((array_rad_test_poles[2,3] >  glob__small) and (array_rad_test_poles[2,3] < glob_large_float))  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2    ",4,array_rad_test_poles[2,3],4," ");
>         if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6
>             glob_least_6_sing := array_rad_test_poles[2,3];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (six term test)                     ",4, array_ord_test_poles[2,3],4," ");
>     else
>         omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
>     fi;# end if 5
>     ;
> 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;
    if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
        rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])*
            (array_x[1] - array_given_rad_poles[2, 1])
             + array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]);
        omniout_float(ALWAYS,
            "Radius of convergence (given) for eq  2           ", 4,
            rad_given, 4, " ");
        omniout_float(ALWAYS,
            "Order of pole (given)                             ", 4,
            array_given_ord_poles[2, 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 2")
    elif glob_type_given_pole = 5 then
        omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
    else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
    end if;
    if array_rad_test_poles[2, 1] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (ratio test) for eq  2      ", 4,
            array_rad_test_poles[2, 1], 4, " ");
        if array_rad_test_poles[2, 1] < glob_least_ratio_sing then
            glob_least_ratio_sing := array_rad_test_poles[2, 1]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (ratio test)                        ", 4,
            array_ord_test_poles[2, 1], 4, " ")
    else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
    end if;
    if glob__small < array_rad_test_poles[2, 2] and
    array_rad_test_poles[2, 2] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (three term test) for eq 2  ", 4,
            array_rad_test_poles[2, 2], 4, " ");
        if array_rad_test_poles[2, 2] < glob_least_3_sing then
            glob_least_3_sing := array_rad_test_poles[2, 2]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (three term test)                   ", 4,
            array_ord_test_poles[2, 2], 4, " ")
    else omniout_str(ALWAYS,
        "NO REAL POLE (three term test) for Equation 2")
    end if;
    if glob__small < array_rad_test_poles[2, 3] and
    array_rad_test_poles[2, 3] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (six term test) for eq 2    ", 4,
            array_rad_test_poles[2, 3], 4, " ");
        if array_rad_test_poles[2, 3] < glob_least_6_sing then
            glob_least_6_sing := array_rad_test_poles[2, 3]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (six term test)                     ", 4,
            array_ord_test_poles[2, 3], 4, " ")
    else omniout_str(ALWAYS,
        "NO COMPLEX POLE (six term test) for Equation 2")
    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 5
>         ret := glob__1;
>     else
>         ret := glob__m1;
>     fi;# end if 5;
>     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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[1]) < min_size) then # if number 5
>         min_size := float_abs(array_y1[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     if (float_abs(array_y2[1]) < min_size) then # if number 5
>         min_size := float_abs(array_y2[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     if (min_size < glob__1) then # if number 5
>         min_size := glob__1;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[1]) < min_size then
        min_size := float_abs(array_y1[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if float_abs(array_y2[1]) < min_size then
        min_size := float_abs(array_y2[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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 5
>         max_estimated_step_error := est_tmp;
>     fi;# end if 5;
>     est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 5
>         max_estimated_step_error := est_tmp;
>     fi;# end if 5;
>     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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[no_terms - 3]
         + array_y1[no_terms - 2]*hn_div_ho
         + array_y1[no_terms - 1]*hn_div_ho_2
         + array_y1[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    est_tmp := float_abs(array_y2[no_terms - 3]
         + array_y2[no_terms - 2]*hn_div_ho
         + array_y2[no_terms - 1]*hn_div_ho_2
         + array_y2[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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
>     fi;# end if 5;
>     if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
>         array_max_est_error[1] := c(est_tmp);
>     fi;# end if 5
>     ;
>     est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
>     fi;# end if 5;
>     if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
>         array_max_est_error[2] := c(est_tmp);
>     fi;# end if 5
>     ;
> 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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[no_terms - 3]))
         + c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
    end if;
    if c(array_max_est_error[1]) <= c(est_tmp) then
        array_max_est_error[1] := c(est_tmp)
    end if;
    est_tmp := c(float_abs(array_y2[no_terms - 3]))
         + c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
    end if;
    if c(array_max_est_error[2]) <= c(est_tmp) then
        array_max_est_error[2] := 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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 5;
>     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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
>         if (iter >= 0)  then # if number 6
>             ind_var := array_x[1];
>             omniout_float(ALWAYS,"x[1]                             ",33,ind_var,20," ");
>             closed_form_val_y := evalf(exact_soln_y1(ind_var));
>             omniout_float(ALWAYS,"y1[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y1[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y1[1] (numeric)                  ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 7
>                 relerr := abserr*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 8
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 7;
>             if (glob_good_digits < glob_min_good_digits) then # if number 7
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 7;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 7;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 7
>                 est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*33*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 8
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[1] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 7
>                 array_1st_rel_error[1] := relerr;
>             else
>                 array_last_rel_error[1] := relerr;
>             fi;# end if 7;
>             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," ");
>             ;
>             closed_form_val_y := evalf(exact_soln_y2(ind_var));
>             omniout_float(ALWAYS,"y2[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y2[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y2[1] (numeric)                  ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 7
>                 relerr := abserr*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 8
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 7;
>             if (glob_good_digits < glob_min_good_digits) then # if number 7
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 7;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 7;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 7
>                 est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*33*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 8
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[2] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 7
>                 array_1st_rel_error[2] := relerr;
>             else
>                 array_last_rel_error[2] := relerr;
>             fi;# end if 7;
>             array_est_rel_error[2] := 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 6;
>         #BOTTOM DISPLAY ALOT
>     fi;# end if 5;
> 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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1(ind_var));
            omniout_float(ALWAYS, "y1[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y1[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y1[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)*33*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, " ");
            closed_form_val_y := evalf(exact_soln_y2(ind_var));
            omniout_float(ALWAYS, "y2[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y2[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y2[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[2]*100.0*
                    sqrt(glob_iter)*33*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[2] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[2] := relerr
            else array_last_rel_error[2] := relerr
            end if;
            array_est_rel_error[2] := 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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
>         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 5;
>     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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1_higher[1,last_no-1],array_y1_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[1,1]) then # if number 8
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_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 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[2,1] :=  glob_larger_float;
>     array_ord_test_poles[2,1] :=  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_y2_higher[1,last_no-1],array_y2_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[2,1]) then # if number 10
>             array_rad_test_poles[2,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[2,1] := rad_c;
>             array_ord_test_poles[2,1] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test2
>     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_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 9;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 10
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 11
>             found_sing := 0;
>         fi;# end if 11;
>         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 11
>         if (rad_c  < array_rad_test_poles[1,2]) then # if number 12
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 13
>                 glob_min_pole_est := rad_c;
>             fi;# end if 13;
>             array_ord_test_poles[1,2] := tmp_ord;
>         fi;# end if 12;
>     fi;# end if 11;
>     #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[2,2] :=  glob_larger_float;
>     array_ord_test_poles[2,2] :=  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_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 11;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 12
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 13
>             found_sing := 0;
>         fi;# end if 13;
>         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 13
>         if (rad_c  < array_rad_test_poles[2,2]) then # if number 14
>             array_rad_test_poles[2,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[2,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 15
>                 glob_min_pole_est := rad_c;
>             fi;# end if 15;
>             array_ord_test_poles[2,2] := tmp_ord;
>         fi;# end if 14;
>     fi;# end if 13;
>     #BOTTOM general radius test2
>     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_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 13;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 14
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 15
>             found_sing := 0;
>         fi;# end if 15;
>         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 15
>         if (rad_c  < array_rad_test_poles[1,3]) then # if number 16
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 17
>                 glob_min_pole_est := rad_c;
>             fi;# end if 17;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 16;
>     fi;# end if 15;
>     #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[2,3] :=  glob_larger_float;
>     array_ord_test_poles[2,3] :=  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_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 15;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 16
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 17
>             found_sing := 0;
>         fi;# end if 17;
>         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 17
>         if (rad_c  < array_rad_test_poles[2,3]) then # if number 18
>             array_rad_test_poles[2,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[2,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 19
>                 glob_min_pole_est := rad_c;
>             fi;# end if 19;
>             array_ord_test_poles[2,3] := tmp_ord;
>         fi;# end if 18;
>     fi;# end if 17;
>     #BOTTOM general radius test2
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
>         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 18
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 18;
>         term := 1;
>         ratio := c(1.0);
>         while (term <= ATS_MAX_TERMS)  do # do number 1
>             array_y1[term] := array_y1[term]* ratio;
>             array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             array_y2[term] := array_y2[term]* ratio;
>             array_y2_higher[1,term] := array_y2_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 17;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 17
>         display_poles();
>     fi;# end if 17
> 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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1_higher[1, last_no - 1],
            array_y1_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_y1_higher[1, last_no - 1],
                array_y1_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[2, 1] := glob_larger_float;
    array_ord_test_poles[2, 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_y2_higher[1, last_no - 1],
            array_y2_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[2, 1] then
            array_rad_test_poles[2, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[2, 1] := rad_c;
            array_ord_test_poles[2, 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_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 2],
                array_y1_higher[1, last_no - 1],
                array_y1_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[2, 2] := glob_larger_float;
    array_ord_test_poles[2, 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_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_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[2, 2] then
            array_rad_test_poles[2, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y2_higher[1, last_no - 2],
                array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[2, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 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_y1_higher[1, last_no - 5],
            array_y1_higher[1, last_no - 4],
            array_y1_higher[1, last_no - 3],
            array_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 5],
                array_y1_higher[1, last_no - 4],
                array_y1_higher[1, last_no - 3],
                array_y1_higher[1, last_no - 2],
                array_y1_higher[1, last_no - 1],
                array_y1_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;
    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[2, 3] := glob_larger_float;
    array_ord_test_poles[2, 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_y2_higher[1, last_no - 5],
            array_y2_higher[1, last_no - 4],
            array_y2_higher[1, last_no - 3],
            array_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_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[2, 3] then
            array_rad_test_poles[2, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y2_higher[1, last_no - 5],
                array_y2_higher[1, last_no - 4],
                array_y2_higher[1, last_no - 3],
                array_y2_higher[1, last_no - 2],
                array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[2, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 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_y1[term] := array_y1[term]*ratio;
            array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            array_y2[term] := array_y2[term]*ratio;
            array_y2_higher[1, term] := array_y2_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_1D0,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre neg FULL $eq_no = 1
>     array_tmp1[1] :=  neg(array_y2[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
>     #emit pre add FULL - CONST $eq_no = 1 i = 1
>     array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,2]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[2] := temporary;
>                 array_y1_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y1_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #emit pre sub FULL - CONST $eq_no = 2 i = 1
>     array_tmp5[1] := array_y1[1] - array_const_1D0[1];
>     #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,2]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[2] := temporary;
>                 array_y2_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y2_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre neg FULL $eq_no = 1
>     array_tmp1[2] :=  neg(array_y2[2]);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre add FULL CONST $eq_no = 1 i = 2
>     array_tmp3[2] := array_tmp2[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,3]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[3] := temporary;
>                 array_y1_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y1_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #emit pre sub FULL CONST $eq_no = 2 i = 2
>     array_tmp5[2] := array_y1[2];
>     #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,3]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[3] := temporary;
>                 array_y2_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y2_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre neg FULL $eq_no = 1
>     array_tmp1[3] :=  neg(array_y2[3]);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp2[3] := array_tmp1[3];
>     #emit pre add FULL CONST $eq_no = 1 i = 3
>     array_tmp3[3] := array_tmp2[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[4] := temporary;
>                 array_y1_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y1_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #emit pre sub FULL CONST $eq_no = 2 i = 3
>     array_tmp5[3] := array_y1[3];
>     #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[4] := temporary;
>                 array_y2_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre neg FULL $eq_no = 1
>     array_tmp1[4] :=  neg(array_y2[4]);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp2[4] := array_tmp1[4];
>     #emit pre add FULL CONST $eq_no = 1 i = 4
>     array_tmp3[4] := array_tmp2[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[5] := temporary;
>                 array_y1_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y1_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #emit pre sub FULL CONST $eq_no = 2 i = 4
>     array_tmp5[4] := array_y1[4];
>     #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[5] := temporary;
>                 array_y2_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre neg FULL $eq_no = 1
>     array_tmp1[5] :=  neg(array_y2[5]);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp2[5] := array_tmp1[5];
>     #emit pre add FULL CONST $eq_no = 1 i = 5
>     array_tmp3[5] := array_tmp2[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[6] := temporary;
>                 array_y1_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y1_higher[2,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #emit pre sub FULL CONST $eq_no = 2 i = 5
>     array_tmp5[5] := array_y1[5];
>     #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[6] := temporary;
>                 array_y2_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_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 neg FULL $eq_no = 1
>         array_tmp1[kkk] := neg(array_y2[kkk]);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp2[kkk] := array_tmp1[kkk];
>         #emit FULL - NOT FULL add $eq_no = 1
>         array_tmp3[kkk] := array_tmp2[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y1_set_initial[1,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y1[kkk + order_d] := c(temporary);
>                 array_y1_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_y1_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;
>         #emit FULL - NOT FULL sub $eq_no = 2
>         array_tmp5[kkk] := array_y1[kkk];
>         #emit assign $eq_no = 2
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y2_set_initial[2,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y2[kkk + order_d] := c(temporary);
>                 array_y2_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_y2_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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    array_tmp1[1] := neg(array_y2[1]);
    array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
    array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
    if not array_y1_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y1[2] := temporary;
                array_y1_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y1_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp5[1] := array_y1[1] - array_const_1D0[1];
    if not array_y2_set_initial[2, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y2[2] := temporary;
                array_y2_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y2_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := neg(array_y2[2]);
    array_tmp2[2] := array_tmp1[2];
    array_tmp3[2] := array_tmp2[2];
    if not array_y1_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y1[3] := temporary;
                array_y1_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y1_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp5[2] := array_y1[2];
    if not array_y2_set_initial[2, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y2[3] := temporary;
                array_y2_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y2_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp1[3] := neg(array_y2[3]);
    array_tmp2[3] := array_tmp1[3];
    array_tmp3[3] := array_tmp2[3];
    if not array_y1_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y1[4] := temporary;
                array_y1_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y1_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp5[3] := array_y1[3];
    if not array_y2_set_initial[2, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y2[4] := temporary;
                array_y2_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp1[4] := neg(array_y2[4]);
    array_tmp2[4] := array_tmp1[4];
    array_tmp3[4] := array_tmp2[4];
    if not array_y1_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y1[5] := temporary;
                array_y1_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y1_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp5[4] := array_y1[4];
    if not array_y2_set_initial[2, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y2[5] := temporary;
                array_y2_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp1[5] := neg(array_y2[5]);
    array_tmp2[5] := array_tmp1[5];
    array_tmp3[5] := array_tmp2[5];
    if not array_y1_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y1[6] := temporary;
                array_y1_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y1_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    array_tmp5[5] := array_y1[5];
    if not array_y2_set_initial[2, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y2[6] := temporary;
                array_y2_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp1[kkk] := neg(array_y2[kkk]);
        array_tmp2[kkk] := array_tmp1[kkk];
        array_tmp3[kkk] := array_tmp2[kkk];
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y1_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y1[kkk + order_d] := c(temporary);
                array_y1_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_y1_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        array_tmp5[kkk] := array_y1[kkk];
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y2_set_initial[2, kkk + order_d] then
                temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y2[kkk + order_d] := c(temporary);
                array_y2_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_y2_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_1D0,
>     #END CONST
>     array_y1_init,
>     array_y2_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_y1,
>     array_x,
>     array_y2,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_m1,
>     array_y1_higher,
>     array_y1_higher_work,
>     array_y1_higher_work2,
>     array_y1_set_initial,
>     array_y2_higher,
>     array_y2_higher_work,
>     array_y2_higher_work2,
>     array_y2_set_initial,
>     array_given_rad_poles,
>     array_given_ord_poles,
>     array_rad_test_poles,
>     array_ord_test_poles,
>     array_fact_2,
>     ATS_MAX_TERMS,
>     glob_last;
>     ATS_MAX_TERMS := 40;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=40;
>     #END BLOCK 1
>     #END FIRST INPUT BLOCK
>     #START OF INITS AFTER INPUT BLOCK
>     glob_html_log := true;
>     #END OF INITS AFTER INPUT BLOCK
>     # before generate arrays
>     array_y1_init:= Array(0..(40),[]);
>     array_y2_init:= Array(0..(40),[]);
>     array_norms:= Array(0..(40),[]);
>     array_fact_1:= Array(0..(40),[]);
>     array_1st_rel_error:= Array(0..(3),[]);
>     array_last_rel_error:= Array(0..(3),[]);
>     array_est_rel_error:= Array(0..(3),[]);
>     array_max_est_error:= Array(0..(3),[]);
>     array_type_pole:= Array(0..(3),[]);
>     array_type_real_pole:= Array(0..(3),[]);
>     array_type_complex_pole:= Array(0..(3),[]);
>     array_est_digits:= Array(0..(3),[]);
>     array_y1:= Array(0..(40),[]);
>     array_x:= Array(0..(40),[]);
>     array_y2:= Array(0..(40),[]);
>     array_tmp0:= Array(0..(40),[]);
>     array_tmp1:= Array(0..(40),[]);
>     array_tmp2:= Array(0..(40),[]);
>     array_tmp3:= Array(0..(40),[]);
>     array_tmp4:= Array(0..(40),[]);
>     array_tmp5:= Array(0..(40),[]);
>     array_m1:= Array(0..(40),[]);
>     array_y1_higher := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
>     array_y2_higher := Array(0..(2) ,(0..40+ 1),[]);
>     array_y2_higher_work := Array(0..(2) ,(0..40+ 1),[]);
>     array_y2_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
>     array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]);
>     array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
>     array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
>     array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
>     array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
>     array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
>     # before generate constants
>     # before generate globals definition
>     #Top Generate Globals Definition
>     #Bottom Generate Globals Deninition
>     # before generate const definition
>     # before arrays initialized
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y1_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y2_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_fact_1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_1st_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_last_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_est_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_max_est_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_real_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_complex_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_est_digits[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp5[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_m1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_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 <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_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 <= 40) do # do number 2
>             array_y2_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_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 <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_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 <=3) 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 <=3) 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 <=3) 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 <=3) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_ord_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=40) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y1);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_y2);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5);
>     zero_ats_ar(array_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_1D0);
>     array_const_1D0[1]   := c(1.0);
>     zero_ats_ar(array_m1);
>     array_m1[1]   := glob__m1;
>     #END SYMBOLS INITIALIZATED
>     # before generate factorials init
>     #Initing Factorial Tables
>     iiif := 0;
>     while (iiif <= ATS_MAX_TERMS) do # do number 1
>         jjjf := 0;
>         while (jjjf <= ATS_MAX_TERMS) do # do number 2
>             array_fact_1[iiif] := 0;
>             array_fact_2[iiif,jjjf] := 0;
>             jjjf := jjjf + 1;
>         od;# end do number 2;
>         iiif := iiif + 1;
>     od;# end do number 1;
>     #Done Initing Factorial Table
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     glob_iolevel := 5;
>     glob_yes_pole := 4;
>     glob_no_pole := 3;
>     glob_not_given := 0;
>     glob_no_sing_tests := 4;
>     glob_ratio_test := 1;
>     glob_three_term_test := 2;
>     glob_six_term_test := 3;
>     glob_log_10 := log(c(10.0));
>     MAX_UNCHANGED := 10;
>     glob__small := c(0.1e-50);
>     glob_small_float := c(0.1e-50);
>     glob_smallish_float := c(0.1e-60);
>     glob_large_float := c(1.0e100);
>     glob_larger_float := c(1.1e100);
>     glob__m2 := c(-2);
>     glob__m1 := c(-1);
>     glob__0 := c(0);
>     glob__1 := c(1);
>     glob__2 := c(2);
>     glob__3 := c(3);
>     glob__4 := c(4);
>     glob__5 := c(5);
>     glob__8 := c(8);
>     glob__10 := c(10);
>     glob__100 := c(100);
>     glob__pi := c(0.0);
>     glob__0_5 := c(0.5);
>     glob__0_8 := c(0.8);
>     glob__m0_8 := c(-0.8);
>     glob__0_25 := c(0.25);
>     glob__0_125 := c(0.125);
>     glob_prec := c(1.0e-16);
>     glob_check_sign := c(1.0);
>     glob_desired_digits_correct := c(8.0);
>     glob_max_estimated_step_error := c(0.0);
>     glob_ratio_of_radius := c(0.1);
>     glob_percent_done := c(0.0);
>     glob_total_exp_sec := c(0.1);
>     glob_optimal_expect_sec := c(0.1);
>     glob_estimated_size_answer := c(100.0);
>     glob_almost_1 := c(0.9990);
>     glob_clock_sec := c(0.0);
>     glob_clock_start_sec := c(0.0);
>     glob_disp_incr := c(0.1);
>     glob_h := c(0.1);
>     glob_diff_rc_fm := c(0.1);
>     glob_diff_rc_fmm1 := c(0.1);
>     glob_diff_rc_fmm2 := c(0.1);
>     glob_diff_ord_fm := c(0.1);
>     glob_diff_ord_fmm1 := c(0.1);
>     glob_diff_ord_fmm2 := c(0.1);
>     glob_six_term_ord_save := c(0.1);
>     glob_guess_error_rc := c(0.1);
>     glob_guess_error_ord := c(0.1);
>     glob_least_given_sing := c(9.9e200);
>     glob_least_ratio_sing := c(9.9e200);
>     glob_least_3_sing := c(9.9e100);
>     glob_least_6_sing := c(9.9e100);
>     glob_last_good_h := c(0.1);
>     glob_max_h := c(0.1);
>     glob_min_h := c(0.000001);
>     glob_display_interval := c(0.1);
>     glob_abserr := c(0.1e-10);
>     glob_relerr := c(0.1e-10);
>     glob_min_pole_est := c(0.1e+10);
>     glob_max_rel_trunc_err := c(0.1e-10);
>     glob_max_trunc_err := c(0.1e-10);
>     glob_max_hours := c(0.0);
>     glob_optimal_clock_start_sec := c(0.0);
>     glob_optimal_start := c(0.0);
>     glob_upper_ratio_limit := c(1.0001);
>     glob_lower_ratio_limit := c(0.9999);
>     glob_max_sec := c(10000.0);
>     glob_orig_start_sec := c(0.0);
>     glob_normmax := c(0.0);
>     glob_max_minutes := c(0.0);
>     glob_next_display := c(0.0);
>     glob_est_digits := 1;
>     glob_subiter_method := 3;
>     glob_html_log := true;
>     glob_min_good_digits := 99999;
>     glob_good_digits := 0;
>     glob_min_apfp_est_good_digits := 99999;
>     glob_apfp_est_good_digits := 0;
>     glob_max_opt_iter := 10;
>     glob_dump := false;
>     glob_djd_debug := true;
>     glob_display_flag := true;
>     glob_djd_debug2 := true;
>     glob_h_reason := 0;
>     glob_sec_in_minute := 60 ;
>     glob_min_in_hour := 60;
>     glob_hours_in_day := 24;
>     glob_days_in_year := 365;
>     glob_sec_in_hour := 3600;
>     glob_sec_in_day := 86400;
>     glob_sec_in_year := 31536000;
>     glob_not_yet_finished := true;
>     glob_initial_pass := true;
>     glob_not_yet_start_msg := true;
>     glob_reached_optimal_h := false;
>     glob_optimal_done := false;
>     glob_type_given_pole := 0;
>     glob_optimize := false;
>     glob_look_poles := false;
>     glob_dump_closed_form := false;
>     glob_max_iter := 1000;
>     glob_no_eqs := 0;
>     glob_unchanged_h_cnt := 0;
>     glob_warned := false;
>     glob_warned2 := false;
>     glob_start := 0;
>     glob_iter := 0;
>     # before generate set diff initial
>     array_y1_set_initial[1,1] := true;
>     array_y1_set_initial[1,2] := false;
>     array_y1_set_initial[1,3] := false;
>     array_y1_set_initial[1,4] := false;
>     array_y1_set_initial[1,5] := false;
>     array_y1_set_initial[1,6] := false;
>     array_y1_set_initial[1,7] := false;
>     array_y1_set_initial[1,8] := false;
>     array_y1_set_initial[1,9] := false;
>     array_y1_set_initial[1,10] := false;
>     array_y1_set_initial[1,11] := false;
>     array_y1_set_initial[1,12] := false;
>     array_y1_set_initial[1,13] := false;
>     array_y1_set_initial[1,14] := false;
>     array_y1_set_initial[1,15] := false;
>     array_y1_set_initial[1,16] := false;
>     array_y1_set_initial[1,17] := false;
>     array_y1_set_initial[1,18] := false;
>     array_y1_set_initial[1,19] := false;
>     array_y1_set_initial[1,20] := false;
>     array_y1_set_initial[1,21] := false;
>     array_y1_set_initial[1,22] := false;
>     array_y1_set_initial[1,23] := false;
>     array_y1_set_initial[1,24] := false;
>     array_y1_set_initial[1,25] := false;
>     array_y1_set_initial[1,26] := false;
>     array_y1_set_initial[1,27] := false;
>     array_y1_set_initial[1,28] := false;
>     array_y1_set_initial[1,29] := false;
>     array_y1_set_initial[1,30] := false;
>     array_y1_set_initial[1,31] := false;
>     array_y1_set_initial[1,32] := false;
>     array_y1_set_initial[1,33] := false;
>     array_y1_set_initial[1,34] := false;
>     array_y1_set_initial[1,35] := false;
>     array_y1_set_initial[1,36] := false;
>     array_y1_set_initial[1,37] := false;
>     array_y1_set_initial[1,38] := false;
>     array_y1_set_initial[1,39] := false;
>     array_y1_set_initial[1,40] := false;
>     array_y2_set_initial[2,1] := true;
>     array_y2_set_initial[2,2] := false;
>     array_y2_set_initial[2,3] := false;
>     array_y2_set_initial[2,4] := false;
>     array_y2_set_initial[2,5] := false;
>     array_y2_set_initial[2,6] := false;
>     array_y2_set_initial[2,7] := false;
>     array_y2_set_initial[2,8] := false;
>     array_y2_set_initial[2,9] := false;
>     array_y2_set_initial[2,10] := false;
>     array_y2_set_initial[2,11] := false;
>     array_y2_set_initial[2,12] := false;
>     array_y2_set_initial[2,13] := false;
>     array_y2_set_initial[2,14] := false;
>     array_y2_set_initial[2,15] := false;
>     array_y2_set_initial[2,16] := false;
>     array_y2_set_initial[2,17] := false;
>     array_y2_set_initial[2,18] := false;
>     array_y2_set_initial[2,19] := false;
>     array_y2_set_initial[2,20] := false;
>     array_y2_set_initial[2,21] := false;
>     array_y2_set_initial[2,22] := false;
>     array_y2_set_initial[2,23] := false;
>     array_y2_set_initial[2,24] := false;
>     array_y2_set_initial[2,25] := false;
>     array_y2_set_initial[2,26] := false;
>     array_y2_set_initial[2,27] := false;
>     array_y2_set_initial[2,28] := false;
>     array_y2_set_initial[2,29] := false;
>     array_y2_set_initial[2,30] := false;
>     array_y2_set_initial[2,31] := false;
>     array_y2_set_initial[2,32] := false;
>     array_y2_set_initial[2,33] := false;
>     array_y2_set_initial[2,34] := false;
>     array_y2_set_initial[2,35] := false;
>     array_y2_set_initial[2,36] := false;
>     array_y2_set_initial[2,37] := false;
>     array_y2_set_initial[2,38] := false;
>     array_y2_set_initial[2,39] := false;
>     array_y2_set_initial[2,40] := false;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 40;
>     glob_iolevel := INFO;
>     # set default block
>     #Write Set Defaults
>     glob_orig_start_sec   :=  elapsed_time_seconds();
>     glob_display_flag   :=   true;
>     glob_no_eqs   := 2;
>     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/mtest1postode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; ");
>     omniout_str(ALWAYS,"diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=40;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(0.1);");
>     omniout_str(ALWAYS,"x_end := c(10.0);");
>     omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
>     omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 3;");
>     omniout_str(ALWAYS,"#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_y1 := proc(x)");
>     omniout_str(ALWAYS,"return(c(1.0) + cos(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
>     omniout_str(ALWAYS,"return(c(1.0) + sin(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(0.1);
>     x_end := c(10.0);
>     array_y1_init[0 + 1] := exact_soln_y1(x_start);
>     array_y2_init[0 + 1] := exact_soln_y2(x_start);
>     glob_look_poles := true;
>     glob_type_given_pole := 3;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=8;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=3;
>     glob_max_iter:=100000;
>     glob_upper_ratio_limit:=c(1.000001);
>     glob_lower_ratio_limit:=c(0.999999);
>     glob_look_poles:=false;
>     glob_h:=c(0.001);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(x_start,x_end));
>     glob__pi := arccos(glob__m1);
>     glob_prec = expt(10.0,c(-Digits));
>     if (glob_optimize)  then # if number 17
>         #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 18
>             glob_display_interval := c(display_max);
>         fi;# end if 18;
>         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_y1
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y1[term_no] := array_y1_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 18
>                         array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 18;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             order_diff := 1;
>             #Start Series array_y2
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y2[term_no] := array_y2_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 18
>                         array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 18;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             if (glob_subiter_method  =  1 ) then # if number 18
>                 atomall();
>             elif
>             (glob_subiter_method  =  2 ) then # if number 19
>                 subiter := 1;
>                 while (subiter <= 2) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 2 + ATS_MAX_TERMS) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             fi;# end if 19;
>             if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19
>                 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 19;
>             if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19
>                 omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>                 glob_h_reason := 2;
>                 glob_h := glob_display_interval;
>                 found_h := true;
>             fi;# end if 19;
>             if (glob_look_poles)  then # if number 19
>                 check_for_pole();
>             fi;# end if 19;
>             if ( not found_h) then # if number 19
>                 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 20
>                     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 20;
>             fi;# end if 19;
>             opt_iter := opt_iter + 1;
>         od;# end do number 1;
>         if (( not found_h) and (opt_iter = 1)) then # if number 19
>             omniout_str(ALWAYS,"Beginning glob_h too large.");
>             found_h := false;
>         fi;# end if 19;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19
>             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 19;
>     else
>         found_h := true;
>         glob_h := glob_h * glob_check_sign;
>     fi;# end if 18;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 18
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 18;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 18
>         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_y1
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y1[term_no] := array_y1_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 19
>                     array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 19;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         order_diff := 1;
>         #Start Series array_y2
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y2[term_no] := array_y2_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 19
>                     array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 19;
>                 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 19
>                 omniout_str(INFO," ");
>                 omniout_str(INFO,"TOP MAIN SOLVE Loop");
>             fi;# end if 19;
>             glob_iter   :=  glob_iter + 1;
>             glob_clock_sec   := elapsed_time_seconds();
>             track_estimated_error();
>             if (glob_subiter_method  =  1 ) then # if number 19
>                 atomall();
>             elif
>             (glob_subiter_method  =  2 ) then # if number 20
>                 subiter := 1;
>                 while (subiter <= 2) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 2 + ATS_MAX_TERMS) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             fi;# end if 20;
>             track_estimated_error();
>             display_alot(current_iter);
>             if (glob_look_poles)  then # if number 20
>                 check_for_pole();
>             fi;# end if 20;
>             if (reached_interval()) then # if number 20
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 20;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y1;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[2,iii] := array_y1_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_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_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_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_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_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_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_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_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_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y1_higher[ord,term_no] := array_y1_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
>             #Jump Series array_y2;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =2
>             #sum_and_adjust array_y2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_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 =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_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 =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_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 =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #END SUM AND ADJUST EQ =2
>             #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_y2[term_no] := array_y2_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y2_higher[ord,term_no] := array_y2_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 20
>             omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
>         fi;# end if 20;
>         if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec  )) then # if number 20
>             omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
>         fi;# end if 20;
>         glob_clock_sec   := elapsed_time_seconds();
>         omniout_str(INFO,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; ");
>         omniout_str(INFO,"diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(x_start,x_end);
>         if (glob_html_log)  then # if number 20
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2016-08-26T16:39:08-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"mtest1.ode.txt\">mtest1</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; ")
>             ;
>             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 21
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             if (glob_min_good_digits <> -16) then # if number 21
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             if (glob_good_digits <> -16) then # if number 21
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             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 21
>                 logitem_str(html_log_file,"Not Given")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 22
>                 logitem_str(html_log_file,"No Solution")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 23
>                 logitem_str(html_log_file,"Some Pole")
>                 ;
>                 logitem_str(html_log_file,"????")
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 24
>                 logitem_str(html_log_file,"No Pole")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 25
>                 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 26
>                 logitem_str(html_log_file,"Complex Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             fi;# end if 26;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_ratio_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             if (glob_least_3_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_3_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             if (glob_least_6_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_6_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             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 26
>                 logitem_time(html_log_file,(glob_total_exp_sec))
>                 ;
>                 0;
>             else
>                 logitem_str(html_log_file,"Done")
>                 ;
>                 0;
>             fi;# end if 26;
>             log_revs(html_log_file,"<td> 308.maple.seems.ok </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.mtest1.mxt.txt\">mtest1 diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.mtest1.mxt.txt\">mtest1 maple results</a>")
>             ;
>             logitem_str(html_log_file,"OK")
>             ;
>             logend(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logitem_str(html_log_file,"diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; ")
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             ;
>             logditto(html_log_file)
>             ;
>             if (array_est_digits[2] <> -16) then # if number 26
>                 logitem_integer(html_log_file,array_est_digits[2])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             if (glob_min_good_digits <> -16) then # if number 26
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             if (glob_good_digits <> -16) then # if number 26
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logditto(html_log_file)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 26
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 27
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 28
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 29
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 30
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 31
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_3_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_6_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 31
>                 logditto(html_log_file)
>                 ;
>                 0;
>             else
>                 logditto(html_log_file)
>                 ;
>                 0;
>             fi;# end if 31;
>             logditto(html_log_file);
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logend(html_log_file)
>             ;
>             ;
>         fi;# end if 30;
>         if (glob_html_log)  then # if number 30
>             fclose(html_log_file);
>         fi;# end if 30
>         ;
>         ;;
>     fi;# end if 29
>     #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_1D0,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    ATS_MAX_TERMS := 40;
    Digits := 32;
    max_terms := 40;
    glob_html_log := true;
    array_y1_init := Array(0 .. 40, []);
    array_y2_init := Array(0 .. 40, []);
    array_norms := Array(0 .. 40, []);
    array_fact_1 := Array(0 .. 40, []);
    array_1st_rel_error := Array(0 .. 3, []);
    array_last_rel_error := Array(0 .. 3, []);
    array_est_rel_error := Array(0 .. 3, []);
    array_max_est_error := Array(0 .. 3, []);
    array_type_pole := Array(0 .. 3, []);
    array_type_real_pole := Array(0 .. 3, []);
    array_type_complex_pole := Array(0 .. 3, []);
    array_est_digits := Array(0 .. 3, []);
    array_y1 := Array(0 .. 40, []);
    array_x := Array(0 .. 40, []);
    array_y2 := Array(0 .. 40, []);
    array_tmp0 := Array(0 .. 40, []);
    array_tmp1 := Array(0 .. 40, []);
    array_tmp2 := Array(0 .. 40, []);
    array_tmp3 := Array(0 .. 40, []);
    array_tmp4 := Array(0 .. 40, []);
    array_tmp5 := Array(0 .. 40, []);
    array_m1 := Array(0 .. 40, []);
    array_y1_higher := Array(0 .. 2, 0 .. 41, []);
    array_y1_higher_work := Array(0 .. 2, 0 .. 41, []);
    array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []);
    array_y1_set_initial := Array(0 .. 3, 0 .. 41, []);
    array_y2_higher := Array(0 .. 2, 0 .. 41, []);
    array_y2_higher_work := Array(0 .. 2, 0 .. 41, []);
    array_y2_higher_work2 := Array(0 .. 2, 0 .. 41, []);
    array_y2_set_initial := Array(0 .. 3, 0 .. 41, []);
    array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
    array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
    array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
    array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
    array_fact_2 := Array(0 .. 40, 0 .. 41, []);
    term := 1;
    while term <= 40 do array_y1_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_y2_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do
        array_last_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
    term := 1;
    while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_y1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_y2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 40 do
            array_y1_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 <= 40 do
            array_y2_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y2_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y2_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 40 do
            array_y2_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 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 <= 3 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 <= 3 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 <= 3 do
        term := 1;
        while term <= 4 do
            array_ord_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 40 do
        term := 1;
        while term <= 40 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y1);
    zero_ats_ar(array_x);
    zero_ats_ar(array_y2);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5);
    zero_ats_ar(array_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_1D0);
    array_const_1D0[1] := c(1.0);
    zero_ats_ar(array_m1);
    array_m1[1] := glob__m1;
    iiif := 0;
    while iiif <= ATS_MAX_TERMS do
        jjjf := 0;
        while jjjf <= ATS_MAX_TERMS do
            array_fact_1[iiif] := 0;
            array_fact_2[iiif, jjjf] := 0;
            jjjf := jjjf + 1
        end do;
        iiif := iiif + 1
    end do;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := 5;
    glob_yes_pole := 4;
    glob_no_pole := 3;
    glob_not_given := 0;
    glob_no_sing_tests := 4;
    glob_ratio_test := 1;
    glob_three_term_test := 2;
    glob_six_term_test := 3;
    glob_log_10 := log(c(10.0));
    MAX_UNCHANGED := 10;
    glob__small := c(0.1*10^(-50));
    glob_small_float := c(0.1*10^(-50));
    glob_smallish_float := c(0.1*10^(-60));
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob__m2 := c(-2);
    glob__m1 := c(-1);
    glob__0 := c(0);
    glob__1 := c(1);
    glob__2 := c(2);
    glob__3 := c(3);
    glob__4 := c(4);
    glob__5 := c(5);
    glob__8 := c(8);
    glob__10 := c(10);
    glob__100 := c(100);
    glob__pi := c(0.);
    glob__0_5 := c(0.5);
    glob__0_8 := c(0.8);
    glob__m0_8 := c(-0.8);
    glob__0_25 := c(0.25);
    glob__0_125 := c(0.125);
    glob_prec := c(0.10*10^(-15));
    glob_check_sign := c(1.0);
    glob_desired_digits_correct := c(8.0);
    glob_max_estimated_step_error := c(0.);
    glob_ratio_of_radius := c(0.1);
    glob_percent_done := c(0.);
    glob_total_exp_sec := c(0.1);
    glob_optimal_expect_sec := c(0.1);
    glob_estimated_size_answer := c(100.0);
    glob_almost_1 := c(0.9990);
    glob_clock_sec := c(0.);
    glob_clock_start_sec := c(0.);
    glob_disp_incr := c(0.1);
    glob_h := c(0.1);
    glob_diff_rc_fm := c(0.1);
    glob_diff_rc_fmm1 := c(0.1);
    glob_diff_rc_fmm2 := c(0.1);
    glob_diff_ord_fm := c(0.1);
    glob_diff_ord_fmm1 := c(0.1);
    glob_diff_ord_fmm2 := c(0.1);
    glob_six_term_ord_save := c(0.1);
    glob_guess_error_rc := c(0.1);
    glob_guess_error_ord := c(0.1);
    glob_least_given_sing := c(0.99*10^201);
    glob_least_ratio_sing := c(0.99*10^201);
    glob_least_3_sing := c(0.99*10^101);
    glob_least_6_sing := c(0.99*10^101);
    glob_last_good_h := c(0.1);
    glob_max_h := c(0.1);
    glob_min_h := c(0.1*10^(-5));
    glob_display_interval := c(0.1);
    glob_abserr := c(0.1*10^(-10));
    glob_relerr := c(0.1*10^(-10));
    glob_min_pole_est := c(0.1*10^10);
    glob_max_rel_trunc_err := c(0.1*10^(-10));
    glob_max_trunc_err := c(0.1*10^(-10));
    glob_max_hours := c(0.);
    glob_optimal_clock_start_sec := c(0.);
    glob_optimal_start := c(0.);
    glob_upper_ratio_limit := c(1.0001);
    glob_lower_ratio_limit := c(0.9999);
    glob_max_sec := c(10000.0);
    glob_orig_start_sec := c(0.);
    glob_normmax := c(0.);
    glob_max_minutes := c(0.);
    glob_next_display := c(0.);
    glob_est_digits := 1;
    glob_subiter_method := 3;
    glob_html_log := true;
    glob_min_good_digits := 99999;
    glob_good_digits := 0;
    glob_min_apfp_est_good_digits := 99999;
    glob_apfp_est_good_digits := 0;
    glob_max_opt_iter := 10;
    glob_dump := false;
    glob_djd_debug := true;
    glob_display_flag := true;
    glob_djd_debug2 := true;
    glob_h_reason := 0;
    glob_sec_in_minute := 60;
    glob_min_in_hour := 60;
    glob_hours_in_day := 24;
    glob_days_in_year := 365;
    glob_sec_in_hour := 3600;
    glob_sec_in_day := 86400;
    glob_sec_in_year := 31536000;
    glob_not_yet_finished := true;
    glob_initial_pass := true;
    glob_not_yet_start_msg := true;
    glob_reached_optimal_h := false;
    glob_optimal_done := false;
    glob_type_given_pole := 0;
    glob_optimize := false;
    glob_look_poles := false;
    glob_dump_closed_form := false;
    glob_max_iter := 1000;
    glob_no_eqs := 0;
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_start := 0;
    glob_iter := 0;
    array_y1_set_initial[1, 1] := true;
    array_y1_set_initial[1, 2] := false;
    array_y1_set_initial[1, 3] := false;
    array_y1_set_initial[1, 4] := false;
    array_y1_set_initial[1, 5] := false;
    array_y1_set_initial[1, 6] := false;
    array_y1_set_initial[1, 7] := false;
    array_y1_set_initial[1, 8] := false;
    array_y1_set_initial[1, 9] := false;
    array_y1_set_initial[1, 10] := false;
    array_y1_set_initial[1, 11] := false;
    array_y1_set_initial[1, 12] := false;
    array_y1_set_initial[1, 13] := false;
    array_y1_set_initial[1, 14] := false;
    array_y1_set_initial[1, 15] := false;
    array_y1_set_initial[1, 16] := false;
    array_y1_set_initial[1, 17] := false;
    array_y1_set_initial[1, 18] := false;
    array_y1_set_initial[1, 19] := false;
    array_y1_set_initial[1, 20] := false;
    array_y1_set_initial[1, 21] := false;
    array_y1_set_initial[1, 22] := false;
    array_y1_set_initial[1, 23] := false;
    array_y1_set_initial[1, 24] := false;
    array_y1_set_initial[1, 25] := false;
    array_y1_set_initial[1, 26] := false;
    array_y1_set_initial[1, 27] := false;
    array_y1_set_initial[1, 28] := false;
    array_y1_set_initial[1, 29] := false;
    array_y1_set_initial[1, 30] := false;
    array_y1_set_initial[1, 31] := false;
    array_y1_set_initial[1, 32] := false;
    array_y1_set_initial[1, 33] := false;
    array_y1_set_initial[1, 34] := false;
    array_y1_set_initial[1, 35] := false;
    array_y1_set_initial[1, 36] := false;
    array_y1_set_initial[1, 37] := false;
    array_y1_set_initial[1, 38] := false;
    array_y1_set_initial[1, 39] := false;
    array_y1_set_initial[1, 40] := false;
    array_y2_set_initial[2, 1] := true;
    array_y2_set_initial[2, 2] := false;
    array_y2_set_initial[2, 3] := false;
    array_y2_set_initial[2, 4] := false;
    array_y2_set_initial[2, 5] := false;
    array_y2_set_initial[2, 6] := false;
    array_y2_set_initial[2, 7] := false;
    array_y2_set_initial[2, 8] := false;
    array_y2_set_initial[2, 9] := false;
    array_y2_set_initial[2, 10] := false;
    array_y2_set_initial[2, 11] := false;
    array_y2_set_initial[2, 12] := false;
    array_y2_set_initial[2, 13] := false;
    array_y2_set_initial[2, 14] := false;
    array_y2_set_initial[2, 15] := false;
    array_y2_set_initial[2, 16] := false;
    array_y2_set_initial[2, 17] := false;
    array_y2_set_initial[2, 18] := false;
    array_y2_set_initial[2, 19] := false;
    array_y2_set_initial[2, 20] := false;
    array_y2_set_initial[2, 21] := false;
    array_y2_set_initial[2, 22] := false;
    array_y2_set_initial[2, 23] := false;
    array_y2_set_initial[2, 24] := false;
    array_y2_set_initial[2, 25] := false;
    array_y2_set_initial[2, 26] := false;
    array_y2_set_initial[2, 27] := false;
    array_y2_set_initial[2, 28] := false;
    array_y2_set_initial[2, 29] := false;
    array_y2_set_initial[2, 30] := false;
    array_y2_set_initial[2, 31] := false;
    array_y2_set_initial[2, 32] := false;
    array_y2_set_initial[2, 33] := false;
    array_y2_set_initial[2, 34] := false;
    array_y2_set_initial[2, 35] := false;
    array_y2_set_initial[2, 36] := false;
    array_y2_set_initial[2, 37] := false;
    array_y2_set_initial[2, 38] := false;
    array_y2_set_initial[2, 39] := false;
    array_y2_set_initial[2, 40] := false;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 40;
    glob_iolevel := INFO;
    glob_orig_start_sec := elapsed_time_seconds();
    glob_display_flag := true;
    glob_no_eqs := 2;
    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/mtest1postode.ode#################");
    omniout_str(ALWAYS,
        "diff  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; ");
    omniout_str(ALWAYS, "diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=40;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(0.1);");
    omniout_str(ALWAYS, "x_end := c(10.0);");
    omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
    omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 3;");
    omniout_str(ALWAYS, "#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_y1 := proc(x)");
    omniout_str(ALWAYS, "return(c(1.0) + cos(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
    omniout_str(ALWAYS, "return(c(1.0) + sin(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(0.1);
    x_end := c(10.0);
    array_y1_init[1] := exact_soln_y1(x_start);
    array_y2_init[1] := exact_soln_y2(x_start);
    glob_look_poles := true;
    glob_type_given_pole := 3;
    glob_desired_digits_correct := 8;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000;
    glob_upper_ratio_limit := c(1.000001);
    glob_lower_ratio_limit := c(0.999999);
    glob_look_poles := false;
    glob_h := c(0.001);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(x_start, x_end));
    glob__pi := arccos(glob__m1);
    glob_prec = expt(10.0, c(-Digits));
    if glob_optimize then
        omniout_str(ALWAYS, "START of Optimize");
        found_h := false;
        glob_min_pole_est := glob_larger_float;
        last_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        glob_min_h := float_abs(glob_min_h)*glob_check_sign;
        glob_max_h := float_abs(glob_max_h)*glob_check_sign;
        glob_h := float_abs(glob_min_h)*glob_check_sign;
        glob_display_interval :=
            c(float_abs(c(glob_display_interval))*glob_check_sign);
        display_max := c(x_end) - c(x_start)/glob__10;
        if display_max < glob_display_interval then
            glob_display_interval := c(display_max)
        end if;
        chk_data();
        min_value := glob_larger_float;
        est_answer := est_size_answer();
        opt_iter := 1;
        est_needed_step_err :=
            estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
            ;
        omniout_float(ALWAYS, "est_needed_step_err", 32,
            est_needed_step_err, 16, "");
        estimated_step_error := glob_small_float;
        while opt_iter <= 100 and not found_h do
            omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
            array_x[1] := c(x_start);
            array_x[2] := c(glob_h);
            glob_next_display := c(x_start);
            order_diff := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] :=
                        array_y1_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;
            order_diff := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] :=
                        array_y2_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;
            if glob_subiter_method = 1 then atomall()
            elif glob_subiter_method = 2 then
                subiter := 1;
                while subiter <= 2 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 2 + ATS_MAX_TERMS do
                    atomall(); subiter := subiter + 1
                end do
            end if;
            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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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();
            if glob_subiter_method = 1 then atomall()
            elif glob_subiter_method = 2 then
                subiter := 1;
                while subiter <= 2 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 2 + ATS_MAX_TERMS do
                    atomall(); subiter := subiter + 1
                end do
            end if;
            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_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y1_higher[ord, term_no] :=
                        array_y1_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y2_higher[ord, term_no] :=
                        array_y2_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  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; ");
        omniout_str(INFO, "diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; ");
        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, "2016-08-26T16:39:08-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"mtest1.ode.txt\">mtest1</a>");
            logitem_str(html_log_file,
                "diff  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; ");
            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.mtest1.mxt.txt\">mtest1 diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.mtest1.mxt.txt\\
                ">mtest1 maple results</a>");
            logitem_str(html_log_file, "OK");
            logend(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logitem_str(html_log_file,
                "diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; ");
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            if array_est_digits[2] <> -16 then
                logitem_integer(html_log_file, array_est_digits[2])
            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");
            logditto(html_log_file);
            if glob_type_given_pole = 0 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 4 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 5 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 3 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 1 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 2 then
                logditto(html_log_file); logditto(html_log_file)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            if glob_least_3_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            if glob_least_6_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            logditto(html_log_file);
            logditto(html_log_file);
            if c(glob_percent_done) < glob__100 then
                logditto(html_log_file); 0
            else logditto(html_log_file); 0
            end if;
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            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/mtest1postode.ode#################
diff  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; 
diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(10.0);
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_look_poles := true;







glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(c(1.0) + cos(c(x)));
end;
exact_soln_y2 := proc(x)
return(c(1.0) + sin(c(x)));
end;




#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
memory used=3.7MB, alloc=40.3MB, time=0.08
x[1]                              = 0.1                                          
y1[1] (closed_form)               = 1.9950041652780257660955619878039            
y1[1] (numeric)                   = 1.9950041652780257660955619878039            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.0998334166468281523068141984106            
y2[1] (numeric)                   = 1.0998334166468281523068141984106            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=45.9MB, alloc=40.3MB, time=0.62
 
TOP MAIN SOLVE Loop
x[1]                              = 0.11                                         
y1[1] (closed_form)               = 1.9939560979566968503578396114198            
y1[1] (numeric)                   = 1.9939560979566968503578396114199            
absolute error                    = 1e-31                                        
relative error                    = 5.0151555544515163299513758223921e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1097783008371748086649494900834            
y2[1] (numeric)                   = 1.1097783008371748086649494900834            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=88.1MB, alloc=40.3MB, time=1.13
memory used=130.2MB, alloc=40.3MB, time=1.65
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y1[1] (closed_form)               = 1.9928086358538662522480981678576            
y1[1] (numeric)                   = 1.9928086358538662522480981678577            
absolute error                    = 1e-31                                        
relative error                    = 5.0180432882935908112451694551819e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.119712207288919359967350614271             
y2[1] (numeric)                   = 1.1197122072889193599673506142709            
absolute error                    = 1e-31                                        
relative error                    = 8.9308662841251848826513335689902e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=172.4MB, alloc=40.3MB, time=2.16
 
TOP MAIN SOLVE Loop
memory used=214.4MB, alloc=40.3MB, time=2.68
x[1]                              = 0.13                                         
y1[1] (closed_form)               = 1.9915618937147880395945121711518            
y1[1] (numeric)                   = 1.991561893714788039594512171152             
absolute error                    = 2e-31                                        
relative error                    = 1.0042369289710964831422071099758e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1296341426196948595412058107083            
y2[1] (numeric)                   = 1.1296341426196948595412058107081            
absolute error                    = 2e-31                                        
relative error                    = 1.7704847300045926851243791841683e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=256.6MB, alloc=40.3MB, time=3.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y1[1] (closed_form)               = 1.9902159962126371718989482270114            
y1[1] (numeric)                   = 1.9902159962126371718989482270116            
absolute error                    = 2e-31                                        
relative error                    = 1.0049160512255864176420440742915e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1395431146442364817179883517054            
y2[1] (numeric)                   = 1.139543114644236481717988351705             
absolute error                    = 4e-31                                        
relative error                    = 3.5101787274181315499106401304621e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=298.8MB, alloc=40.3MB, time=3.71
memory used=340.9MB, alloc=40.3MB, time=4.23
 
TOP MAIN SOLVE Loop
x[1]                              = 0.15                                         
y1[1] (closed_form)               = 1.9887710779360422867349809986543            
y1[1] (numeric)                   = 1.9887710779360422867349809986545            
absolute error                    = 2e-31                                        
relative error                    = 1.0056461611839262823506671282776e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1494381324735992214977254386876            
y2[1] (numeric)                   = 1.1494381324735992214977254386874            
absolute error                    = 2e-31                                        
relative error                    = 1.7399805552787651589749040948674e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=383.1MB, alloc=40.3MB, time=4.74
 
TOP MAIN SOLVE Loop
memory used=425.2MB, alloc=40.3MB, time=5.26
x[1]                              = 0.16                                         
y1[1] (closed_form)               = 1.9872272833756269490409525240183            
y1[1] (numeric)                   = 1.9872272833756269490409525240185            
absolute error                    = 2e-31                                        
relative error                    = 1.0064274060301127337338940958891e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.159318206614245963311463159686             
y2[1] (numeric)                   = 1.1593182066142459633114631596857            
absolute error                    = 3e-31                                        
relative error                    = 2.5877278411432957513901436913893e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=467.3MB, alloc=40.3MB, time=5.78
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y1[1] (closed_form)               = 1.9855847669095607091719299902125            
y1[1] (numeric)                   = 1.9855847669095607091719299902126            
absolute error                    = 1e-31                                        
relative error                    = 5.0362997171681461508806471945451e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1691823490669960101576243766708            
y2[1] (numeric)                   = 1.1691823490669960101576243766706            
absolute error                    = 2e-31                                        
relative error                    = 1.7105971550083645811415309402222e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=509.5MB, alloc=40.3MB, time=6.29
memory used=551.5MB, alloc=40.3MB, time=6.81
 
TOP MAIN SOLVE Loop
x[1]                              = 0.18                                         
y1[1] (closed_form)               = 1.9838436927881214145927160246115            
y1[1] (numeric)                   = 1.9838436927881214145927160246116            
absolute error                    = 1e-31                                        
relative error                    = 5.0407197080864074714095761345369e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1790295734258241783418027396992            
y2[1] (numeric)                   = 1.1790295734258241783418027396989            
absolute error                    = 3e-31                                        
relative error                    = 2.5444654380323207512376551905900e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=593.7MB, alloc=40.3MB, time=7.32
 
TOP MAIN SOLVE Loop
memory used=635.9MB, alloc=40.3MB, time=7.84
x[1]                              = 0.19                                         
y1[1] (closed_form)               = 1.9820042351172703189678775041899            
y1[1] (numeric)                   = 1.9820042351172703189678775041901            
absolute error                    = 2e-31                                        
relative error                    = 1.0090795794296902276075654013421e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1888588949765005779928511529813            
y2[1] (numeric)                   = 1.188858894976500577992851152981             
absolute error                    = 3e-31                                        
relative error                    = 2.5234281483500185301324555349713e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=678.0MB, alloc=40.3MB, time=8.36
 
TOP MAIN SOLVE Loop
x[1]                              = 0.2                                          
y1[1] (closed_form)               = 1.9800665778412416311241965167482            
y1[1] (numeric)                   = 1.9800665778412416311241965167485            
absolute error                    = 3e-31                                        
relative error                    = 1.5151005696337423332428237405056e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.1986693307950612154594126271184            
y2[1] (numeric)                   = 1.1986693307950612154594126271181            
absolute error                    = 3e-31                                        
relative error                    = 2.5027753050210606656367468154235e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=720.1MB, alloc=40.3MB, time=8.88
memory used=762.2MB, alloc=40.3MB, time=9.39
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y1[1] (closed_form)               = 1.9780309147241482449161385680994            
y1[1] (numeric)                   = 1.9780309147241482449161385680997            
absolute error                    = 3e-31                                        
relative error                    = 1.5166598143984889496365564690110e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2084598998460995706087124262276            
y2[1] (numeric)                   = 1.2084598998460995706087124262274            
absolute error                    = 2e-31                                        
relative error                    = 1.6549990614125508560057056837875e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=804.4MB, alloc=40.3MB, time=9.90
 
TOP MAIN SOLVE Loop
memory used=846.5MB, alloc=40.3MB, time=10.42
x[1]                              = 0.22                                         
y1[1] (closed_form)               = 1.9758974493306054894060229810447            
y1[1] (numeric)                   = 1.9758974493306054894060229810452            
absolute error                    = 5e-31                                        
relative error                    = 2.5304957004190171564532112113104e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.218229623080869319951791005457             
y2[1] (numeric)                   = 1.2182296230808693199517910054567            
absolute error                    = 3e-31                                        
relative error                    = 2.4625899281722293393850446163784e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=888.7MB, alloc=40.3MB, time=10.94
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y1[1] (closed_form)               = 1.9736663950053748369677306480716            
y1[1] (numeric)                   = 1.9736663950053748369677306480722            
absolute error                    = 6e-31                                        
relative error                    = 3.0400274409007507817083398467313e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2279775235351883954046172123601            
y2[1] (numeric)                   = 1.2279775235351883954046172123598            
absolute error                    = 3e-31                                        
relative error                    = 2.4430414584164278404004273601661e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=930.9MB, alloc=40.3MB, time=11.48
memory used=973.0MB, alloc=40.3MB, time=12.00
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y1[1] (closed_form)               = 1.9713379748520296049261752469634            
y1[1] (numeric)                   = 1.9713379748520296049261752469641            
absolute error                    = 7e-31                                        
relative error                    = 3.5508878179681118724898367705815e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2377026264271345883607920844898            
y2[1] (numeric)                   = 1.2377026264271345883607920844896            
absolute error                    = 2e-31                                        
relative error                    = 1.6158970315619209864958087473642e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1015.1MB, alloc=40.3MB, time=12.52
 
TOP MAIN SOLVE Loop
memory used=1057.3MB, alloc=40.3MB, time=13.03
x[1]                              = 0.25                                         
y1[1] (closed_form)               = 1.9689124217106447841445954494942            
y1[1] (numeric)                   = 1.968912421710644784144595449495             
absolute error                    = 8e-31                                        
relative error                    = 4.0631568533908592651295073313858e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2474039592545229295968487048494            
y2[1] (numeric)                   = 1.2474039592545229295968487048492            
absolute error                    = 2e-31                                        
relative error                    = 1.6033298476904351319729627552716e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1099.4MB, alloc=40.3MB, time=13.55
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y1[1] (closed_form)               = 1.9663899781345132255582176464501            
y1[1] (numeric)                   = 1.966389978134513225558217646451             
absolute error                    = 9e-31                                        
relative error                    = 4.5769151084354969112124928792545e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2570805518921550973533884643652            
y2[1] (numeric)                   = 1.2570805518921550973533884643649            
absolute error                    = 3e-31                                        
relative error                    = 2.3864819127814888902615199723276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1141.6MB, alloc=40.3MB, time=14.06
memory used=1183.7MB, alloc=40.3MB, time=14.58
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y1[1] (closed_form)               = 1.9637708963658905130162327094922            
y1[1] (numeric)                   = 1.9637708963658905130162327094933            
absolute error                    = 1.1e-30                                      
relative error                    = 5.6014680838565987023130090620512e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2667314366888311287322865210205            
y2[1] (numeric)                   = 1.2667314366888311287322865210202            
absolute error                    = 3e-31                                        
relative error                    = 2.3682999514418313301192155511596e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1225.9MB, alloc=40.3MB, time=15.10
 
TOP MAIN SOLVE Loop
memory used=1268.1MB, alloc=40.3MB, time=15.61
x[1]                              = 0.28                                         
y1[1] (closed_form)               = 1.9610554383107709479245900535965            
y1[1] (numeric)                   = 1.9610554383107709479245900535975            
absolute error                    = 1.0e-30                                      
relative error                    = 5.0992949024500179833358581186582e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2763556485641137333196695584578            
y2[1] (numeric)                   = 1.2763556485641137333196695584576            
absolute error                    = 2e-31                                        
relative error                    = 1.5669613733836476662755628934786e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1310.3MB, alloc=40.3MB, time=16.13
 
TOP MAIN SOLVE Loop
x[1]                              = 0.29                                         
y1[1] (closed_form)               = 1.9582438755126971680701247779319            
y1[1] (numeric)                   = 1.9582438755126971680701247779329            
absolute error                    = 1.0e-30                                      
relative error                    = 5.1066162519629238259191461445522e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.2859522251048355326839402055044            
y2[1] (numeric)                   = 1.2859522251048355326839402055042            
absolute error                    = 2e-31                                        
relative error                    = 1.5552677315340798752445732797177e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1352.5MB, alloc=40.3MB, time=16.65
memory used=1394.6MB, alloc=40.3MB, time=17.17
 
TOP MAIN SOLVE Loop
x[1]                              = 0.3                                          
y1[1] (closed_form)               = 1.955336489125606019642310227568             
y1[1] (numeric)                   = 1.9553364891256060196423102275691            
absolute error                    = 1.1e-30                                      
relative error                    = 5.6256301977564062033316022634293e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.295520206661339575105320745685             
y2[1] (numeric)                   = 1.2955202066613395751053207456848            
absolute error                    = 2e-31                                        
relative error                    = 1.5437814012597780076888756295055e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1436.9MB, alloc=40.3MB, time=17.69
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y1[1] (closed_form)               = 1.9523335698857133978428054362022            
y1[1] (numeric)                   = 1.9523335698857133978428054362033            
absolute error                    = 1.1e-30                                      
relative error                    = 5.6342830803467273621917995925121e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.305058636443443501565643323959             
y2[1] (numeric)                   = 1.3050586364434435015656433239587            
absolute error                    = 3e-31                                        
relative error                    = 2.2987472870764064686855305439498e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1479.1MB, alloc=40.3MB, time=18.21
memory used=1521.1MB, alloc=40.3MB, time=18.72
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y1[1] (closed_form)               = 1.9492354180824408675753072737661            
y1[1] (numeric)                   = 1.9492354180824408675753072737672            
absolute error                    = 1.1e-30                                      
relative error                    = 5.6432383169095312104675503259976e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3145665606161177666617575434172            
y2[1] (numeric)                   = 1.3145665606161177666617575434169            
absolute error                    = 3e-31                                        
relative error                    = 2.2821210350839478866800472968371e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1563.3MB, alloc=40.3MB, time=19.24
memory used=1605.5MB, alloc=40.3MB, time=19.76
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y1[1] (closed_form)               = 1.9460423435283869715294105783662            
y1[1] (numeric)                   = 1.9460423435283869715294105783672            
absolute error                    = 1.0e-30                                      
relative error                    = 5.1386343330376406753083627226715e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3240430283948683467001956961702            
y2[1] (numeric)                   = 1.32404302839486834670019569617              
absolute error                    = 2e-31                                        
relative error                    = 1.5105249278979939004455728596918e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1647.6MB, alloc=40.3MB, time=20.27
 
TOP MAIN SOLVE Loop
x[1]                              = 0.34                                         
y1[1] (closed_form)               = 1.9427546655283462285026440600266            
y1[1] (numeric)                   = 1.9427546655283462285026440600276            
absolute error                    = 1.0e-30                                      
relative error                    = 5.1473303229877599789431571449149e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3334870921408143967817714870308            
y2[1] (numeric)                   = 1.3334870921408143967817714870307            
absolute error                    = 1e-31                                        
relative error                    = 7.4991352064351394557937651507292e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1689.8MB, alloc=40.3MB, time=20.79
memory used=1731.9MB, alloc=40.3MB, time=21.30
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y1[1] (closed_form)               = 1.9393727128473789200350323573037            
y1[1] (numeric)                   = 1.9393727128473789200350323573046            
absolute error                    = 9e-31                                        
relative error                    = 4.6406757919091465277971328208936e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3428978074554513491896349069176            
y2[1] (numeric)                   = 1.3428978074554513491896349069176            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1774.0MB, alloc=40.3MB, time=21.82
memory used=1816.2MB, alloc=40.3MB, time=22.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y1[1] (closed_form)               = 1.9358968236779348583509123681247            
y1[1] (numeric)                   = 1.9358968236779348583509123681256            
absolute error                    = 9e-31                                        
relative error                    = 4.6490080927460023819523534627274e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3522742332750899768499134359207            
y2[1] (numeric)                   = 1.3522742332750899768499134359207            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1858.4MB, alloc=40.3MB, time=22.85
 
TOP MAIN SOLVE Loop
x[1]                              = 0.37                                         
y1[1] (closed_form)               = 1.9323273456060344232038129044909            
y1[1] (numeric)                   = 1.9323273456060344232038129044917            
absolute error                    = 8e-31                                        
relative error                    = 4.1400852801630076839914592661823e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3616154319649619780372924691272            
y2[1] (numeric)                   = 1.3616154319649619780372924691272            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1900.6MB, alloc=40.3MB, time=23.37
memory used=1942.7MB, alloc=40.3MB, time=23.88
 
TOP MAIN SOLVE Loop
x[1]                              = 0.38                                         
y1[1] (closed_form)               = 1.9286646355765102494925308077246            
y1[1] (numeric)                   = 1.9286646355765102494925308077252            
absolute error                    = 6e-31                                        
relative error                    = 3.1109607597520443134137085159000e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3709204694129826718454854663492            
y2[1] (numeric)                   = 1.3709204694129826718454854663494            
absolute error                    = 2e-31                                        
relative error                    = 1.4588738330359778051773601637369e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=1984.9MB, alloc=40.3MB, time=24.40
memory used=2027.0MB, alloc=40.3MB, time=24.92
 
TOP MAIN SOLVE Loop
x[1]                              = 0.39                                         
y1[1] (closed_form)               = 1.9249090598573130414506767528811            
y1[1] (numeric)                   = 1.9249090598573130414506767528817            
absolute error                    = 6e-31                                        
relative error                    = 3.1170303704865722764433345347010e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3801884151231614282311820978472            
y2[1] (numeric)                   = 1.3801884151231614282311820978474            
absolute error                    = 2e-31                                        
relative error                    = 1.4490775158560721171750110187086e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2069.2MB, alloc=40.3MB, time=25.43
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y1[1] (closed_form)               = 1.9210609940028850827985267320518            
y1[1] (numeric)                   = 1.9210609940028850827985267320523            
absolute error                    = 5e-31                                        
relative error                    = 2.6027283962398181476349164956869e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3894183423086504916663117567957            
y2[1] (numeric)                   = 1.389418342308650491666311756796             
absolute error                    = 3e-31                                        
relative error                    = 2.1591769078096487269562799734596e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2111.4MB, alloc=40.3MB, time=25.95
memory used=2153.5MB, alloc=40.3MB, time=26.46
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y1[1] (closed_form)               = 1.917120822816605105475642058277             
y1[1] (numeric)                   = 1.9171208228166051054756420582777            
absolute error                    = 7e-31                                        
relative error                    = 3.6513087316613176131147236089912e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.3986093279844228935937976400511            
y2[1] (numeric)                   = 1.3986093279844228935937976400515            
absolute error                    = 4e-31                                        
relative error                    = 2.8599837852965830296132404161208e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2195.7MB, alloc=40.3MB, time=26.98
memory used=2237.9MB, alloc=40.3MB, time=27.50
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y1[1] (closed_form)               = 1.9130889403123082724360887896657            
y1[1] (numeric)                   = 1.9130889403123082724360887896664            
absolute error                    = 7e-31                                        
relative error                    = 3.6590039555909318025708625671599e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4077604530595701859727871580863            
y2[1] (numeric)                   = 1.4077604530595701859727871580868            
absolute error                    = 5e-31                                        
relative error                    = 3.5517406311089363653815726493951e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2280.0MB, alloc=40.3MB, time=28.01
 
TOP MAIN SOLVE Loop
x[1]                              = 0.43                                         
y1[1] (closed_form)               = 1.9089657496748851224759104776634            
y1[1] (numeric)                   = 1.9089657496748851224759104776642            
absolute error                    = 8e-31                                        
relative error                    = 4.1907509348255595873890222898837e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4168708024292107662169186726246            
y2[1] (numeric)                   = 1.416870802429210766216918672625             
absolute error                    = 4e-31                                        
relative error                    = 2.8231226115620705555107735438864e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2322.2MB, alloc=40.3MB, time=28.53
memory used=2364.4MB, alloc=40.3MB, time=29.04
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y1[1] (closed_form)               = 1.9047516632199634171655373889984            
y1[1] (numeric)                   = 1.9047516632199634171655373889991            
absolute error                    = 7e-31                                        
relative error                    = 3.6750197598812281994924040423398e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4259394650659996027697207507799            
y2[1] (numeric)                   = 1.4259394650659996027697207507804            
absolute error                    = 5e-31                                        
relative error                    = 3.5064602127191809077482146374345e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2406.5MB, alloc=40.3MB, time=29.56
memory used=2448.6MB, alloc=40.3MB, time=30.07
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y1[1] (closed_form)               = 1.9004471023526769216688406114864            
y1[1] (numeric)                   = 1.9004471023526769216688406114873            
absolute error                    = 9e-31                                        
relative error                    = 4.7357277078948225995494293730509e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4349655341112302104208442462319            
y2[1] (numeric)                   = 1.4349655341112302104208442462325            
absolute error                    = 6e-31                                        
relative error                    = 4.1812850952662078217022876062265e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2490.8MB, alloc=40.3MB, time=30.59
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y1[1] (closed_form)               = 1.8960524975255252425363899035004            
y1[1] (numeric)                   = 1.8960524975255252425363899035012            
absolute error                    = 8e-31                                        
relative error                    = 4.2192924565329982571935800869880e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4439481069655197652415136439289            
y2[1] (numeric)                   = 1.4439481069655197652415136439295            
absolute error                    = 6e-31                                        
relative error                    = 4.1552739818393451603310637481914e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2533.0MB, alloc=40.3MB, time=31.11
memory used=2575.1MB, alloc=40.3MB, time=31.62
 
TOP MAIN SOLVE Loop
x[1]                              = 0.47                                         
y1[1] (closed_form)               = 1.8915682881953289364540192765334            
y1[1] (numeric)                   = 1.8915682881953289364540192765343            
absolute error                    = 9e-31                                        
relative error                    = 4.7579566945407753522039746130520e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4528862853790682907032748003964            
y2[1] (numeric)                   = 1.452886285379068290703274800397             
absolute error                    = 6e-31                                        
relative error                    = 4.1297106734231148956894654287902e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2617.3MB, alloc=40.3MB, time=32.14
memory used=2659.4MB, alloc=40.3MB, time=32.66
 
TOP MAIN SOLVE Loop
x[1]                              = 0.48                                         
y1[1] (closed_form)               = 1.8869949227792841943999548311587            
y1[1] (numeric)                   = 1.8869949227792841943999548311596            
absolute error                    = 9e-31                                        
relative error                    = 4.7694881906434792396618320604904e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4617791755414828891366429425886            
y2[1] (numeric)                   = 1.4617791755414828891366429425893            
absolute error                    = 7e-31                                        
relative error                    = 4.7886849923190409489817796102860e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2701.6MB, alloc=40.3MB, time=33.17
 
TOP MAIN SOLVE Loop
x[1]                              = 0.49                                         
y1[1] (closed_form)               = 1.8823328586101214957054681591367            
y1[1] (numeric)                   = 1.8823328586101214957054681591375            
absolute error                    = 8e-31                                        
relative error                    = 4.2500453431530949657466873062150e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.470625888171158036181358337188             
y2[1] (numeric)                   = 1.4706258881711580361813583371885            
absolute error                    = 5e-31                                        
relative error                    = 3.3999129487771383339742580691484e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2743.8MB, alloc=40.3MB, time=33.68
memory used=2785.9MB, alloc=40.3MB, time=34.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y1[1] (closed_form)               = 1.8775825618903727161162815826038            
y1[1] (numeric)                   = 1.8775825618903727161162815826046            
absolute error                    = 8e-31                                        
relative error                    = 4.2607979869313995633948077194479e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4794255386042030002732879352156            
y2[1] (numeric)                   = 1.4794255386042030002732879352161            
absolute error                    = 5e-31                                        
relative error                    = 3.3796902037512218738644431408307e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2828.1MB, alloc=40.3MB, time=34.72
 
TOP MAIN SOLVE Loop
memory used=2870.3MB, alloc=40.3MB, time=35.23
x[1]                              = 0.51                                         
y1[1] (closed_form)               = 1.8727445076457512631058084735755            
y1[1] (numeric)                   = 1.8727445076457512631058084735763            
absolute error                    = 8e-31                                        
relative error                    = 4.2718053462919468607950533130625e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4881772468829074945001302376746            
y2[1] (numeric)                   = 1.4881772468829074945001302376751            
absolute error                    = 5e-31                                        
relative error                    = 3.3598148409222447531071760797816e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2912.5MB, alloc=40.3MB, time=35.75
 
TOP MAIN SOLVE Loop
x[1]                              = 0.52                                         
y1[1] (closed_form)               = 1.8678191796776499003878475719885            
y1[1] (numeric)                   = 1.8678191796776499003878475719893            
absolute error                    = 8e-31                                        
relative error                    = 4.2830698426496766086447025780276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.4968801378437367143344589425478            
y2[1] (numeric)                   = 1.4968801378437367143344589425483            
absolute error                    = 5e-31                                        
relative error                    = 3.3402808104612336398629058143727e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=2954.7MB, alloc=40.3MB, time=36.27
memory used=2996.8MB, alloc=40.3MB, time=36.78
 
TOP MAIN SOLVE Loop
x[1]                              = 0.53                                         
y1[1] (closed_form)               = 1.8628070705147610118066950185642            
y1[1] (numeric)                   = 1.8628070705147610118066950185648            
absolute error                    = 6e-31                                        
relative error                    = 3.2209454725453575015572376807506e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5055333412048469618136610224661            
y2[1] (numeric)                   = 1.5055333412048469618136610224666            
absolute error                    = 5e-31                                        
relative error                    = 3.3210822126321056338591721703018e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3038.9MB, alloc=40.3MB, time=37.30
 
TOP MAIN SOLVE Loop
memory used=3081.1MB, alloc=40.3MB, time=37.82
x[1]                              = 0.54                                         
y1[1] (closed_form)               = 1.8577086813638241425379687789178            
y1[1] (numeric)                   = 1.8577086813638241425379687789183            
absolute error                    = 5e-31                                        
relative error                    = 2.6914876644325547016896916446517e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5141359916531131046772806829582            
y2[1] (numeric)                   = 1.5141359916531131046772806829588            
absolute error                    = 6e-31                                        
relative error                    = 3.9626559523555618777898480986526e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3123.2MB, alloc=40.3MB, time=38.33
 
TOP MAIN SOLVE Loop
x[1]                              = 0.55                                         
y1[1] (closed_form)               = 1.8525245220595057428049817976178            
y1[1] (numeric)                   = 1.8525245220595057428049817976183            
absolute error                    = 5e-31                                        
relative error                    = 2.6990196029585366177845095383462e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5226872289306591677883781077573            
y2[1] (numeric)                   = 1.522687228930659167788378107758             
absolute error                    = 7e-31                                        
relative error                    = 4.5971358181784351351004520689163e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3165.4MB, alloc=40.3MB, time=38.84
memory used=3207.5MB, alloc=40.3MB, time=39.36
 
TOP MAIN SOLVE Loop
x[1]                              = 0.56                                         
y1[1] (closed_form)               = 1.8472551110134161260945255038663            
y1[1] (numeric)                   = 1.8472551110134161260945255038668            
absolute error                    = 5e-31                                        
relative error                    = 2.7067187256323072748962087373348e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.531186197920883403851869441112             
y2[1] (numeric)                   = 1.5311861979208834038518694411127            
absolute error                    = 7e-31                                        
relative error                    = 4.5716190555432964649544973449706e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3249.6MB, alloc=40.3MB, time=39.88
 
TOP MAIN SOLVE Loop
memory used=3291.8MB, alloc=40.3MB, time=40.39
x[1]                              = 0.57                                         
y1[1] (closed_form)               = 1.841900975162268740133756363916             
y1[1] (numeric)                   = 1.8419009751622687401337563639166            
absolute error                    = 6e-31                                        
relative error                    = 3.2575041117351104674930814373731e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5396320487339692409944634930788            
y2[1] (numeric)                   = 1.5396320487339692409944634930796            
absolute error                    = 8e-31                                        
relative error                    = 5.1960466830879202118571122483276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3334.0MB, alloc=40.3MB, time=40.90
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y1[1] (closed_form)               = 1.83646264991518693465788732805              
y1[1] (numeric)                   = 1.8364626499151869346578873280506            
absolute error                    = 6e-31                                        
relative error                    = 3.2671505735643995019872788096361e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5480239367918735561826960595765            
y2[1] (numeric)                   = 1.5480239367918735561826960595773            
absolute error                    = 8e-31                                        
relative error                    = 5.1678787451951217633635930628633e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3376.3MB, alloc=40.3MB, time=41.42
memory used=3418.5MB, alloc=40.3MB, time=41.94
 
TOP MAIN SOLVE Loop
x[1]                              = 0.59                                         
y1[1] (closed_form)               = 1.8309406791001634952479965224907            
y1[1] (numeric)                   = 1.8309406791001634952479965224912            
absolute error                    = 5e-31                                        
relative error                    = 2.7308366989023951066447606287685e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5563610229127837757225433788758            
y2[1] (numeric)                   = 1.5563610229127837757225433788765            
absolute error                    = 7e-31                                        
relative error                    = 4.4976711039057355599970448083517e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3460.7MB, alloc=40.3MB, time=42.48
 
TOP MAIN SOLVE Loop
memory used=3502.9MB, alloc=40.3MB, time=42.99
x[1]                              = 0.6                                          
y1[1] (closed_form)               = 1.8253356149096782972409524989554            
y1[1] (numeric)                   = 1.8253356149096782972409524989559            
absolute error                    = 5e-31                                        
relative error                    = 2.7392222883063678244810698399098e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5646424733950353572009454456587            
y2[1] (numeric)                   = 1.5646424733950353572009454456595            
absolute error                    = 8e-31                                        
relative error                    = 5.1129891563286154652821857122691e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3545.1MB, alloc=40.3MB, time=43.51
 
TOP MAIN SOLVE Loop
x[1]                              = 0.61                                         
y1[1] (closed_form)               = 1.8196480178454795179007465786548            
y1[1] (numeric)                   = 1.8196480178454795179007465786554            
absolute error                    = 6e-31                                        
relative error                    = 3.2973409918607163947175790284959e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5728674601004812611909760321627            
y2[1] (numeric)                   = 1.5728674601004812611909760321635            
absolute error                    = 8e-31                                        
relative error                    = 5.0862518317270846211117817492476e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3587.3MB, alloc=40.3MB, time=44.02
memory used=3629.4MB, alloc=40.3MB, time=44.54
 
TOP MAIN SOLVE Loop
x[1]                              = 0.62                                         
y1[1] (closed_form)               = 1.8138784566625339286839996543607            
y1[1] (numeric)                   = 1.8138784566625339286839996543612            
absolute error                    = 5e-31                                        
relative error                    = 2.7565242762736188216392931606199e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5810351605373050758429632275822            
y2[1] (numeric)                   = 1.581035160537305075842963227583             
absolute error                    = 8e-31                                        
relative error                    = 5.0599760205720214346801590183153e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3671.6MB, alloc=40.3MB, time=45.06
 
TOP MAIN SOLVE Loop
memory used=3713.8MB, alloc=40.3MB, time=45.57
x[1]                              = 0.63                                         
y1[1] (closed_form)               = 1.8080275083121518725237089657771            
y1[1] (numeric)                   = 1.8080275083121518725237089657774            
absolute error                    = 3e-31                                        
relative error                    = 1.6592667900283167397894795205249e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5891447579422695131181120907946            
y2[1] (numeric)                   = 1.5891447579422695131181120907955            
absolute error                    = 9e-31                                        
relative error                    = 5.6634236465995706380680710139379e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3756.1MB, alloc=40.3MB, time=46.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.64                                         
y1[1] (closed_form)               = 1.8020957578842926135861107792603            
y1[1] (numeric)                   = 1.8020957578842926135861107792607            
absolute error                    = 4e-31                                        
relative error                    = 2.2196378757897439639791373119786e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.5971954413623920518835462392079            
y2[1] (numeric)                   = 1.5971954413623920518835462392089            
absolute error                    = 1.0e-30                                      
relative error                    = 6.2609745438980830325611501935312e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3798.3MB, alloc=40.3MB, time=46.61
memory used=3840.5MB, alloc=40.3MB, time=47.12
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y1[1] (closed_form)               = 1.7960837985490558289176045706799            
y1[1] (numeric)                   = 1.7960837985490558289176045706801            
absolute error                    = 2e-31                                        
relative error                    = 1.1135337903585987259748653798338e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6051864057360395603725216786059            
y2[1] (numeric)                   = 1.605186405736039560372521678607             
absolute error                    = 1.1e-30                                      
relative error                    = 6.8527866674500510200641691409838e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3882.7MB, alloc=40.3MB, time=47.64
 
TOP MAIN SOLVE Loop
memory used=3924.8MB, alloc=40.3MB, time=48.16
x[1]                              = 0.66                                         
y1[1] (closed_form)               = 1.7899922314973650927838170912302            
y1[1] (numeric)                   = 1.7899922314973650927838170912305            
absolute error                    = 3e-31                                        
relative error                    = 1.6759849273147060944544637298514e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6131168519734337886151454793963            
y2[1] (numeric)                   = 1.6131168519734337886151454793974            
absolute error                    = 1.1e-30                                      
relative error                    = 6.8190968227397562192516814649674e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=3966.9MB, alloc=40.3MB, time=48.67
 
TOP MAIN SOLVE Loop
x[1]                              = 0.67                                         
y1[1] (closed_form)               = 1.7838216658808492853029421448381            
y1[1] (numeric)                   = 1.7838216658808492853029421448385            
absolute error                    = 4e-31                                        
relative error                    = 2.2423766212217207014451307891782e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6209859870365596803574439141266            
y2[1] (numeric)                   = 1.6209859870365596803574439141276            
absolute error                    = 1.0e-30                                      
relative error                    = 6.1690847915852219097077708295877e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4009.1MB, alloc=40.3MB, time=49.18
memory used=4051.2MB, alloc=40.3MB, time=49.70
 
TOP MAIN SOLVE Loop
x[1]                              = 0.68                                         
y1[1] (closed_form)               = 1.7775727187509279371823940840443            
y1[1] (numeric)                   = 1.7775727187509279371823940840447            
absolute error                    = 4e-31                                        
relative error                    = 2.2502595577697301451039766634115e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6287930240184685137041781874202            
y2[1] (numeric)                   = 1.6287930240184685137041781874211            
absolute error                    = 9e-31                                        
relative error                    = 5.5255639404666010201687723786083e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4093.4MB, alloc=40.3MB, time=50.21
 
TOP MAIN SOLVE Loop
x[1]                              = 0.69                                         
y1[1] (closed_form)               = 1.7712460149971066019735393154978            
y1[1] (numeric)                   = 1.771246014997106601973539315498             
absolute error                    = 2e-31                                        
relative error                    = 1.1291486236615567354709239226839e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6365371822219679402374292070087            
y2[1] (numeric)                   = 1.6365371822219679402374292070096            
absolute error                    = 9e-31                                        
relative error                    = 5.4994167549437968042439004288060e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4135.6MB, alloc=40.3MB, time=50.73
memory used=4177.8MB, alloc=40.3MB, time=51.24
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y1[1] (closed_form)               = 1.7648421872844884262558599901919            
y1[1] (numeric)                   = 1.764842187284488426255859990192             
absolute error                    = 1e-31                                        
relative error                    = 5.6662290101908264424809517128610e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6442176872376910536726143513987            
y2[1] (numeric)                   = 1.6442176872376910536726143513997            
absolute error                    = 1.0e-30                                      
relative error                    = 6.0819197346065175188260274521277e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4220.1MB, alloc=40.3MB, time=51.76
memory used=4262.2MB, alloc=40.3MB, time=52.27
 
TOP MAIN SOLVE Loop
x[1]                              = 0.71                                         
y1[1] (closed_form)               = 1.7583618759905081665414579441396            
y1[1] (numeric)                   = 1.7583618759905081665414579441396            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6518337710215366812101279728528            
y2[1] (numeric)                   = 1.6518337710215366812101279728538            
absolute error                    = 1.0e-30                                      
relative error                    = 6.0538779236943083185531773730902e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4304.4MB, alloc=40.3MB, time=52.79
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y1[1] (closed_form)               = 1.751805729140894979445486962252             
y1[1] (numeric)                   = 1.7518057291408949794454869622519            
absolute error                    = 1e-31                                        
relative error                    = 5.7083955336212487798204503837466e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6593846719714731536180038326482            
y2[1] (numeric)                   = 1.6593846719714731536180038326492            
absolute error                    = 1.0e-30                                      
relative error                    = 6.0263302228284727680754475327508e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4346.6MB, alloc=40.3MB, time=53.30
memory used=4388.7MB, alloc=40.3MB, time=53.81
 
TOP MAIN SOLVE Loop
x[1]                              = 0.73                                         
y1[1] (closed_form)               = 1.7451744023448703887901321585503            
y1[1] (numeric)                   = 1.7451744023448703887901321585502            
absolute error                    = 1e-31                                        
relative error                    = 5.7300863378260019292174571738854e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6668696350036978737325941307615            
y2[1] (numeric)                   = 1.6668696350036978737325941307625            
absolute error                    = 1.0e-30                                      
relative error                    = 5.9992694029595274613422544528161e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4430.8MB, alloc=40.3MB, time=54.33
memory used=4473.0MB, alloc=40.3MB, time=54.84
 
TOP MAIN SOLVE Loop
x[1]                              = 0.74                                         
y1[1] (closed_form)               = 1.7384685587295879097914245606988            
y1[1] (numeric)                   = 1.7384685587295879097914245606986            
absolute error                    = 2e-31                                        
relative error                    = 1.1504378321696712944993922812682e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6742879116281450674838811576082            
y2[1] (numeric)                   = 1.6742879116281450674838811576093            
absolute error                    = 1.1e-30                                      
relative error                    = 6.5699572478565866926210579484038e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4515.2MB, alloc=40.3MB, time=55.35
 
TOP MAIN SOLVE Loop
x[1]                              = 0.75                                         
y1[1] (closed_form)               = 1.7316888688738208863118387530001            
y1[1] (numeric)                   = 1.7316888688738208863118387529997            
absolute error                    = 4e-31                                        
relative error                    = 2.3098837625498758610321808593125e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6816387600233341667332419527799            
y2[1] (numeric)                   = 1.6816387600233341667332419527809            
absolute error                    = 1.0e-30                                      
relative error                    = 5.9465803463409950795293630973964e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4557.3MB, alloc=40.3MB, time=55.87
memory used=4599.5MB, alloc=40.3MB, time=56.38
 
TOP MAIN SOLVE Loop
x[1]                              = 0.76                                         
y1[1] (closed_form)               = 1.724836010740905172339688366667             
y1[1] (numeric)                   = 1.7248360107409051723396883666667            
absolute error                    = 3e-31                                        
relative error                    = 1.7392957830880089047314622841127e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6889214451105513391477556387697            
y2[1] (numeric)                   = 1.6889214451105513391477556387707            
absolute error                    = 1.0e-30                                      
relative error                    = 5.9209384953634905857483909054948e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4641.7MB, alloc=40.3MB, time=56.90
memory used=4683.8MB, alloc=40.3MB, time=57.41
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y1[1] (closed_form)               = 1.7179106696109433633712905653243            
y1[1] (numeric)                   = 1.717910669610943363371290565324             
absolute error                    = 3e-31                                        
relative error                    = 1.7463073331277536436436098781629e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.6961352386273567470198837344522            
y2[1] (numeric)                   = 1.6961352386273567470198837344531            
absolute error                    = 9e-31                                        
relative error                    = 5.3061806600300888047605693798603e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4726.0MB, alloc=40.3MB, time=57.93
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y1[1] (closed_form)               = 1.7109135380122773572162650237646            
y1[1] (numeric)                   = 1.7109135380122773572162650237642            
absolute error                    = 4e-31                                        
relative error                    = 2.3379322865415869835560852635835e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7032794192004101843678973251179            
y2[1] (numeric)                   = 1.7032794192004101843678973251188            
absolute error                    = 9e-31                                        
relative error                    = 5.2839245860347283979756198357756e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4768.2MB, alloc=40.3MB, time=58.45
memory used=4810.3MB, alloc=40.3MB, time=58.96
 
TOP MAIN SOLVE Loop
x[1]                              = 0.79                                         
y1[1] (closed_form)               = 1.703845315652236096912780861085             
y1[1] (numeric)                   = 1.7038453156522360969127808610844            
absolute error                    = 6e-31                                        
relative error                    = 3.5214464276078873548269116380575e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7103532724176078098140288749692            
y2[1] (numeric)                   = 1.7103532724176078098140288749701            
absolute error                    = 9e-31                                        
relative error                    = 5.2620707927072730160340494674210e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4852.6MB, alloc=40.3MB, time=59.48
memory used=4894.7MB, alloc=40.3MB, time=59.99
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y1[1] (closed_form)               = 1.6967067093471654209207499816423            
y1[1] (numeric)                   = 1.6967067093471654209207499816416            
absolute error                    = 7e-31                                        
relative error                    = 4.1256393703384128431764496480596e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7173560908995227616271746105814            
y2[1] (numeric)                   = 1.7173560908995227616271746105825            
absolute error                    = 1.1e-30                                      
relative error                    = 6.4051946234623837643034099777316e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4936.9MB, alloc=40.3MB, time=60.51
 
TOP MAIN SOLVE Loop
x[1]                              = 0.81                                         
y1[1] (closed_form)               = 1.6894984329517470175496392406801            
y1[1] (numeric)                   = 1.6894984329517470175496392406795            
absolute error                    = 6e-31                                        
relative error                    = 3.5513498461891519385642759755239e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7242871743701425109281768525145            
y2[1] (numeric)                   = 1.7242871743701425109281768525156            
absolute error                    = 1.1e-30                                      
relative error                    = 6.3794477877608426596711428358684e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=4979.0MB, alloc=40.3MB, time=61.03
memory used=5021.1MB, alloc=40.3MB, time=61.54
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y1[1] (closed_form)               = 1.6822212072876135516665579784369            
y1[1] (numeric)                   = 1.6822212072876135516665579784365            
absolute error                    = 4e-31                                        
relative error                    = 2.3778085680239020031373752737322e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7311458297268958793813133646877            
y2[1] (numeric)                   = 1.7311458297268958793813133646888            
absolute error                    = 1.1e-30                                      
relative error                    = 6.3541729478303689846719965308294e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5063.3MB, alloc=40.3MB, time=62.06
memory used=5105.5MB, alloc=40.3MB, time=62.57
 
TOP MAIN SOLVE Loop
x[1]                              = 0.83                                         
y1[1] (closed_form)               = 1.6748757600712671021124629178644            
y1[1] (numeric)                   = 1.6748757600712671021124629178641            
absolute error                    = 3e-31                                        
relative error                    = 1.7911776333023937015518563885435e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7379313711099627187285802261381            
y2[1] (numeric)                   = 1.7379313711099627187285802261391            
absolute error                    = 1.0e-30                                      
relative error                    = 5.7539671394580506308555960959128e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5147.7MB, alloc=40.3MB, time=63.09
 
TOP MAIN SOLVE Loop
x[1]                              = 0.84                                         
y1[1] (closed_form)               = 1.6674628258413081179226710368709            
y1[1] (numeric)                   = 1.6674628258413081179226710368706            
absolute error                    = 3e-31                                        
relative error                    = 1.7991405586426602600450780880416e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7446431199708593212565726706296            
y2[1] (numeric)                   = 1.7446431199708593212565726706307            
absolute error                    = 1.1e-30                                      
relative error                    = 6.3050144032802149239545741058735e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5189.9MB, alloc=40.3MB, time=63.60
memory used=5231.9MB, alloc=40.3MB, time=64.12
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y1[1] (closed_form)               = 1.6599831458849821703954160294615            
y1[1] (numeric)                   = 1.6599831458849821703954160294613            
absolute error                    = 2e-31                                        
relative error                    = 1.2048315098607495773354058660782e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7512804051402927027120715242355            
y2[1] (numeric)                   = 1.7512804051402927027120715242365            
absolute error                    = 1.0e-30                                      
relative error                    = 5.7101078563138000370993153595601e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5274.1MB, alloc=40.3MB, time=64.63
memory used=5316.2MB, alloc=40.3MB, time=65.14
 
TOP MAIN SOLVE Loop
x[1]                              = 0.86                                         
y1[1] (closed_form)               = 1.6524374681640518462720306642239            
y1[1] (numeric)                   = 1.6524374681640518462720306642237            
absolute error                    = 2e-31                                        
relative error                    = 1.2103332431829381617794594347584e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7578425628952769722945887295286            
y2[1] (numeric)                   = 1.7578425628952769722945887295296            
absolute error                    = 1.0e-30                                      
relative error                    = 5.6887915966315963416482375164598e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5358.4MB, alloc=40.3MB, time=65.66
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y1[1] (closed_form)               = 1.6448265472400011947776638054828            
y1[1] (numeric)                   = 1.6448265472400011947776638054827            
absolute error                    = 1e-31                                        
relative error                    = 6.0796684104958529208545021706576e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7643289370255050781448028237228            
y2[1] (numeric)                   = 1.7643289370255050781448028237238            
absolute error                    = 1.0e-30                                      
relative error                    = 5.6678773385982504834720026856375e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5400.6MB, alloc=40.3MB, time=66.18
memory used=5442.8MB, alloc=40.3MB, time=66.69
 
TOP MAIN SOLVE Loop
x[1]                              = 0.88                                         
y1[1] (closed_form)               = 1.6371511441985802080154986057221            
y1[1] (numeric)                   = 1.6371511441985802080154986057219            
absolute error                    = 2e-31                                        
relative error                    = 1.2216343048637955235862318432519e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.770738878898969291209645130756             
y2[1] (numeric)                   = 1.7707388788989692912096451307569            
absolute error                    = 9e-31                                        
relative error                    = 5.0826240431317152491304712522212e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5485.0MB, alloc=40.3MB, time=67.23
 
TOP MAIN SOLVE Loop
memory used=5527.1MB, alloc=40.3MB, time=67.75
x[1]                              = 0.89                                         
y1[1] (closed_form)               = 1.6294120265736968802035530573802            
y1[1] (numeric)                   = 1.6294120265736968802035530573801            
absolute error                    = 1e-31                                        
relative error                    = 6.1371831291977448468527348948596e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7770717475268238654903337129732            
y2[1] (numeric)                   = 1.7770717475268238654903337129742            
absolute error                    = 1.0e-30                                      
relative error                    = 5.6272348113784054238570141075072e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5569.4MB, alloc=40.3MB, time=68.26
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y1[1] (closed_form)               = 1.6216099682706644564847161514071            
y1[1] (numeric)                   = 1.6216099682706644564847161514072            
absolute error                    = 1e-31                                        
relative error                    = 6.1667109820891841753494332291975e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7833269096274833884613823157136            
y2[1] (numeric)                   = 1.7833269096274833884613823157146            
absolute error                    = 1.0e-30                                      
relative error                    = 5.6074968341552619311245879096031e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5611.6MB, alloc=40.3MB, time=68.78
memory used=5653.7MB, alloc=40.3MB, time=69.30
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y1[1] (closed_form)               = 1.6137457494888115465211782261747            
y1[1] (numeric)                   = 1.6137457494888115465211782261748            
absolute error                    = 1e-31                                        
relative error                    = 6.1967630298438980922494390229635e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7895037396899504118789575178716            
y2[1] (numeric)                   = 1.7895037396899504118789575178727            
absolute error                    = 1.1e-30                                      
relative error                    = 6.1469555810516836618086184536913e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5695.9MB, alloc=40.3MB, time=69.81
 
TOP MAIN SOLVE Loop
memory used=5738.1MB, alloc=40.3MB, time=70.33
x[1]                              = 0.92                                         
y1[1] (closed_form)               = 1.6058201566434628417974047066744            
y1[1] (numeric)                   = 1.6058201566434628417974047066743            
absolute error                    = 1e-31                                        
relative error                    = 6.2273474141103839376996914003978e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.7956016200363660302682761024816            
y2[1] (numeric)                   = 1.7956016200363660302682761024827            
absolute error                    = 1.1e-30                                      
relative error                    = 6.1260804608637069354695367328441e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5780.3MB, alloc=40.3MB, time=70.90
 
TOP MAIN SOLVE Loop
x[1]                              = 0.93                                         
y1[1] (closed_form)               = 1.597833982287298238494907084433             
y1[1] (numeric)                   = 1.5978339822872982384949070844329            
absolute error                    = 1e-31                                        
relative error                    = 6.2584724763989603782639539155790e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8016199408837771520843192159106            
y2[1] (numeric)                   = 1.8016199408837771520843192159118            
absolute error                    = 1.2e-30                                      
relative error                    = 6.6606722803664406717716384081577e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5822.5MB, alloc=40.3MB, time=71.41
memory used=5864.6MB, alloc=40.3MB, time=71.93
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y1[1] (closed_form)               = 1.589788025031098229960989815224             
y1[1] (numeric)                   = 1.5897880250310982299609898152238            
absolute error                    = 2e-31                                        
relative error                    = 1.2580293526622063428193425676008e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8075581004051142868702197986342            
y2[1] (numeric)                   = 1.8075581004051142868702197986354            
absolute error                    = 1.2e-30                                      
relative error                    = 6.6387907516281391004657365866966e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5906.9MB, alloc=40.3MB, time=72.44
 
TOP MAIN SOLVE Loop
memory used=5948.9MB, alloc=40.3MB, time=72.96
x[1]                              = 0.95                                         
y1[1] (closed_form)               = 1.5816830894638834941661809737605            
y1[1] (numeric)                   = 1.58168308946388349416618097376              
absolute error                    = 5e-31                                        
relative error                    = 3.1611895159698305161625311336748e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8134155047893737506854221021026            
y2[1] (numeric)                   = 1.8134155047893737506854221021038            
absolute error                    = 1.2e-30                                      
relative error                    = 6.6173471928011264134592541873134e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=5991.1MB, alloc=40.3MB, time=73.48
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y1[1] (closed_form)               = 1.5735199860724566621250508003519            
y1[1] (numeric)                   = 1.5735199860724566621250508003513            
absolute error                    = 6e-31                                        
relative error                    = 3.8131069532686030959891061427726e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8191915683009982716332221464304            
y2[1] (numeric)                   = 1.8191915683009982716332221464316            
absolute error                    = 1.2e-30                                      
relative error                    = 6.5963366415595183056497609050378e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6033.3MB, alloc=40.3MB, time=74.00
memory used=6075.5MB, alloc=40.3MB, time=74.51
 
TOP MAIN SOLVE Loop
x[1]                              = 0.97                                         
y1[1] (closed_form)               = 1.5652995311603543130365277548499            
y1[1] (numeric)                   = 1.5652995311603543130365277548493            
absolute error                    = 6e-31                                        
relative error                    = 3.8331321772978546448763949764241e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8248857133384500574766200378563            
y2[1] (numeric)                   = 1.8248857133384500574766200378575            
absolute error                    = 1.2e-30                                      
relative error                    = 6.5757542580829200636082281336399e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6117.7MB, alloc=40.3MB, time=75.03
 
TOP MAIN SOLVE Loop
memory used=6159.9MB, alloc=40.3MB, time=75.54
x[1]                              = 0.98                                         
y1[1] (closed_form)               = 1.5570225467662173008766582673599            
y1[1] (numeric)                   = 1.5570225467662173008766582673593            
absolute error                    = 6e-31                                        
relative error                    = 3.8535087449192112922450918099611e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8304973704919704680845332877192            
y2[1] (numeric)                   = 1.8304973704919704680845332877203            
absolute error                    = 1.1e-30                                      
relative error                    = 6.0092957123689306232259040553489e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6202.1MB, alloc=40.3MB, time=76.06
 
TOP MAIN SOLVE Loop
x[1]                              = 0.99                                         
y1[1] (closed_form)               = 1.5486898605815875753431264086536            
y1[1] (numeric)                   = 1.5486898605815875753431264086531            
absolute error                    = 5e-31                                        
relative error                    = 3.2285353751346469972147487334409e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8360259786005205167892594115471            
y2[1] (numeric)                   = 1.8360259786005205167892594115483            
absolute error                    = 1.2e-30                                      
relative error                    = 6.5358552329127691884278112370427e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6244.3MB, alloc=40.3MB, time=76.58
memory used=6286.5MB, alloc=40.3MB, time=77.09
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y1[1] (closed_form)               = 1.540302305868139717400936607443             
y1[1] (numeric)                   = 1.5403023058681397174009366074424            
absolute error                    = 6e-31                                        
relative error                    = 3.8953392312285745106512994965630e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8414709848078965066525023216303            
y2[1] (numeric)                   = 1.8414709848078965066525023216314            
absolute error                    = 1.1e-30                                      
relative error                    = 5.9734853770435744380681973998392e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6328.7MB, alloc=40.3MB, time=77.61
 
TOP MAIN SOLVE Loop
memory used=6370.9MB, alloc=40.3MB, time=78.12
x[1]                              = 1.01                                         
y1[1] (closed_form)               = 1.5318607213743554662067313557792            
y1[1] (numeric)                   = 1.5318607213743554662067313557784            
absolute error                    = 8e-31                                        
relative error                    = 5.2224068992529272055856311269539e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.846831844618015190123098784782             
y2[1] (numeric)                   = 1.846831844618015190123098784783             
absolute error                    = 1.0e-30                                      
relative error                    = 5.4146781306277100697667690010343e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6413.1MB, alloc=40.3MB, time=78.64
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y1[1] (closed_form)               = 1.5233659512516495698896138080338            
y1[1] (numeric)                   = 1.5233659512516495698896138080331            
absolute error                    = 7e-31                                        
relative error                    = 4.5950876046878693697908454245795e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8521080219493629236165499854554            
y2[1] (numeric)                   = 1.8521080219493629236165499854565            
absolute error                    = 1.1e-30                                      
relative error                    = 5.9391784224455686912587188287402e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6455.4MB, alloc=40.3MB, time=79.16
memory used=6497.5MB, alloc=40.3MB, time=79.67
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y1[1] (closed_form)               = 1.5148188449699553475335022998374            
y1[1] (numeric)                   = 1.5148188449699553475335022998366            
absolute error                    = 8e-31                                        
relative error                    = 5.2811595436407913205679819553151e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8572989891886033721462743852944            
y2[1] (numeric)                   = 1.8572989891886033721462743852957            
absolute error                    = 1.3e-30                                      
relative error                    = 6.9994115517606020612001546146059e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6539.7MB, alloc=40.3MB, time=80.19
 
TOP MAIN SOLVE Loop
memory used=6581.9MB, alloc=40.3MB, time=80.70
x[1]                              = 1.04                                         
y1[1] (closed_form)               = 1.5062202572327784037344734209922            
y1[1] (numeric)                   = 1.5062202572327784037344734209915            
absolute error                    = 7e-31                                        
relative error                    = 4.6473946731139912470772395250600e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8624042272433384032807916921162            
y2[1] (numeric)                   = 1.8624042272433384032807916921174            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4432843442166980626135497348783e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6624.0MB, alloc=40.3MB, time=81.22
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y1[1] (closed_form)               = 1.4975710478917269902908495728121            
y1[1] (numeric)                   = 1.4975710478917269902908495728114            
absolute error                    = 7e-31                                        
relative error                    = 4.6742356630455462459820387855994e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8674232255940168943814094850003            
y2[1] (numeric)                   = 1.8674232255940168943814094850015            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4259669878438333369681345826992e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6666.1MB, alloc=40.3MB, time=81.74
memory used=6708.2MB, alloc=40.3MB, time=82.25
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y1[1] (closed_form)               = 1.4888720818605275619186375399564            
y1[1] (numeric)                   = 1.4888720818605275619186375399559            
absolute error                    = 5e-31                                        
relative error                    = 3.3582468641307916456851203742251e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8723554823449862622829459219974            
y2[1] (numeric)                   = 1.8723554823449862622829459219986            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4090393694742681684315028837423e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6750.4MB, alloc=40.3MB, time=82.77
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y1[1] (closed_form)               = 1.4801242290285341243650930681759            
y1[1] (numeric)                   = 1.4801242290285341243650930681755            
absolute error                    = 4e-31                                        
relative error                    = 2.7024758608440340703949211437902e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8772005042746816103070632577768            
y2[1] (numeric)                   = 1.8772005042746816103070632577781            
absolute error                    = 1.3e-30                                      
relative error                    = 6.9252058959056050268377083921943e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6792.7MB, alloc=40.3MB, time=83.29
memory used=6834.8MB, alloc=40.3MB, time=83.80
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y1[1] (closed_form)               = 1.471328364173740023913524788526             
y1[1] (numeric)                   = 1.4713283641737400239135247885256            
absolute error                    = 4e-31                                        
relative error                    = 2.7186317462494489472062900332304e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8819578068849474737353349876248            
y2[1] (numeric)                   = 1.881957806884947473735334987626             
absolute error                    = 1.2e-30                                      
relative error                    = 6.3763384896830547548809387809117e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6877.0MB, alloc=40.3MB, time=84.32
memory used=6919.1MB, alloc=40.3MB, time=84.84
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y1[1] (closed_form)               = 1.4624853668753008770278970738751            
y1[1] (numeric)                   = 1.4624853668753008770278970738747            
absolute error                    = 4e-31                                        
relative error                    = 2.7350701009380156368116273771998e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.886626914449487231608600628636             
y2[1] (numeric)                   = 1.8866269144494872316086006286373            
absolute error                    = 1.3e-30                                      
relative error                    = 6.8906045495451684396543670149804e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=6961.2MB, alloc=40.3MB, time=85.35
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y1[1] (closed_form)               = 1.4535961214255773877713700517847            
y1[1] (numeric)                   = 1.4535961214255773877713700517843            
absolute error                    = 4e-31                                        
relative error                    = 2.7517960051221805953487480031032e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8912073600614353399518025778717            
y2[1] (numeric)                   = 1.891207360061435339951802577873             
absolute error                    = 1.3e-30                                      
relative error                    = 6.8739157188864253632188556277634e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7003.1MB, alloc=40.3MB, time=85.86
memory used=7045.0MB, alloc=40.3MB, time=86.38
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y1[1] (closed_form)               = 1.4446615167417068486437375119336            
y1[1] (numeric)                   = 1.4446615167417068486437375119331            
absolute error                    = 5e-31                                        
relative error                    = 3.4610183368606733179351061534537e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8956986856800476292406259593394            
y2[1] (numeric)                   = 1.8956986856800476292406259593406            
absolute error                    = 1.2e-30                                      
relative error                    = 6.3301199133844506307150958466920e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7086.9MB, alloc=40.3MB, time=86.89
memory used=7128.8MB, alloc=40.3MB, time=87.40
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y1[1] (closed_form)               = 1.4356824462767121676139887939611            
y1[1] (numeric)                   = 1.4356824462767121676139887939608            
absolute error                    = 3e-31                                        
relative error                    = 2.0895985792541915969706446406115e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9001004421765049971191032473392            
y2[1] (numeric)                   = 1.9001004421765049971191032473404            
absolute error                    = 1.2e-30                                      
relative error                    = 6.3154556115225042011133830149338e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7170.8MB, alloc=40.3MB, time=87.92
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y1[1] (closed_form)               = 1.4266598079301573103712158356535            
y1[1] (numeric)                   = 1.4266598079301573103712158356531            
absolute error                    = 4e-31                                        
relative error                    = 2.8037517968655226646327619856208e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9044121893788259160370815224114            
y2[1] (numeric)                   = 1.9044121893788259160370815224125            
absolute error                    = 1.1e-30                                      
relative error                    = 5.7760604880332860516758634632680e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7212.8MB, alloc=40.3MB, time=88.43
memory used=7254.6MB, alloc=40.3MB, time=88.94
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y1[1] (closed_form)               = 1.4175945039583580921751867408226            
y1[1] (numeric)                   = 1.4175945039583580921751867408222            
absolute error                    = 4e-31                                        
relative error                    = 2.8216813685653935037129581349355e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9086334961158832645942155781022            
y2[1] (numeric)                   = 1.9086334961158832645942155781032            
absolute error                    = 1.0e-30                                      
relative error                    = 5.2393505722027037878934821367571e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7296.6MB, alloc=40.3MB, time=89.46
memory used=7338.5MB, alloc=40.3MB, time=89.97
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y1[1] (closed_form)               = 1.4084874408841572981525767188099            
y1[1] (numeric)                   = 1.4084874408841572981525767188095            
absolute error                    = 4e-31                                        
relative error                    = 2.8399259261332559459646770122429e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9127639402605210809440330497537            
y2[1] (numeric)                   = 1.9127639402605210809440330497545            
absolute error                    = 8e-31                                        
relative error                    = 4.1824293273274427113429530660990e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7380.5MB, alloc=40.3MB, time=90.49
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y1[1] (closed_form)               = 1.399339529406273154451639623394             
y1[1] (numeric)                   = 1.3993395294062731544516396233934            
absolute error                    = 6e-31                                        
relative error                    = 4.2877370887576831451683561801968e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9168031087717669266186616668743            
y2[1] (numeric)                   = 1.916803108771766926618661666875             
absolute error                    = 7e-31                                        
relative error                    = 3.6519139435689884114565642582163e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7422.4MB, alloc=40.3MB, time=91.00
memory used=7464.3MB, alloc=40.3MB, time=91.52
 
TOP MAIN SOLVE Loop
x[1]                              = 1.17                                         
y1[1] (closed_form)               = 1.3901516843082302153326619350505            
y1[1] (numeric)                   = 1.3901516843082302153326619350499            
absolute error                    = 6e-31                                        
relative error                    = 4.3160757690882709719480063350905e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.920750597736135639573013008962             
y2[1] (numeric)                   = 1.9207505977361356395730130089626            
absolute error                    = 6e-31                                        
relative error                    = 3.1237788014080596920625910853260e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7506.3MB, alloc=40.3MB, time=92.03
memory used=7548.2MB, alloc=40.3MB, time=92.54
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y1[1] (closed_form)               = 1.3809248243668817730295994667128            
y1[1] (numeric)                   = 1.3809248243668817730295994667122            
absolute error                    = 6e-31                                        
relative error                    = 4.3449142879670111154211702769903e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9246060124080203461075380258748            
y2[1] (numeric)                   = 1.9246060124080203461075380258755            
absolute error                    = 7e-31                                        
relative error                    = 3.6371080391886388428364436604748e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7590.1MB, alloc=40.3MB, time=93.05
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y1[1] (closed_form)               = 1.3716598722605329380656795583505            
y1[1] (numeric)                   = 1.37165987226053293806567955835              
absolute error                    = 5e-31                                        
relative error                    = 3.6452185422322397015495260973051e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9283689672491666926020211116027            
y2[1] (numeric)                   = 1.9283689672491666926020211116033            
absolute error                    = 6e-31                                        
relative error                    = 3.1114377496745587000916069602963e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7632.1MB, alloc=40.3MB, time=93.57
memory used=7673.8MB, alloc=40.3MB, time=94.08
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y1[1] (closed_form)               = 1.3623577544766735776383733556231            
y1[1] (numeric)                   = 1.3623577544766735776383733556226            
absolute error                    = 5e-31                                        
relative error                    = 3.6701079313198936158870182224103e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9320390859672263496701344354948            
y2[1] (numeric)                   = 1.9320390859672263496701344354954            
absolute error                    = 6e-31                                        
relative error                    = 3.1055272347123620581247067478483e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7715.8MB, alloc=40.3MB, time=94.59
memory used=7757.6MB, alloc=40.3MB, time=95.10
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y1[1] (closed_form)               = 1.3530194012193303387030107136648            
y1[1] (numeric)                   = 1.3530194012193303387030107136642            
absolute error                    = 6e-31                                        
relative error                    = 4.4345262119618149244432275901208e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9356160015533859334164648885436            
y2[1] (numeric)                   = 1.9356160015533859334164648885443            
absolute error                    = 7e-31                                        
relative error                    = 3.6164197828403486951992418383993e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7799.5MB, alloc=40.3MB, time=95.62
 
TOP MAIN SOLVE Loop
x[1]                              = 1.22                                         
y1[1] (closed_form)               = 1.3436457463160470204755229744352            
y1[1] (numeric)                   = 1.3436457463160470204755229744346            
absolute error                    = 6e-31                                        
relative error                    = 4.4654627281413681562211564779427e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9390993563190675809352452718884            
y2[1] (numeric)                   = 1.9390993563190675809352452718889            
absolute error                    = 5e-31                                        
relative error                    = 2.5785166622360937580441889740517e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7841.5MB, alloc=40.3MB, time=96.14
memory used=7883.4MB, alloc=40.3MB, time=96.65
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y1[1] (closed_form)               = 1.3342377271245025982395472454977            
y1[1] (numeric)                   = 1.3342377271245025982395472454972            
absolute error                    = 5e-31                                        
relative error                    = 3.7474581166100032844358135653642e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9424888019316975100238235653892            
y2[1] (numeric)                   = 1.9424888019316975100238235653897            
absolute error                    = 5e-31                                        
relative error                    = 2.5740174126243492231592685466759e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=7925.4MB, alloc=40.3MB, time=97.16
memory used=7967.3MB, alloc=40.3MB, time=97.67
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y1[1] (closed_form)               = 1.3247962844387762365776934156974            
y1[1] (numeric)                   = 1.3247962844387762365776934156969            
absolute error                    = 5e-31                                        
relative error                    = 3.7741651744729576917519206818506e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9457839994495389862847059630818            
y2[1] (numeric)                   = 1.9457839994495389862847059630824            
absolute error                    = 6e-31                                        
relative error                    = 3.0835899574142844497850570195552e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8009.2MB, alloc=40.3MB, time=98.18
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y1[1] (closed_form)               = 1.315322362395268665447538552438             
y1[1] (numeric)                   = 1.3153223623952686654475385524375            
absolute error                    = 5e-31                                        
relative error                    = 3.8013494964798946052030395033268e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.948984619355586214348490847036             
y2[1] (numeric)                   = 1.9489846193555862143484908470366            
absolute error                    = 6e-31                                        
relative error                    = 3.0785260901565475934770177933065e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8051.1MB, alloc=40.3MB, time=98.70
memory used=8093.0MB, alloc=40.3MB, time=99.21
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y1[1] (closed_form)               = 1.3058169083782893268863424891765            
y1[1] (numeric)                   = 1.3058169083782893268863424891759            
absolute error                    = 6e-31                                        
relative error                    = 4.5948248651883949986250696369504e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9520903415905157638568162214254            
y2[1] (numeric)                   = 1.952090341590515763856816221426             
absolute error                    = 6e-31                                        
relative error                    = 3.0736282395164897095969180833147e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8135.0MB, alloc=40.3MB, time=99.72
memory used=8176.8MB, alloc=40.3MB, time=100.23
 
TOP MAIN SOLVE Loop
x[1]                              = 1.27                                         
y1[1] (closed_form)               = 1.296280872925318733551137016088             
y1[1] (numeric)                   = 1.2962808729253187335511370160874            
absolute error                    = 6e-31                                        
relative error                    = 4.6286265001039413538785822801755e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9551008555846922350901817421829            
y2[1] (numeric)                   = 1.9551008555846922350901817421836            
absolute error                    = 7e-31                                        
relative error                    = 3.5803779533954430253479725766800e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8218.8MB, alloc=40.3MB, time=100.75
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y1[1] (closed_form)               = 1.2867152096319555127793868935926            
y1[1] (numeric)                   = 1.286715209631955512779386893592             
absolute error                    = 6e-31                                        
relative error                    = 4.6630365096222068293378630738269e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9580158602892249637007538591603            
y2[1] (numeric)                   = 1.958015860289224963700753859161             
absolute error                    = 7e-31                                        
relative error                    = 3.5750476500052491777052134906350e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8260.8MB, alloc=40.3MB, time=101.26
memory used=8302.7MB, alloc=40.3MB, time=101.77
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y1[1] (closed_form)               = 1.2771208750565576413866060900612            
y1[1] (numeric)                   = 1.2771208750565576413866060900606            
absolute error                    = 6e-31                                        
relative error                    = 4.6980674399627900425012581394146e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9608350642060726589055612912854            
y2[1] (numeric)                   = 1.9608350642060726589055612912861            
absolute error                    = 7e-31                                        
relative error                    = 3.5699076009915434930311400530652e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8344.6MB, alloc=40.3MB, time=102.29
memory used=8386.5MB, alloc=40.3MB, time=102.80
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y1[1] (closed_form)               = 1.2674988286245874069979841092929            
y1[1] (numeric)                   = 1.2674988286245874069979841092924            
absolute error                    = 5e-31                                        
relative error                    = 3.9447768211554843931490763461198e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9635581854171929647013486300396            
y2[1] (numeric)                   = 1.9635581854171929647013486300403            
absolute error                    = 7e-31                                        
relative error                    = 3.5649567463735357177349704320266e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8428.5MB, alloc=40.3MB, time=103.31
 
TOP MAIN SOLVE Loop
memory used=8470.3MB, alloc=40.3MB, time=103.83
x[1]                              = 1.31                                         
y1[1] (closed_form)               = 1.2578500325326696613381769786162            
y1[1] (numeric)                   = 1.2578500325326696613381769786158            
absolute error                    = 4e-31                                        
relative error                    = 3.1800293330247296540453150291050e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9661849516127340291692578059375            
y2[1] (numeric)                   = 1.9661849516127340291692578059382            
absolute error                    = 7e-31                                        
relative error                    = 3.5601940673273660634899321296923e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8512.3MB, alloc=40.3MB, time=104.34
 
TOP MAIN SOLVE Loop
x[1]                              = 1.32                                         
y1[1] (closed_form)               = 1.2481754516523729595739827294274            
y1[1] (numeric)                   = 1.2481754516523729595739827294268            
absolute error                    = 6e-31                                        
relative error                    = 4.8070165072202116355064903575976e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9687151001182652627358998459728            
y2[1] (numeric)                   = 1.9687151001182652627358998459735            
absolute error                    = 7e-31                                        
relative error                    = 3.5556185857361960772126246903190e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8554.2MB, alloc=40.3MB, time=104.85
memory used=8596.1MB, alloc=40.3MB, time=105.37
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y1[1] (closed_form)               = 1.2384760534337232075157849860106            
y1[1] (numeric)                   = 1.2384760534337232075157849860101            
absolute error                    = 5e-31                                        
relative error                    = 4.0372197638681061316968435110434e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9711483779210445623376830377638            
y2[1] (numeric)                   = 1.9711483779210445623376830377646            
absolute error                    = 8e-31                                        
relative error                    = 4.0585478442965009614917397508622e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8638.0MB, alloc=40.3MB, time=105.88
 
TOP MAIN SOLVE Loop
memory used=8679.9MB, alloc=40.3MB, time=106.39
x[1]                              = 1.34                                         
y1[1] (closed_form)               = 1.2287528078084594652326394923001            
y1[1] (numeric)                   = 1.2287528078084594652326394922997            
absolute error                    = 4e-31                                        
relative error                    = 3.2553333547487024677583419710191e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9734845416953193747878703480896            
y2[1] (numeric)                   = 1.9734845416953193747878703480906            
absolute error                    = 1.0e-30                                      
relative error                    = 5.0671792906011378093288912483107e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8721.8MB, alloc=40.3MB, time=106.90
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y1[1] (closed_form)               = 1.2190066870930415814200221730106            
y1[1] (numeric)                   = 1.2190066870930415814200221730103            
absolute error                    = 3e-31                                        
relative error                    = 2.4610201336582354571266789408816e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9757233578266590692611135392652            
y2[1] (numeric)                   = 1.9757233578266590692611135392662            
absolute error                    = 1.0e-30                                      
relative error                    = 5.0614373517354317078567354657180e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8763.7MB, alloc=40.3MB, time=107.42
memory used=8805.5MB, alloc=40.3MB, time=107.93
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y1[1] (closed_form)               = 1.2092386658914193576759752523919            
y1[1] (numeric)                   = 1.2092386658914193576759752523915            
absolute error                    = 4e-31                                        
relative error                    = 3.3078664392949292796602718264750e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9778646024353161856784924394266            
y2[1] (numeric)                   = 1.9778646024353161856784924394277            
absolute error                    = 1.1e-30                                      
relative error                    = 5.5615536000067236657075199581456e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8847.5MB, alloc=40.3MB, time=108.44
 
TOP MAIN SOLVE Loop
memory used=8889.4MB, alloc=40.3MB, time=108.95
x[1]                              = 1.37                                         
y1[1] (closed_form)               = 1.1994497209975729656881983896453            
y1[1] (numeric)                   = 1.199449720997572965688198389645             
absolute error                    = 3e-31                                        
relative error                    = 2.5011469405361347109301122768487e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9799080613986142228876885048919            
y2[1] (numeric)                   = 1.9799080613986142228876885048929            
absolute error                    = 1.0e-30                                      
relative error                    = 5.0507395747133651219664071195626e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8931.3MB, alloc=40.3MB, time=109.47
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y1[1] (closed_form)               = 1.1896408312978343632091500735982            
y1[1] (numeric)                   = 1.189640831297834363209150073598             
absolute error                    = 2e-31                                        
relative error                    = 1.6811796866606429706373023342143e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.981853530372359727878131085206             
y2[1] (numeric)                   = 1.9818535303723597278781310852071            
absolute error                    = 1.1e-30                                      
relative error                    = 5.5503597170136329732435186414709e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=8973.2MB, alloc=40.3MB, time=109.98
memory used=9015.1MB, alloc=40.3MB, time=110.49
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y1[1] (closed_form)               = 1.179812977672999476596163217804             
y1[1] (numeric)                   = 1.179812977672999476596163217804             
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9837008148112765448400382244429            
y2[1] (numeric)                   = 1.983700814811276544840038224444             
absolute error                    = 1.1e-30                                      
relative error                    = 5.5451910478982727110899791208657e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9057.1MB, alloc=40.3MB, time=111.01
 
TOP MAIN SOLVE Loop
memory used=9099.0MB, alloc=40.3MB, time=111.52
x[1]                              = 1.4                                          
y1[1] (closed_form)               = 1.1699671429002409386167480352036            
y1[1] (numeric)                   = 1.1699671429002409386167480352037            
absolute error                    = 1e-31                                        
relative error                    = 8.5472485793155863828236215107460e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9854497299884601806594745788061            
y2[1] (numeric)                   = 1.9854497299884601806594745788073            
absolute error                    = 1.2e-30                                      
relative error                    = 6.0439707028340356570045886922494e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9140.9MB, alloc=40.3MB, time=112.04
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y1[1] (closed_form)               = 1.1601043115548311901635625493609            
y1[1] (numeric)                   = 1.160104311554831190163562549361             
absolute error                    = 1e-31                                        
relative error                    = 8.6199145200981867290946985766988e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9871001010138503414290888619422            
y2[1] (numeric)                   = 1.9871001010138503414290888619435            
absolute error                    = 1.3e-30                                      
relative error                    = 6.5421968391865067597220966184484e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9182.8MB, alloc=40.3MB, time=112.55
memory used=9224.7MB, alloc=40.3MB, time=113.06
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y1[1] (closed_form)               = 1.1502254699116857734869821029759            
y1[1] (numeric)                   = 1.150225469911685773486982102976             
absolute error                    = 1e-31                                        
relative error                    = 8.6939476316480796242789546185500e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9886517628517197927362734733357            
y2[1] (numeric)                   = 1.9886517628517197927362734733369            
absolute error                    = 1.2e-30                                      
relative error                    = 6.0342389875198869636122954247078e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9266.7MB, alloc=40.3MB, time=113.58
 
TOP MAIN SOLVE Loop
memory used=9308.6MB, alloc=40.3MB, time=114.09
x[1]                              = 1.43                                         
y1[1] (closed_form)               = 1.1403316058467366625338976245749            
y1[1] (numeric)                   = 1.140331605846736662533897624575             
absolute error                    = 1e-31                                        
relative error                    = 8.7693789672475536804733641222893e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9901045603371777948572914954818            
y2[1] (numeric)                   = 1.9901045603371777948572914954829            
absolute error                    = 1.1e-30                                      
relative error                    = 5.5273477681676690736892003731658e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9350.5MB, alloc=40.3MB, time=114.61
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y1[1] (closed_form)               = 1.1304237087381454929775201561292            
y1[1] (numeric)                   = 1.1304237087381454929775201561293            
absolute error                    = 1e-31                                        
relative error                    = 8.8462405049542604262797632342193e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.991458348191686462527604463958             
y2[1] (numeric)                   = 1.9914583481916864625276044639592            
absolute error                    = 1.2e-30                                      
relative error                    = 6.0257348645511054392812963653261e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9392.4MB, alloc=40.3MB, time=115.12
memory used=9434.2MB, alloc=40.3MB, time=115.63
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y1[1] (closed_form)               = 1.120502769367366570532866627248             
y1[1] (numeric)                   = 1.120502769367366570532866627248             
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.992712991037588497665354134323             
y2[1] (numeric)                   = 1.9927129910375884976653541343244            
absolute error                    = 1.4e-30                                      
relative error                    = 7.0255977970567254326730166466215e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9476.1MB, alloc=40.3MB, time=116.14
 
TOP MAIN SOLVE Loop
memory used=9518.0MB, alloc=40.3MB, time=116.66
x[1]                              = 1.46                                         
y1[1] (closed_form)               = 1.1105697798200695511746481091234            
y1[1] (numeric)                   = 1.1105697798200695511746481091232            
absolute error                    = 2e-31                                        
relative error                    = 1.8008773841514332183699371263908e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.99386836341164484228683230125              
y2[1] (numeric)                   = 1.9938683634116448422868323012513            
absolute error                    = 1.3e-30                                      
relative error                    = 6.5199891018663402677453310778834e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9560.0MB, alloc=40.3MB, time=117.17
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y1[1] (closed_form)               = 1.1006257333869317009069746014624            
y1[1] (numeric)                   = 1.1006257333869317009069746014622            
absolute error                    = 2e-31                                        
relative error                    = 1.8171481361292938086225480976158e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9949243497775808978599284627356            
y2[1] (numeric)                   = 1.9949243497775808978599284627369            
absolute error                    = 1.3e-30                                      
relative error                    = 6.5165378333516268393615406838906e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9601.9MB, alloc=40.3MB, time=117.69
memory used=9643.8MB, alloc=40.3MB, time=118.20
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y1[1] (closed_form)               = 1.0906716244643096557762265406478            
y1[1] (numeric)                   = 1.0906716244643096557762265406477            
absolute error                    = 1e-31                                        
relative error                    = 9.1686624788754029971031479664537e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9958808445376400564840751325627            
y2[1] (numeric)                   = 1.9958808445376400564840751325639            
absolute error                    = 1.2e-30                                      
relative error                    = 6.0123829700764952481122072872922e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9685.8MB, alloc=40.3MB, time=118.72
 
TOP MAIN SOLVE Loop
memory used=9727.7MB, alloc=40.3MB, time=119.23
x[1]                              = 1.49                                         
y1[1] (closed_form)               = 1.0807084484548006148683184845637            
y1[1] (numeric)                   = 1.0807084484548006148683184845636            
absolute error                    = 1e-31                                        
relative error                    = 9.2531894372603662245462113142182e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9967377520431433885532007170437            
y2[1] (numeric)                   = 1.996737752043143388553200717045             
absolute error                    = 1.3e-30                                      
relative error                    = 6.5106196277893131194106809452181e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9769.6MB, alloc=40.3MB, time=119.74
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y1[1] (closed_form)               = 1.0707372016677029100881898514343            
y1[1] (numeric)                   = 1.0707372016677029100881898514342            
absolute error                    = 1e-31                                        
relative error                    = 9.3393598209016390280655430800655e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9974949866040544309417233711415            
y2[1] (numeric)                   = 1.9974949866040544309417233711426            
absolute error                    = 1.1e-30                                      
relative error                    = 5.5068974259110026167229077966595e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9811.5MB, alloc=40.3MB, time=120.26
memory used=9853.4MB, alloc=40.3MB, time=120.77
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y1[1] (closed_form)               = 1.0607588812193859065815955149162            
y1[1] (numeric)                   = 1.0607588812193859065815955149161            
absolute error                    = 1e-31                                        
relative error                    = 9.4272130802285522527302635247474e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9981524724975481192427378648367            
y2[1] (numeric)                   = 1.9981524724975481192427378648378            
absolute error                    = 1.1e-30                                      
relative error                    = 5.5050853983383882197484659921568e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9895.4MB, alloc=40.3MB, time=121.28
 
TOP MAIN SOLVE Loop
memory used=9937.3MB, alloc=40.3MB, time=121.80
x[1]                              = 1.52                                         
y1[1] (closed_form)               = 1.0507744849335791967261292701527            
y1[1] (numeric)                   = 1.0507744849335791967261292701526            
absolute error                    = 1e-31                                        
relative error                    = 9.5167898948670349845863684406231e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9987101439755830071723123941168            
y2[1] (numeric)                   = 1.9987101439755830071723123941179            
absolute error                    = 1.1e-30                                      
relative error                    = 5.5035493931702285521896375316990e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=9979.3MB, alloc=40.3MB, time=122.33
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y1[1] (closed_form)               = 1.0407850112415910586889890070761            
y1[1] (numeric)                   = 1.040785011241591058688989007076             
absolute error                    = 1e-31                                        
relative error                    = 9.6081322194202517825138776403092e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.999167945271476015924265068709             
y2[1] (numeric)                   = 1.9991679452714760159242650687099            
absolute error                    = 9e-31                                        
relative error                    = 4.5018729023177937560825372378242e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10021.3MB, alloc=40.3MB, time=122.84
memory used=10063.2MB, alloc=40.3MB, time=123.36
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y1[1] (closed_form)               = 1.0307914590824661576224768070764            
y1[1] (numeric)                   = 1.0307914590824661576224768070763            
absolute error                    = 1e-31                                        
relative error                    = 9.7012833312581535851318673240320e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.99952583060547905600596353844              
y2[1] (numeric)                   = 1.9995258306054790560059635384409            
absolute error                    = 9e-31                                        
relative error                    = 4.5010671341388463686923932564950e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10105.2MB, alloc=40.3MB, time=123.88
 
TOP MAIN SOLVE Loop
memory used=10147.0MB, alloc=40.3MB, time=124.39
x[1]                              = 1.55                                         
y1[1] (closed_form)               = 1.0207948278030924736439127746956            
y1[1] (numeric)                   = 1.0207948278030924736439127746954            
absolute error                    = 2e-31                                        
relative error                    = 1.9592575760834405038747057926026e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9997837641893569638976113476345            
y2[1] (numeric)                   = 1.9997837641893569638976113476353            
absolute error                    = 8e-31                                        
relative error                    = 4.0004325183842677922859062475748e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10188.9MB, alloc=40.3MB, time=124.90
 
TOP MAIN SOLVE Loop
x[1]                              = 1.56                                         
y1[1] (closed_form)               = 1.0107961170582674458239206637609            
y1[1] (numeric)                   = 1.0107961170582674458239206637606            
absolute error                    = 3e-31                                        
relative error                    = 2.9679575825151935089528063740599e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9999417202299662957451700234135            
y2[1] (numeric)                   = 1.9999417202299662957451700234142            
absolute error                    = 7e-31                                        
relative error                    = 3.5001019925696107334760124941429e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10230.9MB, alloc=40.3MB, time=125.41
memory used=10272.8MB, alloc=40.3MB, time=125.92
 
TOP MAIN SOLVE Loop
x[1]                              = 1.57                                         
y1[1] (closed_form)               = 1.0007963267107333254854085336454            
y1[1] (numeric)                   = 1.0007963267107333254854085336449            
absolute error                    = 5e-31                                        
relative error                    = 4.9960215346045954614283444324374e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9999996829318346202105299238233            
y2[1] (numeric)                   = 1.999999682931834620210529923824             
absolute error                    = 7e-31                                        
relative error                    = 3.5000005548693773803393283384316e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10314.8MB, alloc=40.3MB, time=126.44
 
TOP MAIN SOLVE Loop
memory used=10356.7MB, alloc=40.3MB, time=126.96
x[1]                              = 1.58                                         
y1[1] (closed_form)               = 0.99079645673119173519461094301727           
y1[1] (numeric)                   = 0.99079645673119173519461094301682           
absolute error                    = 4.5e-31                                      
relative error                    = 4.5418006588823253676674487866347e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9999576464987400525517942322517            
y2[1] (numeric)                   = 1.9999576464987400525517942322524            
absolute error                    = 7e-31                                        
relative error                    = 3.5000741201968298329443013249212e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10398.7MB, alloc=40.3MB, time=127.47
 
TOP MAIN SOLVE Loop
x[1]                              = 1.59                                         
y1[1] (closed_form)               = 0.9807975070983074319049726537566            
y1[1] (numeric)                   = 0.98079750709830743190497265375614           
absolute error                    = 4.6e-31                                      
relative error                    = 4.6900608603799521702271418958084e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9998156151342908719815843437455            
y2[1] (numeric)                   = 1.9998156151342908719815843437464            
absolute error                    = 9e-31                                        
relative error                    = 4.5004149041988730337202687422574e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10440.7MB, alloc=40.3MB, time=127.98
memory used=10482.5MB, alloc=40.3MB, time=128.49
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y1[1] (closed_form)               = 0.9708004776987112737942295370535            
y1[1] (numeric)                   = 0.97080047769871127379422953705303           
absolute error                    = 4.7e-31                                      
relative error                    = 4.8413655616871759133777576018057e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9995736030415051643421138255462            
y2[1] (numeric)                   = 1.9995736030415051643421138255471            
absolute error                    = 9e-31                                        
relative error                    = 4.5009595977413925343755045393346e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10524.6MB, alloc=40.3MB, time=129.01
 
TOP MAIN SOLVE Loop
memory used=10566.3MB, alloc=40.3MB, time=129.52
x[1]                              = 1.61                                         
y1[1] (closed_form)               = 0.96080636822701239041467239039898           
y1[1] (numeric)                   = 0.96080636822701239041467239039849           
absolute error                    = 4.9e-31                                      
relative error                    = 5.0998829337924031997722918285918e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9992316344213905321324131478443            
y2[1] (numeric)                   = 1.9992316344213905321324131478452            
absolute error                    = 9e-31                                        
relative error                    = 4.5017294869910075742432375232002e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10608.2MB, alloc=40.3MB, time=130.03
 
TOP MAIN SOLVE Loop
x[1]                              = 1.62                                         
y1[1] (closed_form)               = 0.95081617808582955485625572528767           
y1[1] (numeric)                   = 0.95081617808582955485625572528716           
absolute error                    = 5.1e-31                                      
relative error                    = 5.3638128142363458332130042437965e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9987897434705240139155188912468            
y2[1] (numeric)                   = 1.9987897434705240139155188912479            
absolute error                    = 1.1e-30                                      
relative error                    = 5.5033302206667122038905321001137e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10650.2MB, alloc=40.3MB, time=130.54
memory used=10692.1MB, alloc=40.3MB, time=131.06
 
TOP MAIN SOLVE Loop
x[1]                              = 1.63                                         
y1[1] (closed_form)               = 0.9408309062858517547020283025802            
y1[1] (numeric)                   = 0.94083090628585175470202830257967           
absolute error                    = 5.3e-31                                      
relative error                    = 5.6333183408302129771644267089766e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9982479743776324551116699849331            
y2[1] (numeric)                   = 1.9982479743776324551116699849341            
absolute error                    = 1.0e-30                                      
relative error                    = 5.0043839044123470833332322765080e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10734.1MB, alloc=40.3MB, time=131.57
 
TOP MAIN SOLVE Loop
memory used=10776.0MB, alloc=40.3MB, time=132.08
x[1]                              = 1.64                                         
y1[1] (closed_form)               = 0.9308515513459379556355072925434            
y1[1] (numeric)                   = 0.93085155134593795563550729254285           
absolute error                    = 5.5e-31                                      
relative error                    = 5.9085683340672673486044118287071e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9976063813191736721375819743679            
y2[1] (numeric)                   = 1.9976063813191736721375819743689            
absolute error                    = 1.0e-30                                      
relative error                    = 5.0059912170465876182875276265409e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10818.0MB, alloc=40.3MB, time=132.59
 
TOP MAIN SOLVE Loop
x[1]                              = 1.65                                         
y1[1] (closed_form)               = 0.92087911119326604764038540265872           
y1[1] (numeric)                   = 0.92087911119326604764038540265815           
absolute error                    = 5.7e-31                                      
relative error                    = 6.1897375352710480698772457030047e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9968650284539188517717030402022            
y2[1] (numeric)                   = 1.9968650284539188517717030402032            
absolute error                    = 1.0e-30                                      
relative error                    = 5.0078497332103322304545545822587e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10859.9MB, alloc=40.3MB, time=133.11
memory used=10901.8MB, alloc=40.3MB, time=133.62
 
TOP MAIN SOLVE Loop
x[1]                              = 1.66                                         
y1[1] (closed_form)               = 0.91091458306354095881474206834938           
y1[1] (numeric)                   = 0.91091458306354095881474206834878           
absolute error                    = 6.0e-31                                      
relative error                    = 6.5867866335184901324585645158138e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.996023989916536727501000590613             
y2[1] (numeric)                   = 1.996023989916536727501000590614             
absolute error                    = 1.0e-30                                      
relative error                    = 5.0099598253917517504966016349489e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=10943.7MB, alloc=40.3MB, time=134.13
 
TOP MAIN SOLVE Loop
memory used=10985.6MB, alloc=40.3MB, time=134.64
x[1]                              = 1.67                                         
y1[1] (closed_form)               = 0.90095896340127191590521765755139           
y1[1] (numeric)                   = 0.90095896340127191590521765755078           
absolute error                    = 6.1e-31                                      
relative error                    = 6.7705636414021256103052520623069e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9950833498101801744262972465342            
y2[1] (numeric)                   = 1.9950833498101801744262972465354            
absolute error                    = 1.2e-30                                      
relative error                    = 6.0147863001020612428791359564700e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11027.5MB, alloc=40.3MB, time=135.15
 
TOP MAIN SOLVE Loop
x[1]                              = 1.68                                         
y1[1] (closed_form)               = 0.89101324776012882375199526582718           
y1[1] (numeric)                   = 0.89101324776012882375199526582656           
absolute error                    = 6.2e-31                                      
relative error                    = 6.9583701651864916337274333665009e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9940432021980759640604878691936            
y2[1] (numeric)                   = 1.9940432021980759640604878691948            
absolute error                    = 1.2e-30                                      
relative error                    = 6.0179237775651733076725211984556e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11069.5MB, alloc=40.3MB, time=135.67
memory used=11111.4MB, alloc=40.3MB, time=136.18
 
TOP MAIN SOLVE Loop
x[1]                              = 1.69                                         
y1[1] (closed_form)               = 0.88107843070338772792360953016691           
y1[1] (numeric)                   = 0.88107843070338772792360953016629           
absolute error                    = 6.2e-31                                      
relative error                    = 7.0368309834237792460622252208564e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9929036510941185200371492939456            
y2[1] (numeric)                   = 1.9929036510941185200371492939468            
absolute error                    = 1.2e-30                                      
relative error                    = 6.0213648529430477978673206033982e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11153.2MB, alloc=40.3MB, time=136.69
 
TOP MAIN SOLVE Loop
memory used=11195.1MB, alloc=40.3MB, time=137.20
x[1]                              = 1.7                                          
y1[1] (closed_form)               = 0.87115550570447531591235714266513           
y1[1] (numeric)                   = 0.87115550570447531591235714266449           
absolute error                    = 6.4e-31                                      
relative error                    = 7.3465643712192655474464808567822e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9916648104524686153461333986479            
y2[1] (numeric)                   = 1.9916648104524686153461333986492            
absolute error                    = 1.3e-30                                      
relative error                    = 6.5272027360099040038539945094548e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11237.1MB, alloc=40.3MB, time=137.72
 
TOP MAIN SOLVE Loop
x[1]                              = 1.71                                         
y1[1] (closed_form)               = 0.86124546504762240235731021694889           
y1[1] (numeric)                   = 0.86124546504762240235731021694823           
absolute error                    = 6.6e-31                                      
relative error                    = 7.6633204676846156389281103802041e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9903268041561580512177522238611            
y2[1] (numeric)                   = 1.9903268041561580512177522238625            
absolute error                    = 1.4e-30                                      
relative error                    = 7.0340207300456880299195300188708e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11279.1MB, alloc=40.3MB, time=138.23
memory used=11321.0MB, alloc=40.3MB, time=138.74
 
TOP MAIN SOLVE Loop
x[1]                              = 1.72                                         
y1[1] (closed_form)               = 0.85134929972863633286362171966881           
y1[1] (numeric)                   = 0.85134929972863633286362171966813           
absolute error                    = 6.8e-31                                      
relative error                    = 7.9873208354872302972617885809452e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9888897660047014571781706570855            
y2[1] (numeric)                   = 1.988889766004701457178170657087             
absolute error                    = 1.5e-30                                      
relative error                    = 7.5418961153046337804785524930123e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11363.0MB, alloc=40.3MB, time=139.26
 
TOP MAIN SOLVE Loop
memory used=11404.9MB, alloc=40.3MB, time=139.77
x[1]                              = 1.73                                         
y1[1] (closed_form)               = 0.84146799935580222909505164865743           
y1[1] (numeric)                   = 0.84146799935580222909505164865676           
absolute error                    = 6.7e-31                                      
relative error                    = 7.9622754580438948378346576047334e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9873538397007164510856776762221            
y2[1] (numeric)                   = 1.9873538397007164510856776762236            
absolute error                    = 1.5e-30                                      
relative error                    = 7.5477248692960031139254987505827e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11446.8MB, alloc=40.3MB, time=140.28
 
TOP MAIN SOLVE Loop
x[1]                              = 1.74                                         
y1[1] (closed_form)               = 0.83160255205092298493262268465491           
y1[1] (numeric)                   = 0.83160255205092298493262268465422           
absolute error                    = 6.9e-31                                      
relative error                    = 8.2972328343425768339805560724073e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9857191788355534971206826956656            
y2[1] (numeric)                   = 1.9857191788355534971206826956673            
absolute error                    = 1.7e-30                                      
relative error                    = 8.5611299831273110176373811698660e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11488.7MB, alloc=40.3MB, time=140.80
memory used=11530.6MB, alloc=40.3MB, time=141.31
 
TOP MAIN SOLVE Loop
x[1]                              = 1.75                                         
y1[1] (closed_form)               = 0.82175394435050790961732305605737           
y1[1] (numeric)                   = 0.82175394435050790961732305605666           
absolute error                    = 7.1e-31                                      
relative error                    = 8.6400558814617530743630764553778e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.983985946873936898731662936968             
y2[1] (numeric)                   = 1.9839859468739368987316629369698            
absolute error                    = 1.8e-30                                      
relative error                    = 9.0726449087815669663649050797303e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11572.5MB, alloc=40.3MB, time=141.82
 
TOP MAIN SOLVE Loop
memory used=11614.3MB, alloc=40.3MB, time=142.34
x[1]                              = 1.76                                         
y1[1] (closed_form)               = 0.8119231611071198989301998234959            
y1[1] (numeric)                   = 0.81192316110711989893019982349518           
absolute error                    = 7.2e-31                                      
relative error                    = 8.8678342297591859109170425615518e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.982154317137618462424968099456             
y2[1] (numeric)                   = 1.9821543171376184624249680994577            
absolute error                    = 1.7e-30                                      
relative error                    = 8.5765269903653578868348423623293e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11656.3MB, alloc=40.3MB, time=142.85
 
TOP MAIN SOLVE Loop
x[1]                              = 1.77                                         
y1[1] (closed_form)               = 0.80211118539089099961051415826961           
y1[1] (numeric)                   = 0.80211118539089099961051415826887           
absolute error                    = 7.4e-31                                      
relative error                    = 9.2256536684422060708232351994145e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9802244727880454670184814488984            
y2[1] (numeric)                   = 1.9802244727880454670184814489               
absolute error                    = 1.6e-30                                      
relative error                    = 8.0798920626775678419190522292110e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11698.3MB, alloc=40.3MB, time=143.36
memory used=11740.2MB, alloc=40.3MB, time=143.87
 
TOP MAIN SOLVE Loop
x[1]                              = 1.78                                         
y1[1] (closed_form)               = 0.79231899839121621537344670968737           
y1[1] (numeric)                   = 0.79231899839121621537344670968662           
absolute error                    = 7.5e-31                                      
relative error                    = 9.4658843410653552862626667394715e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9781966068080446715477686473056            
y2[1] (numeric)                   = 1.9781966068080446715477686473071            
absolute error                    = 1.5e-30                                      
relative error                    = 7.5826639012405973354829016858857e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11782.1MB, alloc=40.3MB, time=144.39
 
TOP MAIN SOLVE Loop
memory used=11824.0MB, alloc=40.3MB, time=144.90
x[1]                              = 1.79                                         
y1[1] (closed_form)               = 0.78254757931863538506482973553539           
y1[1] (numeric)                   = 0.78254757931863538506482973553463           
absolute error                    = 7.6e-31                                      
relative error                    = 9.7118695410409731893005042101762e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9760709219825241934086604331086            
y2[1] (numeric)                   = 1.97607092198252419340866043311              
absolute error                    = 1.4e-30                                      
relative error                    = 7.0847659586804101556628266085147e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11866.0MB, alloc=40.3MB, time=145.41
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y1[1] (closed_form)               = 0.77279790530691294468332569346942           
y1[1] (numeric)                   = 0.77279790530691294468332569346865           
absolute error                    = 7.7e-31                                      
relative error                    = 9.9637951230496442644516152105761e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9738476308781951865323731788434            
y2[1] (numeric)                   = 1.9738476308781951865323731788447            
absolute error                    = 1.3e-30                                      
relative error                    = 6.5861213381582548714316252023486e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11908.0MB, alloc=40.3MB, time=145.93
memory used=11949.9MB, alloc=40.3MB, time=146.44
 
TOP MAIN SOLVE Loop
x[1]                              = 1.81                                         
y1[1] (closed_form)               = 0.76307095131532536521225014915802           
y1[1] (numeric)                   = 0.76307095131532536521225014915724           
absolute error                    = 7.8e-31                                      
relative error                    = 1.0221854188729024353585504833852e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9715269558223153474084512690904            
y2[1] (numeric)                   = 1.9715269558223153474084512690917            
absolute error                    = 1.3e-30                                      
relative error                    = 6.5938738304380709572169265038231e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=11991.9MB, alloc=40.3MB, time=146.96
 
TOP MAIN SOLVE Loop
memory used=12033.9MB, alloc=40.3MB, time=147.47
x[1]                              = 1.82                                         
y1[1] (closed_form)               = 0.75336769003116603743582895516913           
y1[1] (numeric)                   = 0.75336769003116603743582895516833           
absolute error                    = 8.0e-31                                      
relative error                    = 1.0618984734624135957078552142076e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.969109128880456374587215318498             
y2[1] (numeric)                   = 1.9691091288804563745872153184995            
absolute error                    = 1.5e-30                                      
relative error                    = 7.6176580464731787143272518946755e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12075.9MB, alloc=40.3MB, time=147.99
 
TOP MAIN SOLVE Loop
x[1]                              = 1.83                                         
y1[1] (closed_form)               = 0.74368909177247735317016241638147           
y1[1] (numeric)                   = 0.74368909177247735317016241638065           
absolute error                    = 8.2e-31                                      
relative error                    = 1.1026113050087186737170605518746e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9665943918332976048972389297428            
y2[1] (numeric)                   = 1.9665943918332976048972389297443            
absolute error                    = 1.5e-30                                      
relative error                    = 7.6273989503329701722371187635271e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12118.0MB, alloc=40.3MB, time=148.50
memory used=12159.9MB, alloc=40.3MB, time=149.02
 
TOP MAIN SOLVE Loop
x[1]                              = 1.84                                         
y1[1] (closed_form)               = 0.7340361243910197096197170167184            
y1[1] (numeric)                   = 0.73403612439101970961971701671756           
absolute error                    = 8.4e-31                                      
relative error                    = 1.1443578484599669734975326418233e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9639829961524481469948936717271            
y2[1] (numeric)                   = 1.9639829961524481469948936717287            
absolute error                    = 1.6e-30                                      
relative error                    = 8.1467100434906459596278303966782e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12202.0MB, alloc=40.3MB, time=149.53
 
TOP MAIN SOLVE Loop
memory used=12243.9MB, alloc=40.3MB, time=150.04
x[1]                              = 1.85                                         
y1[1] (closed_form)               = 0.7244097531754871398780501645252            
y1[1] (numeric)                   = 0.72440975317548713987805016452433           
absolute error                    = 8.7e-31                                      
relative error                    = 1.2009777562854594097276141233685e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9612752029752999300124591686361            
y2[1] (numeric)                   = 1.9612752029752999300124591686376            
absolute error                    = 1.5e-30                                      
relative error                    = 7.6480852749500184455051950799183e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12285.8MB, alloc=40.3MB, time=150.56
 
TOP MAIN SOLVE Loop
x[1]                              = 1.86                                         
y1[1] (closed_form)               = 0.71481094075497924792906451171088           
y1[1] (numeric)                   = 0.71481094075497924792906451170998           
absolute error                    = 9.0e-31                                      
relative error                    = 1.2590741812785141782125560767396e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9584712830789141819789777659032            
y2[1] (numeric)                   = 1.9584712830789141819789777659048            
absolute error                    = 1.6e-30                                      
relative error                    = 8.1696372769103807978723647383440e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12327.8MB, alloc=40.3MB, time=151.07
memory used=12369.7MB, alloc=40.3MB, time=151.58
 
TOP MAIN SOLVE Loop
x[1]                              = 1.87                                         
y1[1] (closed_form)               = 0.70524064700273910087485193519011           
y1[1] (numeric)                   = 0.70524064700273910087485193518921           
absolute error                    = 9.0e-31                                      
relative error                    = 1.2761601360117073181900690529575e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9555715168529439493442504921726            
y2[1] (numeric)                   = 1.9555715168529439493442504921742            
absolute error                    = 1.6e-30                                      
relative error                    = 8.1817514021417279870547958656279e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12411.7MB, alloc=40.3MB, time=152.10
 
TOP MAIN SOLVE Loop
memory used=12453.6MB, alloc=40.3MB, time=152.62
x[1]                              = 1.88                                         
y1[1] (closed_form)               = 0.69569982894016670452068624047776           
y1[1] (numeric)                   = 0.69569982894016670452068624047683           
absolute error                    = 9.3e-31                                      
relative error                    = 1.3367834248525942323482363415278e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9525761942715953653314574258151            
y2[1] (numeric)                   = 1.9525761942715953653314574258166            
absolute error                    = 1.5e-30                                      
relative error                    = 7.6821585984744221094980441875925e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12495.7MB, alloc=40.3MB, time=153.13
 
TOP MAIN SOLVE Loop
x[1]                              = 1.89                                         
y1[1] (closed_form)               = 0.68618944064111766088961758444877           
y1[1] (numeric)                   = 0.68618944064111766088961758444783           
absolute error                    = 9.4e-31                                      
relative error                    = 1.3698840937012133473758855588864e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9494856148646304709682016721383            
y2[1] (numeric)                   = 1.9494856148646304709682016721399            
absolute error                    = 1.6e-30                                      
relative error                    = 8.2072931844182997026118572150934e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12537.7MB, alloc=40.3MB, time=153.65
memory used=12579.5MB, alloc=40.3MB, time=154.16
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y1[1] (closed_form)               = 0.67671043313649657772116630491969           
y1[1] (numeric)                   = 0.67671043313649657772116630491873           
absolute error                    = 9.6e-31                                      
relative error                    = 1.4186274556910255397774981901638e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.946300087687414488489709611635             
y2[1] (numeric)                   = 1.9463000876874144884897096116363            
absolute error                    = 1.3e-30                                      
relative error                    = 6.6793399857709223440179690754898e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12621.5MB, alloc=40.3MB, time=154.68
 
TOP MAIN SOLVE Loop
memory used=12663.4MB, alloc=40.3MB, time=155.19
x[1]                              = 1.91                                         
y1[1] (closed_form)               = 0.66726375431915477053366106060247           
y1[1] (numeric)                   = 0.6672637543191547705336610606015            
absolute error                    = 9.7e-31                                      
relative error                    = 1.4536980222906658006042175263875e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9430199312900105423618865769482            
y2[1] (numeric)                   = 1.9430199312900105423618865769496            
absolute error                    = 1.4e-30                                      
relative error                    = 7.2052786358733410413698211826255e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12705.4MB, alloc=40.3MB, time=155.71
 
TOP MAIN SOLVE Loop
x[1]                              = 1.92                                         
y1[1] (closed_form)               = 0.65785034884910176740076339684095           
y1[1] (numeric)                   = 0.65785034884910176740076339683997           
absolute error                    = 9.8e-31                                      
relative error                    = 1.4897005097200201896053610435718e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.939645473685324918426371339687             
y2[1] (numeric)                   = 1.9396454736853249184263713396884            
absolute error                    = 1.4e-30                                      
relative error                    = 7.2178138685313510895050149535335e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12747.4MB, alloc=40.3MB, time=156.22
memory used=12789.4MB, alloc=40.3MB, time=156.74
 
TOP MAIN SOLVE Loop
x[1]                              = 1.93                                         
y1[1] (closed_form)               = 0.64847115805904009521271093528813           
y1[1] (numeric)                   = 0.64847115805904009521271093528712           
absolute error                    = 1.01e-30                                     
relative error                    = 1.5575095167271024409041311237332e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9361770523163060466151293727488            
y2[1] (numeric)                   = 1.9361770523163060466151293727502            
absolute error                    = 1.4e-30                                      
relative error                    = 7.2307436880585815609299401100179e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12831.4MB, alloc=40.3MB, time=157.26
 
TOP MAIN SOLVE Loop
memory used=12873.4MB, alloc=40.3MB, time=157.77
x[1]                              = 1.94                                         
y1[1] (closed_form)               = 0.63912711986023279386493231415927           
y1[1] (numeric)                   = 0.63912711986023279386493231415826           
absolute error                    = 1.01e-30                                     
relative error                    = 1.5802803051462929051744347578454e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9326150140222004873089793388657            
y2[1] (numeric)                   = 1.9326150140222004873089793388671            
absolute error                    = 1.4e-30                                      
relative error                    = 7.2440708048018807837082487345934e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12915.4MB, alloc=40.3MB, time=158.28
 
TOP MAIN SOLVE Loop
x[1]                              = 1.95                                         
y1[1] (closed_form)               = 0.62981916864871307154417154086931           
y1[1] (numeric)                   = 0.62981916864871307154417154086828           
absolute error                    = 1.03e-30                                     
relative error                    = 1.6353900472890991771948111397949e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9289597150038692957132970350915            
y2[1] (numeric)                   = 1.9289597150038692957132970350929            
absolute error                    = 1.4e-30                                      
relative error                    = 7.2577980198886203454143516169082e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=12957.4MB, alloc=40.3MB, time=158.80
memory used=12999.3MB, alloc=40.3MB, time=159.32
 
TOP MAIN SOLVE Loop
x[1]                              = 1.96                                         
y1[1] (closed_form)               = 0.62054823521184548006843478455255           
y1[1] (numeric)                   = 0.6205482352118454800684347845515            
absolute error                    = 1.05e-30                                     
relative error                    = 1.6920521893701726371714354371894e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.92521152078816823258555628949              
y2[1] (numeric)                   = 1.9252115207881682325855562894914            
absolute error                    = 1.4e-30                                      
relative error                    = 7.2719282264987159344607953529800e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13041.3MB, alloc=40.3MB, time=159.83
 
TOP MAIN SOLVE Loop
memory used=13083.2MB, alloc=40.3MB, time=160.34
x[1]                              = 1.97                                         
y1[1] (closed_form)               = 0.61131524663524795408536018612069           
y1[1] (numeric)                   = 0.61131524663524795408536018611964           
absolute error                    = 1.05e-30                                     
relative error                    = 1.7176080684709325711522215680132e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9213708061913953832639509971532            
y2[1] (numeric)                   = 1.9213708061913953832639509971546            
absolute error                    = 1.4e-30                                      
relative error                    = 7.2864644111832124669965709990369e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13125.2MB, alloc=40.3MB, time=160.86
 
TOP MAIN SOLVE Loop
x[1]                              = 1.98                                         
y1[1] (closed_form)               = 0.60212112621008402184752614009281           
y1[1] (numeric)                   = 0.60212112621008402184752614009175           
absolute error                    = 1.06e-30                                     
relative error                    = 1.7604431298930358856703263231955e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.917437955281809840204735217402             
y2[1] (numeric)                   = 1.9174379552818098402047352174033            
absolute error                    = 1.3e-30                                      
relative error                    = 6.7798803941425906474869270573044e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13167.1MB, alloc=40.3MB, time=161.37
memory used=13209.0MB, alloc=40.3MB, time=161.89
 
TOP MAIN SOLVE Loop
x[1]                              = 1.99                                         
y1[1] (closed_form)               = 0.59296679334073445826636428386971           
y1[1] (numeric)                   = 0.59296679334073445826636428386864           
absolute error                    = 1.07e-30                                     
relative error                    = 1.8044855327761155076015168196456e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9134133613412251971287932710576            
y2[1] (numeric)                   = 1.9134133613412251971287932710589            
absolute error                    = 1.3e-30                                      
relative error                    = 6.7941409120753327529190882818614e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13251.1MB, alloc=40.3MB, time=162.40
 
TOP MAIN SOLVE Loop
memory used=13293.1MB, alloc=40.3MB, time=162.92
x[1]                              = 2                                            
y1[1] (closed_form)               = 0.58385316345285761300243177049924           
y1[1] (numeric)                   = 0.58385316345285761300243177049814           
absolute error                    = 1.10e-30                                     
relative error                    = 1.8840353514481178685179234134476e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9092974268256816953960198659117            
y2[1] (numeric)                   = 1.909297426825681695396019865913             
absolute error                    = 1.3e-30                                      
relative error                    = 6.8087872624503862865151844492397e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13335.1MB, alloc=40.3MB, time=163.43
 
TOP MAIN SOLVE Loop
x[1]                              = 2.01                                         
y1[1] (closed_form)               = 0.57478114790184760748261765983457           
y1[1] (numeric)                   = 0.57478114790184760748261765983345           
absolute error                    = 1.12e-30                                     
relative error                    = 1.9485677358911162223084808688537e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9050905633252009553600997102737            
y2[1] (numeric)                   = 1.905090563325200955360099710275             
absolute error                    = 1.3e-30                                      
relative error                    = 6.8238225784444696649741577230336e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13377.0MB, alloc=40.3MB, time=163.94
memory used=13419.0MB, alloc=40.3MB, time=164.46
 
TOP MAIN SOLVE Loop
x[1]                              = 2.02                                         
y1[1] (closed_form)               = 0.5657516538816995549482971259098            
y1[1] (numeric)                   = 0.56575165388169955494829712590865           
absolute error                    = 1.15e-30                                     
relative error                    = 2.0326940135476273949286880426170e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.9007931915226273171970135245537            
y2[1] (numeric)                   = 1.9007931915226273171970135245551            
absolute error                    = 1.4e-30                                      
relative error                    = 7.3653462472607672817400226958471e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13460.9MB, alloc=40.3MB, time=164.98
 
TOP MAIN SOLVE Loop
memory used=13502.8MB, alloc=40.3MB, time=165.49
x[1]                              = 2.03                                         
y1[1] (closed_form)               = 0.5567655843342909169364832683039            
y1[1] (numeric)                   = 0.55676558433429091693648326830274           
absolute error                    = 1.16e-30                                     
relative error                    = 2.0834621115940196840773360948884e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8964057411515599070388888319676            
y2[1] (numeric)                   = 1.8964057411515599070388888319689            
absolute error                    = 1.3e-30                                      
relative error                    = 6.8550731090415137890309105137497e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13544.8MB, alloc=40.3MB, time=166.00
 
TOP MAIN SOLVE Loop
x[1]                              = 2.04                                         
y1[1] (closed_form)               = 0.54782383785908806798272979470864           
y1[1] (numeric)                   = 0.54782383785908806798272979470746           
absolute error                    = 1.18e-30                                     
relative error                    = 2.1539770971111357046768041107408e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8919286509533796351715256485842            
y2[1] (numeric)                   = 1.8919286509533796351715256485853            
absolute error                    = 1.1e-30                                      
relative error                    = 5.8141727461323058395823515044765e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13586.8MB, alloc=40.3MB, time=166.52
memory used=13628.7MB, alloc=40.3MB, time=167.03
 
TOP MAIN SOLVE Loop
x[1]                              = 2.05                                         
y1[1] (closed_form)               = 0.5389273086232870978140700058326            
y1[1] (numeric)                   = 0.53892730862328709781407000583141           
absolute error                    = 1.19e-30                                     
relative error                    = 2.2080899983337381620051245687169e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8873623686333754235599666046803            
y2[1] (numeric)                   = 1.8873623686333754235599666046815            
absolute error                    = 1.2e-30                                      
relative error                    = 6.3580795079055792102411780890845e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13670.7MB, alloc=40.3MB, time=167.55
 
TOP MAIN SOLVE Loop
memory used=13712.7MB, alloc=40.3MB, time=168.06
x[1]                              = 2.06                                         
y1[1] (closed_form)               = 0.5300768862723978368768903735121            
y1[1] (numeric)                   = 0.53007688627239783687689037351089           
absolute error                    = 1.21e-30                                     
relative error                    = 2.2826877219811482258573687390355e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8827073508159740500427975851999            
y2[1] (numeric)                   = 1.8827073508159740500427975852011            
absolute error                    = 1.2e-30                                      
relative error                    = 6.3737999401761217157047530538172e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13754.7MB, alloc=40.3MB, time=168.57
 
TOP MAIN SOLVE Loop
x[1]                              = 2.07                                         
y1[1] (closed_form)               = 0.52127345584128004672267286098827           
y1[1] (numeric)                   = 0.52127345584128004672267286098706           
absolute error                    = 1.21e-30                                     
relative error                    = 2.3212384717483616924883936925280e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8779640629990780861734511204438            
y2[1] (numeric)                   = 1.8779640629990780861734511204451            
absolute error                    = 1.3e-30                                      
relative error                    = 6.9223901863378638290937046282683e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13796.7MB, alloc=40.3MB, time=169.09
memory used=13838.7MB, alloc=40.3MB, time=169.60
 
TOP MAIN SOLVE Loop
x[1]                              = 2.08                                         
y1[1] (closed_form)               = 0.51251789766564067155843115022765           
y1[1] (numeric)                   = 0.51251789766564067155843115022641           
absolute error                    = 1.24e-30                                     
relative error                    = 2.4194277032037585974336765107922e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8731329795075164948766768050246            
y2[1] (numeric)                   = 1.8731329795075164948766768050259            
absolute error                    = 1.3e-30                                      
relative error                    = 6.9402440415191214624701101207812e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13880.7MB, alloc=40.3MB, time=170.12
 
TOP MAIN SOLVE Loop
memory used=13922.7MB, alloc=40.3MB, time=170.63
x[1]                              = 2.09                                         
y1[1] (closed_form)               = 0.50381108729400100116293368812955           
y1[1] (numeric)                   = 0.50381108729400100116293368812829           
absolute error                    = 1.26e-30                                     
relative error                    = 2.5009374183635658957923426709989e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8682145834456125428216220587275            
y2[1] (numeric)                   = 1.8682145834456125428216220587289            
absolute error                    = 1.4e-30                                      
relative error                    = 7.4937858445464639831745567709696e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=13964.7MB, alloc=40.3MB, time=171.14
 
TOP MAIN SOLVE Loop
x[1]                              = 2.1                                          
y1[1] (closed_form)               = 0.49515389540014254837906147628083           
y1[1] (numeric)                   = 0.49515389540014254837906147627954           
absolute error                    = 1.29e-30                                     
relative error                    = 2.6052506341640074790877855175894e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.863209366648873770680759313269             
y2[1] (numeric)                   = 1.8632093666488737706807593132702            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4405000397689759434826307471079e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14006.7MB, alloc=40.3MB, time=171.66
memory used=14048.6MB, alloc=40.3MB, time=172.18
 
TOP MAIN SOLVE Loop
x[1]                              = 2.11                                         
y1[1] (closed_form)               = 0.48654718769604039652158984292831           
y1[1] (numeric)                   = 0.486547187696040396521589842927             
absolute error                    = 1.31e-30                                     
relative error                    = 2.6924418291333204679256093899869e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8581178296348088522373755083107            
y2[1] (numeric)                   = 1.8581178296348088522373755083119            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4581480294812404288199451083363e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14090.7MB, alloc=40.3MB, time=172.69
 
TOP MAIN SOLVE Loop
memory used=14132.6MB, alloc=40.3MB, time=173.21
x[1]                              = 2.12                                         
y1[1] (closed_form)               = 0.47799182484529272329309811701611           
y1[1] (numeric)                   = 0.47799182484529272329309811701479           
absolute error                    = 1.32e-30                                     
relative error                    = 2.7615535065421514739870955061948e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8529404815528762606147273336542            
y2[1] (numeric)                   = 1.8529404815528762606147273336554            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4761929049891952161791782948017e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14174.6MB, alloc=40.3MB, time=173.72
 
TOP MAIN SOLVE Loop
x[1]                              = 2.13                                         
y1[1] (closed_form)               = 0.46948866237705515818347379039028           
y1[1] (numeric)                   = 0.46948866237705515818347379038895           
absolute error                    = 1.33e-30                                     
relative error                    = 2.8328692609233916552162234592256e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8476778401335697467185299963159            
y2[1] (numeric)                   = 1.8476778401335697467185299963171            
absolute error                    = 1.2e-30                                      
relative error                    = 6.4946386969345872298939751781115e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14216.6MB, alloc=40.3MB, time=174.24
memory used=14258.6MB, alloc=40.3MB, time=174.75
 
TOP MAIN SOLVE Loop
x[1]                              = 2.14                                         
y1[1] (closed_form)               = 0.4610385506004885798455500879914            
y1[1] (numeric)                   = 0.46103855060048857984555008799007           
absolute error                    = 1.33e-30                                     
relative error                    = 2.8847913005706697818859639298334e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8423304316366457213025066370689            
y2[1] (numeric)                   = 1.84233043163664572130250663707              
absolute error                    = 1.1e-30                                      
relative error                    = 5.9706987471449849755230517330437e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14300.6MB, alloc=40.3MB, time=175.27
 
TOP MAIN SOLVE Loop
memory used=14342.4MB, alloc=40.3MB, time=175.78
x[1]                              = 2.15                                         
y1[1] (closed_form)               = 0.45264233451972890859584611773597           
y1[1] (numeric)                   = 0.45264233451972890859584611773464           
absolute error                    = 1.33e-30                                     
relative error                    = 2.9383022721707673214675327051576e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8368987907984977178756481370438            
y2[1] (numeric)                   = 1.8368987907984977178756481370448            
absolute error                    = 1.0e-30                                      
relative error                    = 5.4439580722098531640546833609281e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14384.4MB, alloc=40.3MB, time=176.29
 
TOP MAIN SOLVE Loop
x[1]                              = 2.16                                         
y1[1] (closed_form)               = 0.44430085374938739699030125601663           
y1[1] (numeric)                   = 0.44430085374938739699030125601528           
absolute error                    = 1.35e-30                                     
relative error                    = 3.0384816698134948902646402178424e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8313834607786831989610381203463            
y2[1] (numeric)                   = 1.8313834607786831989610381203473            
absolute error                    = 1.0e-30                                      
relative error                    = 5.4603529048734091617148145897672e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14426.4MB, alloc=40.3MB, time=176.81
memory used=14468.3MB, alloc=40.3MB, time=177.32
 
TOP MAIN SOLVE Loop
x[1]                              = 2.17                                         
y1[1] (closed_form)               = 0.43601494243058986837553000558349           
y1[1] (numeric)                   = 0.43601494243058986837553000558214           
absolute error                    = 1.35e-30                                     
relative error                    = 3.0962241625811008223958255552813e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8257849931056080529810564239434            
y2[1] (numeric)                   = 1.8257849931056080529810564239444            
absolute error                    = 1.0e-30                                      
relative error                    = 5.4770961738437153082079098280508e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14510.3MB, alloc=40.3MB, time=177.83
 
TOP MAIN SOLVE Loop
memory used=14552.2MB, alloc=40.3MB, time=178.35
x[1]                              = 2.18                                         
y1[1] (closed_form)               = 0.42778542914756329942177513233751           
y1[1] (numeric)                   = 0.42778542914756329942177513233613           
absolute error                    = 1.38e-30                                     
relative error                    = 3.2259163262056154400867355113686e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8201039476213742132740097460839            
y2[1] (numeric)                   = 1.820103947621374213274009746085             
absolute error                    = 1.1e-30                                      
relative error                    = 6.0436108686954328389960470776416e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14594.1MB, alloc=40.3MB, time=178.86
 
TOP MAIN SOLVE Loop
x[1]                              = 2.19                                         
y1[1] (closed_form)               = 0.41961313684477808790979483620305           
y1[1] (numeric)                   = 0.41961313684477808790979483620167           
absolute error                    = 1.38e-30                                     
relative error                    = 3.2887435564499141579699809518397e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.814340892425795914434327645905             
y2[1] (numeric)                   = 1.814340892425795914434327645906             
absolute error                    = 1.0e-30                                      
relative error                    = 5.5116433971952635456861645933305e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
memory used=14636.1MB, alloc=40.3MB, time=179.38
memory used=14678.1MB, alloc=40.3MB, time=179.89
 
TOP MAIN SOLVE Loop
x[1]                              = 2.2                                          
y1[1] (closed_form)               = 0.41149888274465429147585738734507           
y1[1] (numeric)                   = 0.4114988827446542914758573873437            
absolute error                    = 1.37e-30                                     
relative error                    = 3.3292921498650106005054383633293e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y2[1] (closed_form)               = 1.8084964038195901843040369104161            
y2[1] (numeric)                   = 1.8084964038195901843040369104171            
absolute error                    = 1.0e-30                                      
relative error                    = 5.5294552861038301567256314290129e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
Finished!
Maximum Time Reached before Solution Completed!
diff  (  y1  ,  x  ,  1  )   =  neg (  y2 )   +  1.0 ; 
diff  (  y2  ,  x  ,  1  )   =  y1  -  1.0 ; 
Iterations                       = 2102                                
Total Elapsed Time               = 3 Minutes 0 Seconds
Elapsed Time(since restart)      = 3 Minutes 0 Seconds
Expected Time Remaining          = 11 Minutes 7 Seconds
Optimized Time Remaining         = 11 Minutes 7 Seconds
Expected Total Time              = 14 Minutes 7 Seconds
Time to Timeout                  0.0 Seconds
Percent Done                     = 21.24                                      % 
> quit
memory used=14701.7MB, alloc=40.3MB, time=180.17