|\^/|     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_x1 := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
    c1 := c(1.0);
    c2 := c(0.0002);
    c3 := c(0.0003);
    return c(2.0)*c1 + c(6.0)*c3*exp(neg(c(t)))
end proc

> exact_soln_x1p := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return(   c(-6.0) * c3 * exp(neg( c(t))));
> end;
exact_soln_x1p := proc(t)
local c1, c2, c3;
    c1 := c(1.0);
    c2 := c(0.0002);
    c3 := c(0.0003);
    return c(-6.0)*c3*exp(neg(c(t)))
end proc

> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
    c1 := c(1.0);
    c2 := c(0.0002);
    c3 := c(0.0003);
    return c1 + c2*exp(c(2.0)*c(t)) + c3*exp(neg(c(t)))
end proc

> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return(   c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t))));
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
    c1 := c(1.0);
    c2 := c(0.0002);
    c3 := c(0.0003);
    return c(2.0)*c2*exp(c(2.0)*c(t)) - c3*exp(neg(c(t)))
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_t ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 1
>         rad_given := sqrt((array_t[1] - array_given_rad_poles[1,1]) * (array_t[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_t[1] - array_given_rad_poles[2,1]) * (array_t[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_t;
    if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
        rad_given := sqrt((array_t[1] - array_given_rad_poles[1, 1])*
            (array_t[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_t[1] - array_given_rad_poles[2, 1])*
            (array_t[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1[1]) < min_size) then # if number 5
>         min_size := float_abs(array_x1[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     if (float_abs(array_x2[1]) < min_size) then # if number 5
>         min_size := float_abs(array_x2[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1[1]) < min_size then
        min_size := float_abs(array_x1[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if float_abs(array_x2[1]) < min_size then
        min_size := float_abs(array_x2[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1[no_terms-3] + array_x1[no_terms - 2] * hn_div_ho + array_x1[no_terms - 1] * hn_div_ho_2 + array_x1[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_x2[no_terms-3] + array_x2[no_terms - 2] * hn_div_ho + array_x2[no_terms - 1] * hn_div_ho_2 + array_x2[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1[no_terms - 3]
         + array_x1[no_terms - 2]*hn_div_ho
         + array_x1[no_terms - 1]*hn_div_ho_2
         + array_x1[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_x2[no_terms - 3]
         + array_x2[no_terms - 2]*hn_div_ho
         + array_x2[no_terms - 1]*hn_div_ho_2
         + array_x2[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1[no_terms-3])) + c(float_abs(array_x1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_x1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_x1[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_x1[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_x1[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_x2[no_terms-3])) + c(float_abs(array_x2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_x2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_x2[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_x2[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_x2[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1[no_terms - 3]))
         + c(float_abs(array_x1[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_x1[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_x1[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_x1[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_x1[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_x2[no_terms - 3]))
         + c(float_abs(array_x2[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_x2[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_x2[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_x2[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_x2[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_t[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_t[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_t[1];
>             omniout_float(ALWAYS,"t[1]                             ",33,ind_var,20," ");
>             closed_form_val_y := evalf(exact_soln_x1(ind_var));
>             omniout_float(ALWAYS,"x1[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_x1[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"x1[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)*76*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_x2(ind_var));
>             omniout_float(ALWAYS,"x2[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_x2[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"x2[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)*76*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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_t[1];
            omniout_float(ALWAYS, "t[1]                             ", 33,
                ind_var, 20, " ");
            closed_form_val_y := evalf(exact_soln_x1(ind_var));
            omniout_float(ALWAYS, "x1[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_x1[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "x1[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)*76*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_x2(ind_var));
            omniout_float(ALWAYS, "x2[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_x2[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "x2[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)*76*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(t_start,t_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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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((t_end),(t_start),(array_t[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((t_end),(t_start),(array_t[1]) +( glob_h) ,( opt_clock_sec));
>     glob_total_exp_sec   := glob_optimal_expect_sec + c(total_clock_sec);
>     percent_done   :=  comp_percent((t_end),(t_start),(array_t[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(t_start, t_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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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(t_end, t_start, array_t[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(t_end, t_start, array_t[1] + glob_h, opt_clock_sec)
        ;
    glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
    percent_done := comp_percent(t_end, t_start, array_t[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-1],array_x1_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 - 2 - 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_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-1],array_x2_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_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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 - 2 - 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_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x1_higher[1,last_no-5],array_x1_higher[1,last_no-4],array_x1_higher[1,last_no-3],array_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-5],array_x1_higher[1,last_no-4],array_x1_higher[1,last_no-3],array_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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 - 2 - 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_x2_higher[1,last_no-5],array_x2_higher[1,last_no-4],array_x2_higher[1,last_no-3],array_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-5],array_x2_higher[1,last_no-4],array_x2_higher[1,last_no-3],array_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x1[term] := array_x1[term]* ratio;
>             array_x1_higher[1,term] := array_x1_higher[1,term]* ratio;
>             array_t[term] := array_t[term]* ratio;
>             array_x2[term] := array_x2[term]* ratio;
>             array_x2_higher[1,term] := array_x2_higher[1,term]* ratio;
>             array_t[term] := array_t[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1_higher[1, last_no - 1],
            array_x1_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_x1_higher[1, last_no - 1],
                array_x1_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 - 12;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_x2_higher[1, last_no - 1],
            array_x2_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_x2_higher[1, last_no - 1],
                array_x2_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_x1_higher[1, last_no - 2],
            array_x1_higher[1, last_no - 1], array_x1_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_x1_higher[1, last_no - 2],
                array_x1_higher[1, last_no - 1],
                array_x1_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 - 12;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_x2_higher[1, last_no - 2],
            array_x2_higher[1, last_no - 1], array_x2_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_x2_higher[1, last_no - 2],
                array_x2_higher[1, last_no - 1],
                array_x2_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_x1_higher[1, last_no - 5],
            array_x1_higher[1, last_no - 4],
            array_x1_higher[1, last_no - 3],
            array_x1_higher[1, last_no - 2],
            array_x1_higher[1, last_no - 1], array_x1_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_x1_higher[1, last_no - 5],
                array_x1_higher[1, last_no - 4],
                array_x1_higher[1, last_no - 3],
                array_x1_higher[1, last_no - 2],
                array_x1_higher[1, last_no - 1],
                array_x1_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 - 12;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_x2_higher[1, last_no - 5],
            array_x2_higher[1, last_no - 4],
            array_x2_higher[1, last_no - 3],
            array_x2_higher[1, last_no - 2],
            array_x2_higher[1, last_no - 1], array_x2_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_x2_higher[1, last_no - 5],
                array_x2_higher[1, last_no - 4],
                array_x2_higher[1, last_no - 3],
                array_x2_higher[1, last_no - 2],
                array_x2_higher[1, last_no - 1],
                array_x2_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_x1[term] := array_x1[term]*ratio;
            array_x1_higher[1, term] := array_x1_higher[1, term]*ratio;
            array_t[term] := array_t[term]*ratio;
            array_x2[term] := array_x2[term]*ratio;
            array_x2_higher[1, term] := array_x2_higher[1, term]*ratio;
            array_t[term] := array_t[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre mult CONST FULL $eq_no = 1 i = 1
>     array_tmp1[1] := array_const_4D0[1] * array_x2[1];
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
>     #emit pre diff $eq_no = 1 i = 1 order_d = 1
>     array_tmp3[1] := array_x2_higher[2,1];
>     #emit pre mult CONST FULL $eq_no = 1 i = 1
>     array_tmp4[1] := array_const_2D0[1] * array_tmp3[1];
>     #emit pre sub FULL FULL $eq_no = 1 i = 1
>     array_tmp5[1] := array_tmp2[1] - array_tmp4[1];
>     #emit pre mult CONST FULL $eq_no = 1 i = 1
>     array_tmp6[1] := array_const_2D0[1] * array_x1[1];
>     #emit pre sub FULL FULL $eq_no = 1 i = 1
>     array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if ( not  array_x1_set_initial[1,2]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_x1[2] := temporary;
>                 array_x1_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_x1_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #emit pre diff $eq_no = 2 i = 1 order_d = 1
>     array_tmp9[1] := array_x2_higher[2,1];
>     #emit pre mult CONST FULL $eq_no = 2 i = 1
>     array_tmp10[1] := array_const_3D0[1] * array_tmp9[1];
>     #emit pre mult CONST FULL $eq_no = 2 i = 1
>     array_tmp11[1] := array_const_2D0[1] * array_x2[1];
>     #emit pre sub FULL FULL $eq_no = 2 i = 1
>     array_tmp12[1] := array_tmp10[1] - array_tmp11[1];
>     #emit pre diff $eq_no = 2 i = 1 order_d = 2
>     array_tmp13[1] := array_x1_higher[3,1];
>     #emit pre sub FULL FULL $eq_no = 2 i = 1
>     array_tmp14[1] := array_tmp12[1] - array_tmp13[1];
>     #emit pre diff $eq_no = 2 i = 1 order_d = 1
>     array_tmp15[1] := array_x1_higher[2,1];
>     #emit pre sub FULL FULL $eq_no = 2 i = 1
>     array_tmp16[1] := array_tmp14[1] - array_tmp15[1];
>     #emit pre add FULL FULL $eq_no = 2 i = 1
>     array_tmp17[1] := array_tmp16[1] + array_x1[1];
>     #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
>     if ( not  array_x2_set_initial[2,3]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp17[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_x2[3] := temporary;
>                 array_x2_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_x2_higher[2,2] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_x2_higher[3,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre mult CONST FULL $eq_no = 1 i = 2
>     array_tmp1[2] := array_const_4D0[1] * array_x2[2];
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre diff $eq_no = 1 i = 2 order_d = 1
>     array_tmp3[2] := array_x2_higher[2,2];
>     #emit pre mult CONST FULL $eq_no = 1 i = 2
>     array_tmp4[2] := array_const_2D0[1] * array_tmp3[2];
>     #emit pre sub FULL FULL $eq_no = 1 i = 2
>     array_tmp5[2] := array_tmp2[2] - array_tmp4[2];
>     #emit pre mult CONST FULL $eq_no = 1 i = 2
>     array_tmp6[2] := array_const_2D0[1] * array_x1[2];
>     #emit pre sub FULL FULL $eq_no = 1 i = 2
>     array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if ( not  array_x1_set_initial[1,3]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_x1[3] := temporary;
>                 array_x1_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_x1_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #emit pre diff $eq_no = 2 i = 2 order_d = 1
>     array_tmp9[2] := array_x2_higher[2,2];
>     #emit pre mult CONST FULL $eq_no = 2 i = 2
>     array_tmp10[2] := array_const_3D0[1] * array_tmp9[2];
>     #emit pre mult CONST FULL $eq_no = 2 i = 2
>     array_tmp11[2] := array_const_2D0[1] * array_x2[2];
>     #emit pre sub FULL FULL $eq_no = 2 i = 2
>     array_tmp12[2] := array_tmp10[2] - array_tmp11[2];
>     #emit pre diff $eq_no = 2 i = 2 order_d = 2
>     array_tmp13[2] := array_x1_higher[3,2];
>     #emit pre sub FULL FULL $eq_no = 2 i = 2
>     array_tmp14[2] := array_tmp12[2] - array_tmp13[2];
>     #emit pre diff $eq_no = 2 i = 2 order_d = 1
>     array_tmp15[2] := array_x1_higher[2,2];
>     #emit pre sub FULL FULL $eq_no = 2 i = 2
>     array_tmp16[2] := array_tmp14[2] - array_tmp15[2];
>     #emit pre add FULL FULL $eq_no = 2 i = 2
>     array_tmp17[2] := array_tmp16[2] + array_x1[2];
>     #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
>     if ( not  array_x2_set_initial[2,4]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp17[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_x2[4] := temporary;
>                 array_x2_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_x2_higher[2,3] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_x2_higher[3,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre mult CONST FULL $eq_no = 1 i = 3
>     array_tmp1[3] := array_const_4D0[1] * array_x2[3];
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp2[3] := array_tmp1[3];
>     #emit pre diff $eq_no = 1 i = 3 order_d = 1
>     array_tmp3[3] := array_x2_higher[2,3];
>     #emit pre mult CONST FULL $eq_no = 1 i = 3
>     array_tmp4[3] := array_const_2D0[1] * array_tmp3[3];
>     #emit pre sub FULL FULL $eq_no = 1 i = 3
>     array_tmp5[3] := array_tmp2[3] - array_tmp4[3];
>     #emit pre mult CONST FULL $eq_no = 1 i = 3
>     array_tmp6[3] := array_const_2D0[1] * array_x1[3];
>     #emit pre sub FULL FULL $eq_no = 1 i = 3
>     array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_x1_set_initial[1,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_x1[4] := temporary;
>                 array_x1_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_x1_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #emit pre diff $eq_no = 2 i = 3 order_d = 1
>     array_tmp9[3] := array_x2_higher[2,3];
>     #emit pre mult CONST FULL $eq_no = 2 i = 3
>     array_tmp10[3] := array_const_3D0[1] * array_tmp9[3];
>     #emit pre mult CONST FULL $eq_no = 2 i = 3
>     array_tmp11[3] := array_const_2D0[1] * array_x2[3];
>     #emit pre sub FULL FULL $eq_no = 2 i = 3
>     array_tmp12[3] := array_tmp10[3] - array_tmp11[3];
>     #emit pre diff $eq_no = 2 i = 3 order_d = 2
>     array_tmp13[3] := array_x1_higher[3,3];
>     #emit pre sub FULL FULL $eq_no = 2 i = 3
>     array_tmp14[3] := array_tmp12[3] - array_tmp13[3];
>     #emit pre diff $eq_no = 2 i = 3 order_d = 1
>     array_tmp15[3] := array_x1_higher[2,3];
>     #emit pre sub FULL FULL $eq_no = 2 i = 3
>     array_tmp16[3] := array_tmp14[3] - array_tmp15[3];
>     #emit pre add FULL FULL $eq_no = 2 i = 3
>     array_tmp17[3] := array_tmp16[3] + array_x1[3];
>     #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
>     if ( not  array_x2_set_initial[2,5]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp17[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_x2[5] := temporary;
>                 array_x2_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_x2_higher[2,4] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_x2_higher[3,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre mult CONST FULL $eq_no = 1 i = 4
>     array_tmp1[4] := array_const_4D0[1] * array_x2[4];
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp2[4] := array_tmp1[4];
>     #emit pre diff $eq_no = 1 i = 4 order_d = 1
>     array_tmp3[4] := array_x2_higher[2,4];
>     #emit pre mult CONST FULL $eq_no = 1 i = 4
>     array_tmp4[4] := array_const_2D0[1] * array_tmp3[4];
>     #emit pre sub FULL FULL $eq_no = 1 i = 4
>     array_tmp5[4] := array_tmp2[4] - array_tmp4[4];
>     #emit pre mult CONST FULL $eq_no = 1 i = 4
>     array_tmp6[4] := array_const_2D0[1] * array_x1[4];
>     #emit pre sub FULL FULL $eq_no = 1 i = 4
>     array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_x1_set_initial[1,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_x1[5] := temporary;
>                 array_x1_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_x1_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #emit pre diff $eq_no = 2 i = 4 order_d = 1
>     array_tmp9[4] := array_x2_higher[2,4];
>     #emit pre mult CONST FULL $eq_no = 2 i = 4
>     array_tmp10[4] := array_const_3D0[1] * array_tmp9[4];
>     #emit pre mult CONST FULL $eq_no = 2 i = 4
>     array_tmp11[4] := array_const_2D0[1] * array_x2[4];
>     #emit pre sub FULL FULL $eq_no = 2 i = 4
>     array_tmp12[4] := array_tmp10[4] - array_tmp11[4];
>     #emit pre diff $eq_no = 2 i = 4 order_d = 2
>     array_tmp13[4] := array_x1_higher[3,4];
>     #emit pre sub FULL FULL $eq_no = 2 i = 4
>     array_tmp14[4] := array_tmp12[4] - array_tmp13[4];
>     #emit pre diff $eq_no = 2 i = 4 order_d = 1
>     array_tmp15[4] := array_x1_higher[2,4];
>     #emit pre sub FULL FULL $eq_no = 2 i = 4
>     array_tmp16[4] := array_tmp14[4] - array_tmp15[4];
>     #emit pre add FULL FULL $eq_no = 2 i = 4
>     array_tmp17[4] := array_tmp16[4] + array_x1[4];
>     #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
>     if ( not  array_x2_set_initial[2,6]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp17[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_x2[6] := temporary;
>                 array_x2_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_x2_higher[2,5] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_x2_higher[3,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre mult CONST FULL $eq_no = 1 i = 5
>     array_tmp1[5] := array_const_4D0[1] * array_x2[5];
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp2[5] := array_tmp1[5];
>     #emit pre diff $eq_no = 1 i = 5 order_d = 1
>     array_tmp3[5] := array_x2_higher[2,5];
>     #emit pre mult CONST FULL $eq_no = 1 i = 5
>     array_tmp4[5] := array_const_2D0[1] * array_tmp3[5];
>     #emit pre sub FULL FULL $eq_no = 1 i = 5
>     array_tmp5[5] := array_tmp2[5] - array_tmp4[5];
>     #emit pre mult CONST FULL $eq_no = 1 i = 5
>     array_tmp6[5] := array_const_2D0[1] * array_x1[5];
>     #emit pre sub FULL FULL $eq_no = 1 i = 5
>     array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_x1_set_initial[1,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp7[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_x1[6] := temporary;
>                 array_x1_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_x1_higher[2,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #emit pre diff $eq_no = 2 i = 5 order_d = 1
>     array_tmp9[5] := array_x2_higher[2,5];
>     #emit pre mult CONST FULL $eq_no = 2 i = 5
>     array_tmp10[5] := array_const_3D0[1] * array_tmp9[5];
>     #emit pre mult CONST FULL $eq_no = 2 i = 5
>     array_tmp11[5] := array_const_2D0[1] * array_x2[5];
>     #emit pre sub FULL FULL $eq_no = 2 i = 5
>     array_tmp12[5] := array_tmp10[5] - array_tmp11[5];
>     #emit pre diff $eq_no = 2 i = 5 order_d = 2
>     array_tmp13[5] := array_x1_higher[3,5];
>     #emit pre sub FULL FULL $eq_no = 2 i = 5
>     array_tmp14[5] := array_tmp12[5] - array_tmp13[5];
>     #emit pre diff $eq_no = 2 i = 5 order_d = 1
>     array_tmp15[5] := array_x1_higher[2,5];
>     #emit pre sub FULL FULL $eq_no = 2 i = 5
>     array_tmp16[5] := array_tmp14[5] - array_tmp15[5];
>     #emit pre add FULL FULL $eq_no = 2 i = 5
>     array_tmp17[5] := array_tmp16[5] + array_x1[5];
>     #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
>     if ( not  array_x2_set_initial[2,7]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp17[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6));
>             if (7 <= ATS_MAX_TERMS) then # if number 3
>                 array_x2[7] := temporary;
>                 array_x2_higher[1,7] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(6);
>             array_x2_higher[2,6] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_x2_higher[3,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #END ATOMHDR5
>     #BEGIN OUTFILE3
>     #Top Atomall While Loop-- outfile3
>     while (kkk <= ATS_MAX_TERMS) do # do number 1
>         #END OUTFILE3
>         #BEGIN OUTFILE4
>         #emit mult CONST FULL $eq_no = 1 i = 1
>         array_tmp1[kkk] := array_const_4D0[1] * array_x2[kkk];
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp2[kkk] := array_tmp1[kkk];
>         #emit diff $eq_no = 1
>         if (kkk <= ATS_MAX_TERMS) then # if number 1
>             array_tmp3[kkk] :=  array_x2_higher[2,kkk];
>         fi;# end if 1;
>         #emit mult CONST FULL $eq_no = 1 i = 1
>         array_tmp4[kkk] := array_const_2D0[1] * array_tmp3[kkk];
>         #emit FULL - FULL sub $eq_no = 1
>         array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk];
>         #emit mult CONST FULL $eq_no = 1 i = 1
>         array_tmp6[kkk] := array_const_2D0[1] * array_x1[kkk];
>         #emit FULL - FULL sub $eq_no = 1
>         array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_x1_set_initial[1,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp7[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_x1[kkk + order_d] := c(temporary);
>                 array_x1_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_x1_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 diff $eq_no = 2
>         if (kkk <= ATS_MAX_TERMS) then # if number 1
>             array_tmp9[kkk] :=  array_x2_higher[2,kkk];
>         fi;# end if 1;
>         #emit mult CONST FULL $eq_no = 2 i = 1
>         array_tmp10[kkk] := array_const_3D0[1] * array_tmp9[kkk];
>         #emit mult CONST FULL $eq_no = 2 i = 1
>         array_tmp11[kkk] := array_const_2D0[1] * array_x2[kkk];
>         #emit FULL - FULL sub $eq_no = 2
>         array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk];
>         #emit diff $eq_no = 2
>         if (kkk <= ATS_MAX_TERMS) then # if number 1
>             array_tmp13[kkk] :=  array_x1_higher[3,kkk];
>         fi;# end if 1;
>         #emit FULL - FULL sub $eq_no = 2
>         array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk];
>         #emit diff $eq_no = 2
>         if (kkk <= ATS_MAX_TERMS) then # if number 1
>             array_tmp15[kkk] :=  array_x1_higher[2,kkk];
>         fi;# end if 1;
>         #emit FULL - FULL sub $eq_no = 2
>         array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk];
>         #emit FULL - FULL add $eq_no = 2
>         array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
>         #emit assign $eq_no = 2
>         order_d  := 2;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_x2_set_initial[2,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp17[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_x2[kkk + order_d] := c(temporary);
>                 array_x2_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_x2_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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    array_tmp1[1] := array_const_4D0[1]*array_x2[1];
    array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
    array_tmp3[1] := array_x2_higher[2, 1];
    array_tmp4[1] := array_const_2D0[1]*array_tmp3[1];
    array_tmp5[1] := array_tmp2[1] - array_tmp4[1];
    array_tmp6[1] := array_const_2D0[1]*array_x1[1];
    array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
    if not array_x1_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_x1[2] := temporary;
                array_x1_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_x1_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp9[1] := array_x2_higher[2, 1];
    array_tmp10[1] := array_const_3D0[1]*array_tmp9[1];
    array_tmp11[1] := array_const_2D0[1]*array_x2[1];
    array_tmp12[1] := array_tmp10[1] - array_tmp11[1];
    array_tmp13[1] := array_x1_higher[3, 1];
    array_tmp14[1] := array_tmp12[1] - array_tmp13[1];
    array_tmp15[1] := array_x1_higher[2, 1];
    array_tmp16[1] := array_tmp14[1] - array_tmp15[1];
    array_tmp17[1] := array_tmp16[1] + array_x1[1];
    if not array_x2_set_initial[2, 3] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp17[1])*expt(glob_h, c(2))*c(factorial_3(0, 2));
            if 3 <= ATS_MAX_TERMS then
                array_x2[3] := temporary;
                array_x2_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_x2_higher[2, 2] := c(temporary);
            temporary := c(temporary)*c(1)/c(glob_h);
            array_x2_higher[3, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := array_const_4D0[1]*array_x2[2];
    array_tmp2[2] := array_tmp1[2];
    array_tmp3[2] := array_x2_higher[2, 2];
    array_tmp4[2] := array_const_2D0[1]*array_tmp3[2];
    array_tmp5[2] := array_tmp2[2] - array_tmp4[2];
    array_tmp6[2] := array_const_2D0[1]*array_x1[2];
    array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
    if not array_x1_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_x1[3] := temporary;
                array_x1_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_x1_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp9[2] := array_x2_higher[2, 2];
    array_tmp10[2] := array_const_3D0[1]*array_tmp9[2];
    array_tmp11[2] := array_const_2D0[1]*array_x2[2];
    array_tmp12[2] := array_tmp10[2] - array_tmp11[2];
    array_tmp13[2] := array_x1_higher[3, 2];
    array_tmp14[2] := array_tmp12[2] - array_tmp13[2];
    array_tmp15[2] := array_x1_higher[2, 2];
    array_tmp16[2] := array_tmp14[2] - array_tmp15[2];
    array_tmp17[2] := array_tmp16[2] + array_x1[2];
    if not array_x2_set_initial[2, 4] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp17[2])*expt(glob_h, c(2))*c(factorial_3(1, 3));
            if 4 <= ATS_MAX_TERMS then
                array_x2[4] := temporary;
                array_x2_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_x2_higher[2, 3] := c(temporary);
            temporary := c(temporary)*c(2)/c(glob_h);
            array_x2_higher[3, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp1[3] := array_const_4D0[1]*array_x2[3];
    array_tmp2[3] := array_tmp1[3];
    array_tmp3[3] := array_x2_higher[2, 3];
    array_tmp4[3] := array_const_2D0[1]*array_tmp3[3];
    array_tmp5[3] := array_tmp2[3] - array_tmp4[3];
    array_tmp6[3] := array_const_2D0[1]*array_x1[3];
    array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
    if not array_x1_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_x1[4] := temporary;
                array_x1_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_x1_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp9[3] := array_x2_higher[2, 3];
    array_tmp10[3] := array_const_3D0[1]*array_tmp9[3];
    array_tmp11[3] := array_const_2D0[1]*array_x2[3];
    array_tmp12[3] := array_tmp10[3] - array_tmp11[3];
    array_tmp13[3] := array_x1_higher[3, 3];
    array_tmp14[3] := array_tmp12[3] - array_tmp13[3];
    array_tmp15[3] := array_x1_higher[2, 3];
    array_tmp16[3] := array_tmp14[3] - array_tmp15[3];
    array_tmp17[3] := array_tmp16[3] + array_x1[3];
    if not array_x2_set_initial[2, 5] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp17[3])*expt(glob_h, c(2))*c(factorial_3(2, 4));
            if 5 <= ATS_MAX_TERMS then
                array_x2[5] := temporary;
                array_x2_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_x2_higher[2, 4] := c(temporary);
            temporary := c(temporary)*c(3)/c(glob_h);
            array_x2_higher[3, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp1[4] := array_const_4D0[1]*array_x2[4];
    array_tmp2[4] := array_tmp1[4];
    array_tmp3[4] := array_x2_higher[2, 4];
    array_tmp4[4] := array_const_2D0[1]*array_tmp3[4];
    array_tmp5[4] := array_tmp2[4] - array_tmp4[4];
    array_tmp6[4] := array_const_2D0[1]*array_x1[4];
    array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
    if not array_x1_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_x1[5] := temporary;
                array_x1_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_x1_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp9[4] := array_x2_higher[2, 4];
    array_tmp10[4] := array_const_3D0[1]*array_tmp9[4];
    array_tmp11[4] := array_const_2D0[1]*array_x2[4];
    array_tmp12[4] := array_tmp10[4] - array_tmp11[4];
    array_tmp13[4] := array_x1_higher[3, 4];
    array_tmp14[4] := array_tmp12[4] - array_tmp13[4];
    array_tmp15[4] := array_x1_higher[2, 4];
    array_tmp16[4] := array_tmp14[4] - array_tmp15[4];
    array_tmp17[4] := array_tmp16[4] + array_x1[4];
    if not array_x2_set_initial[2, 6] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp17[4])*expt(glob_h, c(2))*c(factorial_3(3, 5));
            if 6 <= ATS_MAX_TERMS then
                array_x2[6] := temporary;
                array_x2_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_x2_higher[2, 5] := c(temporary);
            temporary := c(temporary)*c(4)/c(glob_h);
            array_x2_higher[3, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp1[5] := array_const_4D0[1]*array_x2[5];
    array_tmp2[5] := array_tmp1[5];
    array_tmp3[5] := array_x2_higher[2, 5];
    array_tmp4[5] := array_const_2D0[1]*array_tmp3[5];
    array_tmp5[5] := array_tmp2[5] - array_tmp4[5];
    array_tmp6[5] := array_const_2D0[1]*array_x1[5];
    array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
    if not array_x1_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp7[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_x1[6] := temporary;
                array_x1_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_x1_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    array_tmp9[5] := array_x2_higher[2, 5];
    array_tmp10[5] := array_const_3D0[1]*array_tmp9[5];
    array_tmp11[5] := array_const_2D0[1]*array_x2[5];
    array_tmp12[5] := array_tmp10[5] - array_tmp11[5];
    array_tmp13[5] := array_x1_higher[3, 5];
    array_tmp14[5] := array_tmp12[5] - array_tmp13[5];
    array_tmp15[5] := array_x1_higher[2, 5];
    array_tmp16[5] := array_tmp14[5] - array_tmp15[5];
    array_tmp17[5] := array_tmp16[5] + array_x1[5];
    if not array_x2_set_initial[2, 7] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp17[5])*expt(glob_h, c(2))*c(factorial_3(4, 6));
            if 7 <= ATS_MAX_TERMS then
                array_x2[7] := temporary;
                array_x2_higher[1, 7] := temporary
            end if;
            temporary := c(temporary)*c(6)/c(glob_h);
            array_x2_higher[2, 6] := c(temporary);
            temporary := c(temporary)*c(5)/c(glob_h);
            array_x2_higher[3, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp1[kkk] := array_const_4D0[1]*array_x2[kkk];
        array_tmp2[kkk] := array_tmp1[kkk];
        if kkk <= ATS_MAX_TERMS then
            array_tmp3[kkk] := array_x2_higher[2, kkk]
        end if;
        array_tmp4[kkk] := array_const_2D0[1]*array_tmp3[kkk];
        array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk];
        array_tmp6[kkk] := array_const_2D0[1]*array_x1[kkk];
        array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_x1_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp7[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_x1[kkk + order_d] := c(temporary);
                array_x1_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_x1_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        if kkk <= ATS_MAX_TERMS then
            array_tmp9[kkk] := array_x2_higher[2, kkk]
        end if;
        array_tmp10[kkk] := array_const_3D0[1]*array_tmp9[kkk];
        array_tmp11[kkk] := array_const_2D0[1]*array_x2[kkk];
        array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk];
        if kkk <= ATS_MAX_TERMS then
            array_tmp13[kkk] := array_x1_higher[3, kkk]
        end if;
        array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk];
        if kkk <= ATS_MAX_TERMS then
            array_tmp15[kkk] := array_x1_higher[2, kkk]
        end if;
        array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk];
        array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
        order_d := 2;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_x2_set_initial[2, kkk + order_d] then
                temporary := c(array_tmp17[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_x2[kkk + order_d] := c(temporary);
                array_x2_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_x2_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,
>     t_start,t_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_4D0,
>     array_const_2D0,
>     array_const_2,
>     array_const_3D0,
>     #END CONST
>     array_x1_init,
>     array_x2_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_x1,
>     array_t,
>     array_x2,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_tmp6,
>     array_tmp7,
>     array_tmp8,
>     array_tmp9,
>     array_tmp10,
>     array_tmp11,
>     array_tmp12,
>     array_tmp13,
>     array_tmp14,
>     array_tmp15,
>     array_tmp16,
>     array_tmp17,
>     array_m1,
>     array_x1_higher,
>     array_x1_higher_work,
>     array_x1_higher_work2,
>     array_x1_set_initial,
>     array_x2_higher,
>     array_x2_higher_work,
>     array_x2_higher_work2,
>     array_x2_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:=64;
>     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_x1_init:= Array(0..(40),[]);
>     array_x2_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_x1:= Array(0..(40),[]);
>     array_t:= Array(0..(40),[]);
>     array_x2:= 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_tmp6:= Array(0..(40),[]);
>     array_tmp7:= Array(0..(40),[]);
>     array_tmp8:= Array(0..(40),[]);
>     array_tmp9:= Array(0..(40),[]);
>     array_tmp10:= Array(0..(40),[]);
>     array_tmp11:= Array(0..(40),[]);
>     array_tmp12:= Array(0..(40),[]);
>     array_tmp13:= Array(0..(40),[]);
>     array_tmp14:= Array(0..(40),[]);
>     array_tmp15:= Array(0..(40),[]);
>     array_tmp16:= Array(0..(40),[]);
>     array_tmp17:= Array(0..(40),[]);
>     array_m1:= Array(0..(40),[]);
>     array_x1_higher := Array(0..(3) ,(0..40+ 1),[]);
>     array_x1_higher_work := Array(0..(3) ,(0..40+ 1),[]);
>     array_x1_higher_work2 := Array(0..(3) ,(0..40+ 1),[]);
>     array_x1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
>     array_x2_higher := Array(0..(3) ,(0..40+ 1),[]);
>     array_x2_higher_work := Array(0..(3) ,(0..40+ 1),[]);
>     array_x2_higher_work2 := Array(0..(3) ,(0..40+ 1),[]);
>     array_x2_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_x1_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_x2_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_x1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_t[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_x2[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_tmp6[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp7[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp8[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp9[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp10[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp11[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp12[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp13[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp14[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp15[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp16[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp17[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 <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_x1_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 <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_x1_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 <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_x1_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_x1_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 <= 40) do # do number 2
>             array_x2_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 <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_x2_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 <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_x2_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_x2_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_x1);
>     zero_ats_ar(array_t);
>     zero_ats_ar(array_x2);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5);
>     zero_ats_ar(array_tmp6);
>     zero_ats_ar(array_tmp7);
>     zero_ats_ar(array_tmp8);
>     zero_ats_ar(array_tmp9);
>     zero_ats_ar(array_tmp10);
>     zero_ats_ar(array_tmp11);
>     zero_ats_ar(array_tmp12);
>     zero_ats_ar(array_tmp13);
>     zero_ats_ar(array_tmp14);
>     zero_ats_ar(array_tmp15);
>     zero_ats_ar(array_tmp16);
>     zero_ats_ar(array_tmp17);
>     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_4D0);
>     array_const_4D0[1]   := c(4.0);
>     zero_ats_ar(array_const_2D0);
>     array_const_2D0[1]   := c(2.0);
>     zero_ats_ar(array_const_2);
>     array_const_2[1]   := c(2);
>     zero_ats_ar(array_const_3D0);
>     array_const_3D0[1]   := c(3.0);
>     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_x1_set_initial[1,1] := true;
>     array_x1_set_initial[1,2] := false;
>     array_x1_set_initial[1,3] := false;
>     array_x1_set_initial[1,4] := false;
>     array_x1_set_initial[1,5] := false;
>     array_x1_set_initial[1,6] := false;
>     array_x1_set_initial[1,7] := false;
>     array_x1_set_initial[1,8] := false;
>     array_x1_set_initial[1,9] := false;
>     array_x1_set_initial[1,10] := false;
>     array_x1_set_initial[1,11] := false;
>     array_x1_set_initial[1,12] := false;
>     array_x1_set_initial[1,13] := false;
>     array_x1_set_initial[1,14] := false;
>     array_x1_set_initial[1,15] := false;
>     array_x1_set_initial[1,16] := false;
>     array_x1_set_initial[1,17] := false;
>     array_x1_set_initial[1,18] := false;
>     array_x1_set_initial[1,19] := false;
>     array_x1_set_initial[1,20] := false;
>     array_x1_set_initial[1,21] := false;
>     array_x1_set_initial[1,22] := false;
>     array_x1_set_initial[1,23] := false;
>     array_x1_set_initial[1,24] := false;
>     array_x1_set_initial[1,25] := false;
>     array_x1_set_initial[1,26] := false;
>     array_x1_set_initial[1,27] := false;
>     array_x1_set_initial[1,28] := false;
>     array_x1_set_initial[1,29] := false;
>     array_x1_set_initial[1,30] := false;
>     array_x1_set_initial[1,31] := false;
>     array_x1_set_initial[1,32] := false;
>     array_x1_set_initial[1,33] := false;
>     array_x1_set_initial[1,34] := false;
>     array_x1_set_initial[1,35] := false;
>     array_x1_set_initial[1,36] := false;
>     array_x1_set_initial[1,37] := false;
>     array_x1_set_initial[1,38] := false;
>     array_x1_set_initial[1,39] := false;
>     array_x1_set_initial[1,40] := false;
>     array_x2_set_initial[2,1] := true;
>     array_x2_set_initial[2,2] := true;
>     array_x2_set_initial[2,3] := false;
>     array_x2_set_initial[2,4] := false;
>     array_x2_set_initial[2,5] := false;
>     array_x2_set_initial[2,6] := false;
>     array_x2_set_initial[2,7] := false;
>     array_x2_set_initial[2,8] := false;
>     array_x2_set_initial[2,9] := false;
>     array_x2_set_initial[2,10] := false;
>     array_x2_set_initial[2,11] := false;
>     array_x2_set_initial[2,12] := false;
>     array_x2_set_initial[2,13] := false;
>     array_x2_set_initial[2,14] := false;
>     array_x2_set_initial[2,15] := false;
>     array_x2_set_initial[2,16] := false;
>     array_x2_set_initial[2,17] := false;
>     array_x2_set_initial[2,18] := false;
>     array_x2_set_initial[2,19] := false;
>     array_x2_set_initial[2,20] := false;
>     array_x2_set_initial[2,21] := false;
>     array_x2_set_initial[2,22] := false;
>     array_x2_set_initial[2,23] := false;
>     array_x2_set_initial[2,24] := false;
>     array_x2_set_initial[2,25] := false;
>     array_x2_set_initial[2,26] := false;
>     array_x2_set_initial[2,27] := false;
>     array_x2_set_initial[2,28] := false;
>     array_x2_set_initial[2,29] := false;
>     array_x2_set_initial[2,30] := false;
>     array_x2_set_initial[2,31] := false;
>     array_x2_set_initial[2,32] := false;
>     array_x2_set_initial[2,33] := false;
>     array_x2_set_initial[2,34] := false;
>     array_x2_set_initial[2,35] := false;
>     array_x2_set_initial[2,36] := false;
>     array_x2_set_initial[2,37] := false;
>     array_x2_set_initial[2,38] := false;
>     array_x2_set_initial[2,39] := false;
>     array_x2_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/mtest6postode.ode#################");
>     omniout_str(ALWAYS,"diff  ( x1 , t , 1 )   =  4.0  *  x2  -   2.0  *  diff  ( x2 , t  , 1 )   -  2.0  *  x1 ; ");
>     omniout_str(ALWAYS,"diff  ( x2 , t , 2 )   =  3.0  *  diff ( x2 , t , 1 )   -  2.0  *  x2  -  diff ( x1 , t , 2 )   -  diff  ( x1 , t , 1 )   +  x1 ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=64;");
>     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,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"t_start := c(1.5);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"t_end := c(8.0);");
>     omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);");
>     omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"glob_max_h := c(0.0001);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 0;");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
>     omniout_str(ALWAYS,"glob_look_poles:=false;");
>     omniout_str(ALWAYS,"glob_h:=c(0.001);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
>     omniout_str(ALWAYS,"local c1,c2,c3;");
>     omniout_str(ALWAYS,"c1 := c(1.0);");
>     omniout_str(ALWAYS,"c2 := c(0.0002);");
>     omniout_str(ALWAYS,"c3 := c(0.0003);");
>     omniout_str(ALWAYS,"return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_x1p := proc(t)");
>     omniout_str(ALWAYS,"local c1,c2,c3;");
>     omniout_str(ALWAYS,"c1 := c(1.0);");
>     omniout_str(ALWAYS,"c2 := c(0.0002);");
>     omniout_str(ALWAYS,"c3 := c(0.0003);");
>     omniout_str(ALWAYS,"return(   c(-6.0) * c3 * exp(neg( c(t))));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
>     omniout_str(ALWAYS,"local c1,c2,c3;");
>     omniout_str(ALWAYS,"c1 := c(1.0);");
>     omniout_str(ALWAYS,"c2 := c(0.0002);");
>     omniout_str(ALWAYS,"c3 := c(0.0003);");
>     omniout_str(ALWAYS,"return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
>     omniout_str(ALWAYS,"local c1,c2,c3;");
>     omniout_str(ALWAYS,"c1 := c(1.0);");
>     omniout_str(ALWAYS,"c2 := c(0.0002);");
>     omniout_str(ALWAYS,"c3 := c(0.0003);");
>     omniout_str(ALWAYS,"return(   c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t))));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     t_start := c(1.5);
>     t_end := c(8.0);
>     array_x1_init[0 + 1] := exact_soln_x1(t_start);
>     array_x2_init[0 + 1] := exact_soln_x2(t_start);
>     array_x2_init[1 + 1] := exact_soln_x2p(t_start);
>     glob_look_poles := true;
>     glob_max_h := c(0.0001);
>     glob_type_given_pole := 0;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=8;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=3;
>     glob_max_iter:=100000;
>     glob_upper_ratio_limit:=c(1.000001);
>     glob_lower_ratio_limit:=c(0.999999);
>     glob_look_poles:=false;
>     glob_h:=c(0.001);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(t_start,t_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(t_end) - c(t_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(t_start,t_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_t[1]   := c(t_start);
>             array_t[2]   :=  c(glob_h);
>             glob_next_display := c(t_start);
>             order_diff := 2;
>             #Start Series array_x1
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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 := 2;
>             #Start Series array_x2
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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 <= 3) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 3 + 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(t_start,t_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_t[1]   := c(t_start);
>         array_t[2]   :=  c(glob_h);
>         glob_next_display := c(t_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 := 2;
>         #Start Series array_x1
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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 := 2;
>         #Start Series array_x2
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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_t[1] < glob_check_sign * t_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 <= 3) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 3 + 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_t[1]   := array_t[1] + glob_h;
>             array_t[2]   :=  glob_h;
>             #Jump Series array_x1;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_x1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_x1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x1_higher_work[2,iii] := array_x1_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_x1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x1_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_x1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x1_higher_work[1,iii] := array_x1_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_x1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x1_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_x1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x1_higher_work[1,iii] := array_x1_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_x1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x1_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_x1[term_no] := array_x1_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_x1_higher[ord,term_no] := array_x1_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_x2;
>             order_diff  := 3;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =2
>             #sum_and_adjust array_x2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 3;
>             calc_term := 1;
>             #adjust_subseriesarray_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x2_higher_work[3,iii] := array_x2_higher[3,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 := 3;
>             calc_term := 1;
>             #sum_subseriesarray_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x2_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 := 2;
>             calc_term := 2;
>             #adjust_subseriesarray_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x2_higher_work[2,iii] := array_x2_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 := 2;
>             #sum_subseriesarray_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x2_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 := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x2_higher_work[2,iii] := array_x2_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_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x2_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 := 3;
>             #adjust_subseriesarray_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x2_higher_work[1,iii] := array_x2_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 := 3;
>             #sum_subseriesarray_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x2_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_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x2_higher_work[1,iii] := array_x2_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_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x2_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_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_x2_higher_work[1,iii] := array_x2_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_x2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_x2_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_x2[term_no] := array_x2_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_x2_higher[ord,term_no] := array_x2_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  ( x1 , t , 1 )   =  4.0  *  x2  -   2.0  *  diff  ( x2 , t  , 1 )   -  2.0  *  x1 ; ");
>         omniout_str(INFO,"diff  ( x2 , t , 2 )   =  3.0  *  diff ( x2 , t , 1 )   -  2.0  *  x2  -  diff ( x1 , t , 2 )   -  diff  ( x1 , t , 1 )   +  x1 ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(t_start,t_end);
>         if (glob_html_log)  then # if number 20
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2016-08-26T16:49:28-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"mtest6.ode.txt\">mtest6</a>")
>             ;
>             logitem_str(html_log_file,"diff  ( x1 , t , 1 )   =  4.0  *  x2  -   2.0  *  diff  ( x2 , t  , 1 )   -  2.0  *  x1 ; ")
>             ;
>             logitem_float(html_log_file,t_start)
>             ;
>             logitem_float(html_log_file,t_end)
>             ;
>             logitem_float(html_log_file,array_t[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.mtest6.mxt.txt\">mtest6 diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.mtest6.mxt.txt\">mtest6 maple results</a>")
>             ;
>             logitem_str(html_log_file,"???")
>             ;
>             logend(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logitem_str(html_log_file,"diff  ( x2 , t , 2 )   =  3.0  *  diff ( x2 , t , 1 )   -  2.0  *  x2  -  diff ( x1 , t , 2 )   -  diff  ( x1 , t , 1 )   +  x1 ; ")
>             ;
>             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, t_start, t_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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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 := 64;
    max_terms := 40;
    glob_html_log := true;
    array_x1_init := Array(0 .. 40, []);
    array_x2_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_x1 := Array(0 .. 40, []);
    array_t := Array(0 .. 40, []);
    array_x2 := 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_tmp6 := Array(0 .. 40, []);
    array_tmp7 := Array(0 .. 40, []);
    array_tmp8 := Array(0 .. 40, []);
    array_tmp9 := Array(0 .. 40, []);
    array_tmp10 := Array(0 .. 40, []);
    array_tmp11 := Array(0 .. 40, []);
    array_tmp12 := Array(0 .. 40, []);
    array_tmp13 := Array(0 .. 40, []);
    array_tmp14 := Array(0 .. 40, []);
    array_tmp15 := Array(0 .. 40, []);
    array_tmp16 := Array(0 .. 40, []);
    array_tmp17 := Array(0 .. 40, []);
    array_m1 := Array(0 .. 40, []);
    array_x1_higher := Array(0 .. 3, 0 .. 41, []);
    array_x1_higher_work := Array(0 .. 3, 0 .. 41, []);
    array_x1_higher_work2 := Array(0 .. 3, 0 .. 41, []);
    array_x1_set_initial := Array(0 .. 3, 0 .. 41, []);
    array_x2_higher := Array(0 .. 3, 0 .. 41, []);
    array_x2_higher_work := Array(0 .. 3, 0 .. 41, []);
    array_x2_higher_work2 := Array(0 .. 3, 0 .. 41, []);
    array_x2_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_x1_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_x2_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_x1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_t[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_x2[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_tmp6[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp8[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp9[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp10[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_tmp11[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_tmp12[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_tmp13[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_tmp14[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_tmp15[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_tmp16[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_tmp17[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 <= 3 do
        term := 1;
        while term <= 40 do
            array_x1_higher[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_x1_higher_work[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_x1_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_x1_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 <= 40 do
            array_x2_higher[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_x2_higher_work[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_x2_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_x2_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_x1);
    zero_ats_ar(array_t);
    zero_ats_ar(array_x2);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5);
    zero_ats_ar(array_tmp6);
    zero_ats_ar(array_tmp7);
    zero_ats_ar(array_tmp8);
    zero_ats_ar(array_tmp9);
    zero_ats_ar(array_tmp10);
    zero_ats_ar(array_tmp11);
    zero_ats_ar(array_tmp12);
    zero_ats_ar(array_tmp13);
    zero_ats_ar(array_tmp14);
    zero_ats_ar(array_tmp15);
    zero_ats_ar(array_tmp16);
    zero_ats_ar(array_tmp17);
    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_4D0);
    array_const_4D0[1] := c(4.0);
    zero_ats_ar(array_const_2D0);
    array_const_2D0[1] := c(2.0);
    zero_ats_ar(array_const_2);
    array_const_2[1] := c(2);
    zero_ats_ar(array_const_3D0);
    array_const_3D0[1] := c(3.0);
    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_x1_set_initial[1, 1] := true;
    array_x1_set_initial[1, 2] := false;
    array_x1_set_initial[1, 3] := false;
    array_x1_set_initial[1, 4] := false;
    array_x1_set_initial[1, 5] := false;
    array_x1_set_initial[1, 6] := false;
    array_x1_set_initial[1, 7] := false;
    array_x1_set_initial[1, 8] := false;
    array_x1_set_initial[1, 9] := false;
    array_x1_set_initial[1, 10] := false;
    array_x1_set_initial[1, 11] := false;
    array_x1_set_initial[1, 12] := false;
    array_x1_set_initial[1, 13] := false;
    array_x1_set_initial[1, 14] := false;
    array_x1_set_initial[1, 15] := false;
    array_x1_set_initial[1, 16] := false;
    array_x1_set_initial[1, 17] := false;
    array_x1_set_initial[1, 18] := false;
    array_x1_set_initial[1, 19] := false;
    array_x1_set_initial[1, 20] := false;
    array_x1_set_initial[1, 21] := false;
    array_x1_set_initial[1, 22] := false;
    array_x1_set_initial[1, 23] := false;
    array_x1_set_initial[1, 24] := false;
    array_x1_set_initial[1, 25] := false;
    array_x1_set_initial[1, 26] := false;
    array_x1_set_initial[1, 27] := false;
    array_x1_set_initial[1, 28] := false;
    array_x1_set_initial[1, 29] := false;
    array_x1_set_initial[1, 30] := false;
    array_x1_set_initial[1, 31] := false;
    array_x1_set_initial[1, 32] := false;
    array_x1_set_initial[1, 33] := false;
    array_x1_set_initial[1, 34] := false;
    array_x1_set_initial[1, 35] := false;
    array_x1_set_initial[1, 36] := false;
    array_x1_set_initial[1, 37] := false;
    array_x1_set_initial[1, 38] := false;
    array_x1_set_initial[1, 39] := false;
    array_x1_set_initial[1, 40] := false;
    array_x2_set_initial[2, 1] := true;
    array_x2_set_initial[2, 2] := true;
    array_x2_set_initial[2, 3] := false;
    array_x2_set_initial[2, 4] := false;
    array_x2_set_initial[2, 5] := false;
    array_x2_set_initial[2, 6] := false;
    array_x2_set_initial[2, 7] := false;
    array_x2_set_initial[2, 8] := false;
    array_x2_set_initial[2, 9] := false;
    array_x2_set_initial[2, 10] := false;
    array_x2_set_initial[2, 11] := false;
    array_x2_set_initial[2, 12] := false;
    array_x2_set_initial[2, 13] := false;
    array_x2_set_initial[2, 14] := false;
    array_x2_set_initial[2, 15] := false;
    array_x2_set_initial[2, 16] := false;
    array_x2_set_initial[2, 17] := false;
    array_x2_set_initial[2, 18] := false;
    array_x2_set_initial[2, 19] := false;
    array_x2_set_initial[2, 20] := false;
    array_x2_set_initial[2, 21] := false;
    array_x2_set_initial[2, 22] := false;
    array_x2_set_initial[2, 23] := false;
    array_x2_set_initial[2, 24] := false;
    array_x2_set_initial[2, 25] := false;
    array_x2_set_initial[2, 26] := false;
    array_x2_set_initial[2, 27] := false;
    array_x2_set_initial[2, 28] := false;
    array_x2_set_initial[2, 29] := false;
    array_x2_set_initial[2, 30] := false;
    array_x2_set_initial[2, 31] := false;
    array_x2_set_initial[2, 32] := false;
    array_x2_set_initial[2, 33] := false;
    array_x2_set_initial[2, 34] := false;
    array_x2_set_initial[2, 35] := false;
    array_x2_set_initial[2, 36] := false;
    array_x2_set_initial[2, 37] := false;
    array_x2_set_initial[2, 38] := false;
    array_x2_set_initial[2, 39] := false;
    array_x2_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/mtest6postode.ode#################");
    omniout_str(ALWAYS, "diff  ( x1 , t , 1 )   =  4.0  *  x2  -   2.0  *\
          diff  ( x2 , t  , 1 )   -  2.0  *  x1 ; ");
    omniout_str(ALWAYS, "diff  ( x2 , t , 2 )   =  3.0  *  diff ( x2 , t \
        , 1 )   -  2.0  *  x2  -  diff ( x1 , t , 2 )   -  diff  ( x1 , \
        t , 1 )   +  x1 ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=64;");
    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, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "t_start := c(1.5);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "t_end := c(8.0);");
    omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);");
    omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);")
        ;
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_h := c(0.0001);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 0;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
    omniout_str(ALWAYS, "glob_look_poles:=false;");
    omniout_str(ALWAYS, "glob_h:=c(0.001);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := c(1.0);");
    omniout_str(ALWAYS, "c2 := c(0.0002);");
    omniout_str(ALWAYS, "c3 := c(0.0003);");
    omniout_str(ALWAYS,
        "return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x1p := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := c(1.0);");
    omniout_str(ALWAYS, "c2 := c(0.0002);");
    omniout_str(ALWAYS, "c3 := c(0.0003);");
    omniout_str(ALWAYS, "return(   c(-6.0) * c3 * exp(neg( c(t))));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := c(1.0);");
    omniout_str(ALWAYS, "c2 := c(0.0002);");
    omniout_str(ALWAYS, "c3 := c(0.0003);");
    omniout_str(ALWAYS,
        "return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := c(1.0);");
    omniout_str(ALWAYS, "c2 := c(0.0002);");
    omniout_str(ALWAYS, "c3 := c(0.0003);");
    omniout_str(ALWAYS, "return(   c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 \
        * exp(neg(c(t))));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    t_start := c(1.5);
    t_end := c(8.0);
    array_x1_init[1] := exact_soln_x1(t_start);
    array_x2_init[1] := exact_soln_x2(t_start);
    array_x2_init[2] := exact_soln_x2p(t_start);
    glob_look_poles := true;
    glob_max_h := c(0.0001);
    glob_type_given_pole := 0;
    glob_desired_digits_correct := 8;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000;
    glob_upper_ratio_limit := c(1.000001);
    glob_lower_ratio_limit := c(0.999999);
    glob_look_poles := false;
    glob_h := c(0.001);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(t_start, t_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(t_end) - c(t_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(t_start, t_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_t[1] := c(t_start);
            array_t[2] := c(glob_h);
            glob_next_display := c(t_start);
            order_diff := 2;
            term_no := 1;
            while term_no <= order_diff do
                array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] :=
                        array_x1_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 := 2;
            term_no := 1;
            while term_no <= order_diff do
                array_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] :=
                        array_x2_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 <= 3 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 3 + 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(t_start,
                    t_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_t[1] := c(t_start);
        array_t[2] := c(glob_h);
        glob_next_display := c(t_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 := 2;
        term_no := 1;
        while term_no <= order_diff do
            array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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 := 2;
        term_no := 1;
        while term_no <= order_diff do
            array_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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_t[1] < glob_check_sign*t_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 <= 3 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 3 + 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_t[1] := array_t[1] + glob_h;
            array_t[2] := glob_h;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_x1_higher_work[2, iii] := array_x1_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_x1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x1_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_x1[term_no] := array_x1_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_x1_higher[ord, term_no] :=
                        array_x1_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do;
            order_diff := 3;
            ord := 3;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_x2_higher_work[3, iii] := array_x2_higher[3, 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 := 3;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_x2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_x2_higher_work[2, iii] := array_x2_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 := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_x2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_x2_higher_work[1, iii] := array_x2_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 := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_x2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_x2_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_x2[term_no] := array_x2_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_x2_higher[ord, term_no] :=
                        array_x2_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  ( x1 , t , 1 )   =  4.0  *  x2  -   2.0 \
             *  diff  ( x2 , t  , 1 )   -  2.0  *  x1 ; ");
        omniout_str(INFO, "diff  ( x2 , t , 2 )   =  3.0  *  diff ( x2 , \
            t , 1 )   -  2.0  *  x2  -  diff ( x1 , t , 2 )   -  diff  (\
             x1 , t , 1 )   +  x1 ; ");
        omniout_int(INFO, "Iterations                      ", 32, glob_iter,
            4, " ");
        prog_report(t_start, t_end);
        if glob_html_log then
            logstart(html_log_file);
            logitem_str(html_log_file, "2016-08-26T16:49:28-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"mtest6.ode.txt\">mtest6</a>");
            logitem_str(html_log_file, "diff  ( x1 , t , 1 )   =  4.0  * \
                 x2  -   2.0  *  diff  ( x2 , t  , 1 )   -  2.0  *  x1 ;\
                 ");
            logitem_float(html_log_file, t_start);
            logitem_float(html_log_file, t_end);
            logitem_float(html_log_file, array_t[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.mtest6.mxt.txt\">mtest6 diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.mtest6.mxt.txt\\
                ">mtest6 maple results</a>");
            logitem_str(html_log_file, "???");
            logend(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logitem_str(html_log_file, "diff  ( x2 , t , 2 )   =  3.0  * \
                 diff ( x2 , t , 1 )   -  2.0  *  x2  -  diff ( x1 , t ,\
                 2 )   -  diff  ( x1 , t , 1 )   +  x1 ; ");
            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/mtest6postode.ode#################
diff  ( x1 , t , 1 )   =  4.0  *  x2  -   2.0  *  diff  ( x2 , t  , 1 )   -  2.0  *  x1 ; 
diff  ( x2 , t , 2 )   =  3.0  *  diff ( x2 , t , 1 )   -  2.0  *  x2  -  diff ( x1 , t , 2 )   -  diff  ( x1 , t , 1 )   +  x1 ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK




t_start := c(1.5);




t_end := c(8.0);
array_x1_init[0 + 1] := exact_soln_x1(t_start);


array_x2_init[0 + 1] := exact_soln_x2(t_start);
array_x2_init[1 + 1] := exact_soln_x2p(t_start);
glob_look_poles := true;
glob_max_h := c(0.0001);







glob_type_given_pole := 0;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=false;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));
end;
exact_soln_x1p := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return(   c(-6.0) * c3 * exp(neg( c(t))));
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return(   c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t))));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
t[1]                              = 1.5                                          
x1[1] (closed_form)               = 2.0004016342882671736920799048474            
x1[1] (numeric)                   = 2.0004016342882671736920799048474            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 64                                  
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0040840464326820624968656900721            
x2[1] (numeric)                   = 1.0040840464326820624968656900721            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 64                                  
h                                 = 0.001                                        
memory used=40.7MB, alloc=40.3MB, time=0.50
memory used=80.0MB, alloc=40.3MB, time=0.94
memory used=119.2MB, alloc=40.3MB, time=1.37
 
TOP MAIN SOLVE Loop
t[1]                              = 1.51                                         
x1[1] (closed_form)               = 2.0003976379603268807512153627942            
x1[1] (numeric)                   = 2.0003975977965633576779707691815            
absolute error                    = 4.0163763523073244593612711869169e-08        
relative error                    = 2.0077889895943676930955491127694e-06      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0041645313302264015612661796507            
x2[1] (numeric)                   = 1.0041645516812098525218220902821            
absolute error                    = 2.0350983450960555910631451293815e-08        
relative error                    = 2.0266582632630344574393138003430e-06      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.001                                        
memory used=158.7MB, alloc=40.3MB, time=1.81
memory used=198.0MB, alloc=40.3MB, time=2.25
memory used=237.3MB, alloc=40.3MB, time=2.69
 
TOP MAIN SOLVE Loop
t[1]                              = 1.52                                         
x1[1] (closed_form)               = 2.0003936813965139865699168717796            
x1[1] (numeric)                   = 2.0003935207374434844547166802246            
absolute error                    = 1.6065907050211520019155496336745e-07        
relative error                    = 8.0313726241104680045932219688359e-06      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0042466622131042155964806543355            
x2[1] (numeric)                   = 1.0042467447063251410512563962409            
absolute error                    = 8.2493220925454775741905370855987e-08        
relative error                    = 8.2144381484585369485624176934887e-06      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.001                                        
memory used=276.6MB, alloc=40.3MB, time=3.13
memory used=315.9MB, alloc=40.3MB, time=3.58
memory used=355.3MB, alloc=40.3MB, time=4.01
 
TOP MAIN SOLVE Loop
t[1]                              = 1.53                                         
x1[1] (closed_form)               = 2.0003897642011688127112650821416            
x1[1] (numeric)                   = 2.0003894027031982444744035693659            
absolute error                    = 3.6149797056823686151277578688807e-07        
relative error                    = 1.8071376740552192081864063528532e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0043304721326001823690307320913            
x2[1] (numeric)                   = 1.0043306602210869456859991268261            
absolute error                    = 1.8808848676331696839473476158754e-07        
relative error                    = 1.8727748682555550250003004154341e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
memory used=394.7MB, alloc=40.3MB, time=4.45
memory used=434.1MB, alloc=40.3MB, time=4.89
memory used=473.5MB, alloc=40.3MB, time=5.33
 
TOP MAIN SOLVE Loop
t[1]                              = 1.54                                         
x1[1] (closed_form)               = 2.000385885982568560317538699541             
x1[1] (numeric)                   = 2.0003852432820207815063900364881            
absolute error                    = 6.4270054777881114866305288347948e-07        
relative error                    = 3.2128828356690958276373831109667e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0044159948096675089551337275755            
x2[1] (numeric)                   = 1.0044163336460126841775630592965            
absolute error                    = 3.3883634517522242933172096989176e-07        
relative error                    = 3.3734662423354822487436458520861e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
memory used=512.9MB, alloc=40.3MB, time=5.77
memory used=552.3MB, alloc=40.3MB, time=6.21
memory used=591.6MB, alloc=40.3MB, time=6.65
 
TOP MAIN SOLVE Loop
memory used=631.0MB, alloc=40.3MB, time=7.09
t[1]                              = 1.55                                         
x1[1] (closed_form)               = 2.0003820463528881375038919589956            
x1[1] (numeric)                   = 2.0003810420579655116085107617261            
absolute error                    = 1.0042949226258953811972695533618e-06        
relative error                    = 5.0205155782963238114557796625660e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0045032646484363495982809213755            
x2[1] (numeric)                   = 1.0045038011234321744818968733111            
absolute error                    = 5.3647499582488361595193556284994e-07        
relative error                    = 5.3406993755529823267293647831272e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
memory used=670.5MB, alloc=40.3MB, time=7.53
memory used=709.8MB, alloc=40.3MB, time=7.97
memory used=749.2MB, alloc=40.3MB, time=8.41
 
TOP MAIN SOLVE Loop
t[1]                              = 1.56                                         
x1[1] (closed_form)               = 2.0003782449281613765259774864397            
x1[1] (numeric)                   = 2.0003767986109065282220598135761            
absolute error                    = 1.4463172548483039176728636704559e-06        
relative error                    = 7.2302188774315770207245047800034e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0045923167499953085613611752895            
x2[1] (numeric)                   = 1.0045930995321322319025866452685            
absolute error                    = 7.8278213692334122546997906531530e-07        
relative error                    = 7.7920378632374691716626623608419e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
memory used=788.6MB, alloc=40.3MB, time=8.85
memory used=828.0MB, alloc=40.3MB, time=9.29
memory used=867.3MB, alloc=40.3MB, time=9.73
 
TOP MAIN SOLVE Loop
t[1]                              = 1.57                                         
x1[1] (closed_form)               = 2.0003744813282426368431989909583            
x1[1] (numeric)                   = 2.0003725125164955892310286891526            
absolute error                    = 1.9688117470476121703018057234207e-06        
relative error                    = 9.8422158722017244193921396034876e-05      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0046831869264515426974489820757            
x2[1] (numeric)                   = 1.0046842665022977400761135452086            
absolute error                    = 1.0795758461973786645631329062760e-06        
relative error                    = 0.00010745435578553278662040422373441      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=906.8MB, alloc=40.3MB, time=10.17
memory used=946.1MB, alloc=40.3MB, time=10.61
memory used=985.5MB, alloc=40.3MB, time=11.05
 
TOP MAIN SOLVE Loop
t[1]                              = 1.58                                         
x1[1] (closed_form)               = 2.0003707551767687902378681154121            
x1[1] (numeric)                   = 2.0003681833461196817842699994942            
absolute error                    = 2.5718306491084535981159178443302e-06        
relative error                    = 0.00012856769888545916240209313771138      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0047759117152750898876826308634            
x2[1] (numeric)                   = 1.0047773404307551913333898719169            
absolute error                    = 1.4287154801014457072410535403718e-06        
relative error                    = 0.0001421924494251115198961103927321       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1024.9MB, alloc=40.3MB, time=11.49
memory used=1064.3MB, alloc=40.3MB, time=11.93
memory used=1103.6MB, alloc=40.3MB, time=12.36
 
TOP MAIN SOLVE Loop
t[1]                              = 1.59                                         
x1[1] (closed_form)               = 2.0003670661011215841887456819654            
x1[1] (numeric)                   = 2.000363810666858160637033653522             
absolute error                    = 3.2554342634235517120284434631313e-06        
relative error                    = 0.00016274184466397251616050385289192      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0048705283939331631696911430512            
x2[1] (numeric)                   = 1.004872360496524813153593652515             
absolute error                    = 1.8321025916499839025094637903683e-06        
relative error                    = 0.00018232225345271108223018135914189      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1143.1MB, alloc=40.3MB, time=12.80
memory used=1182.5MB, alloc=40.3MB, time=13.24
memory used=1221.8MB, alloc=40.3MB, time=13.68
 
TOP MAIN SOLVE Loop
t[1]                              = 1.6                                          
x1[1] (closed_form)               = 2.0003634137323903797352733226818            
x1[1] (numeric)                   = 2.0003593940414394557256739761002            
absolute error                    = 4.0196909509240095993465815963798e-06        
relative error                    = 0.00020094803390869084700321675510922      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0049670749948202663512576065259            
x2[1] (numeric)                   = 1.0049693666766875210567977673337            
absolute error                    = 2.2916818672547055401608077724313e-06        
relative error                    = 0.00022803551721000582756174556225165      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1261.3MB, alloc=40.3MB, time=14.12
memory used=1300.6MB, alloc=40.3MB, time=14.56
memory used=1339.9MB, alloc=40.3MB, time=14.99
 
TOP MAIN SOLVE Loop
memory used=1379.3MB, alloc=40.3MB, time=15.44
t[1]                              = 1.61                                         
x1[1] (closed_form)               = 2.0003597977053352601062508664658            
x1[1] (numeric)                   = 2.0003549330281973446462491537708            
absolute error                    = 4.8646771379154600017126950449201e-06        
relative error                    = 0.00024319010727449420070580786945042      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0050655903204901052177196549322            
x2[1] (numeric)                   = 1.0050683997625730644105159705681            
absolute error                    = 2.8094420829591927963156358992857e-06        
relative error                    = 0.0002795282327856167545192528612954       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1418.8MB, alloc=40.3MB, time=15.88
memory used=1458.2MB, alloc=40.3MB, time=16.32
 
TOP MAIN SOLVE Loop
memory used=1497.6MB, alloc=40.3MB, time=16.76
t[1]                              = 1.62                                         
x1[1] (closed_form)               = 2.0003562176583505064237916071803            
x1[1] (numeric)                   = 2.000350427181026785664224428383             
absolute error                    = 5.7904773237207595671787973422615e-06        
relative error                    = 0.00028947230861207242457229694549919      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0051661139591953891453303337642            
x2[1] (numeric)                   = 1.0051695013762758603025377798785            
absolute error                    = 3.3874170804711572074461142549917e-06        
relative error                    = 0.00033700072390310095963026011257578      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1537.1MB, alloc=40.3MB, time=17.19
memory used=1576.5MB, alloc=40.3MB, time=17.63
memory used=1615.9MB, alloc=40.3MB, time=18.07
 
TOP MAIN SOLVE Loop
t[1]                              = 1.63                                         
x1[1] (closed_form)               = 2.0003526732334284368300954114481            
x1[1] (numeric)                   = 2.0003458760493393068385432029891            
absolute error                    = 6.7971840891299915522084590087951e-06        
relative error                    = 0.00033979928540015020601015057933311      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0052686863007417410747157107045            
x2[1] (numeric)                   = 1.0052727139875051419097891995896            
absolute error                    = 4.0276867634008350734888850144776e-06        
relative error                    = 0.00040065773641295835820454560773561      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1655.4MB, alloc=40.3MB, time=18.51
memory used=1694.8MB, alloc=40.3MB, time=18.95
memory used=1734.1MB, alloc=40.3MB, time=19.39
 
TOP MAIN SOLVE Loop
t[1]                              = 1.64                                         
x1[1] (closed_form)               = 2.0003491640761236054209222092897            
x1[1] (numeric)                   = 2.000341279178017946798941291264             
absolute error                    = 7.8848981056586219809180256930573e-06        
relative error                    = 0.00039417608921792020355992979157994      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0053733485526620594279258956137            
x2[1] (numeric)                   = 1.0053780809307761817229690959371            
absolute error                    = 4.7323781141222950432003233273632e-06        
relative error                    = 0.00047070853041161655949572261587096      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1773.6MB, alloc=40.3MB, time=19.83
memory used=1812.9MB, alloc=40.3MB, time=20.26
memory used=1852.3MB, alloc=40.3MB, time=20.70
 
TOP MAIN SOLVE Loop
t[1]                              = 1.65                                         
x1[1] (closed_form)               = 2.0003456898355173574056293806241            
x1[1] (numeric)                   = 2.0003366361073717426705444923959            
absolute error                    = 9.0537281456147350848882281716775e-06        
relative error                    = 0.00045260817625773458055618060494798      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0054801427567178037196352378594            
x2[1] (numeric)                   = 1.0054856464229494866229655256529            
absolute error                    = 5.5036662316829033302877935218673e-06        
relative error                    = 0.00054736697401040069335050704345637      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=1891.7MB, alloc=40.3MB, time=21.14
memory used=1931.1MB, alloc=40.3MB, time=21.58
memory used=1970.5MB, alloc=40.3MB, time=22.02
 
TOP MAIN SOLVE Loop
t[1]                              = 1.66                                         
x1[1] (closed_form)               = 2.0003422501641827369492595039049            
x1[1] (numeric)                   = 2.0003319463730897605945040243487            
absolute error                    = 1.0303791092976354755479556200086e-05        
relative error                    = 0.00051510140787810921685832051358958      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0055891118057338063690720987107            
x2[1] (numeric)                   = 1.0055954555811250012022289313269            
absolute error                    = 6.3437753911948331568326162577931e-06        
relative error                    = 0.0006308516387775253301414072451749       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=2010.0MB, alloc=40.3MB, time=22.46
memory used=2049.4MB, alloc=40.3MB, time=22.90
memory used=2088.8MB, alloc=40.3MB, time=23.34
 
TOP MAIN SOLVE Loop
memory used=2128.1MB, alloc=40.3MB, time=23.77
t[1]                              = 1.67                                         
x1[1] (closed_form)               = 2.0003388447181497441874334321061            
x1[1] (numeric)                   = 2.0003272095061946642476835710136            
absolute error                    = 1.1635211955079939749861092509777e-05        
relative error                    = 0.00058166205119709884597700433727861      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0057002994607733466165511263743            
x2[1] (numeric)                   = 1.0057075544408984979381509655155            
absolute error                    = 7.2549801251513215998391411202142e-06        
relative error                    = 0.00072138589687615949100787119130657      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=2167.5MB, alloc=40.3MB, time=24.21
memory used=2207.0MB, alloc=40.3MB, time=24.65
 
TOP MAIN SOLVE Loop
memory used=2246.4MB, alloc=40.3MB, time=25.09
t[1]                              = 1.68                                         
x1[1] (closed_form)               = 2.0003354731568709379397212327797            
x1[1] (numeric)                   = 2.0003224250329958167182112189248            
absolute error                    = 1.3048123875121221510013854975284e-05        
relative error                    = 0.00065229677972610534380634443455792      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0058137503686603585404003230836            
x2[1] (numeric)                   = 1.005821989974987477912976819649             
absolute error                    = 8.2396063271193725764965654280187e-06        
relative error                    = 0.00081919801992161214927691036365054      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=2285.8MB, alloc=40.3MB, time=25.52
memory used=2325.2MB, alloc=40.3MB, time=25.96
memory used=2364.6MB, alloc=40.3MB, time=26.40
 
TOP MAIN SOLVE Loop
t[1]                              = 1.69                                         
x1[1] (closed_form)               = 2.0003321351431873806817336647786            
x1[1] (numeric)                   = 2.0003175924750419110470447568318            
absolute error                    = 1.4542668145469634688907946858848e-05        
relative error                    = 0.0007270126740441853814301617277507       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.005929510079855784011058223843             
x2[1] (numeric)                   = 1.0059388101122340537939230306695            
absolute error                    = 9.3000323782697828648068265492967e-06        
relative error                    = 0.00092452127958066357439385788642287      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
memory used=2404.0MB, alloc=40.3MB, time=26.84
memory used=2443.4MB, alloc=40.3MB, time=27.28
memory used=2482.9MB, alloc=40.3MB, time=27.71
 
TOP MAIN SOLVE Loop
t[1]                              = 1.7                                          
x1[1] (closed_form)               = 2.000328830343294922370403021508             
x1[1] (numeric)                   = 2.0003127113490731246985650199794            
absolute error                    = 1.6118994221797671838001528604182e-05        
relative error                    = 0.00080581722251292764847709743069627      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0060476250666952230646997208581            
x2[1] (numeric)                   = 1.0060580637569924377972124492985            
absolute error                    = 1.0438690297214732512728440420847e-05        
relative error                    = 0.0010375940499360263234672966752566       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=2522.4MB, alloc=40.3MB, time=28.16
memory used=2561.8MB, alloc=40.3MB, time=28.60
memory used=2601.1MB, alloc=40.3MB, time=29.04
 
TOP MAIN SOLVE Loop
t[1]                              = 1.71                                         
x1[1] (closed_form)               = 2.0003255584267108197508077718832            
x1[1] (numeric)                   = 2.0003077811669727931756044670206            
absolute error                    = 1.7777259738026575203304862564345e-05        
relative error                    = 0.00088871832203197385563208422751881      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0061681427419951786855908768716            
x2[1] (numeric)                   = 1.0061798008089088114211006193637            
absolute error                    = 1.1658066913632735509742492054225e-05        
relative error                    = 0.0011586599116388575566746021621947       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=2640.6MB, alloc=40.3MB, time=29.48
memory used=2679.8MB, alloc=40.3MB, time=29.92
memory used=2719.2MB, alloc=40.3MB, time=30.38
 
TOP MAIN SOLVE Loop
t[1]                              = 1.72                                         
x1[1] (closed_form)               = 2.0003223190662406878064438641218            
x1[1] (numeric)                   = 2.0003028014357185979462322203               
absolute error                    = 1.9517630522089860211643821747440e-05        
relative error                    = 0.0009757242788352617355487738372903       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 6                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0062911114780353404122764437494            
x2[1] (numeric)                   = 1.0063040721831015109073012611674            
absolute error                    = 1.2960705066170495024817417997620e-05        
relative error                    = 0.0012879677578721605113207515020162       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=2758.7MB, alloc=40.3MB, time=30.82
memory used=2798.1MB, alloc=40.3MB, time=31.26
memory used=2837.5MB, alloc=40.3MB, time=31.70
 
TOP MAIN SOLVE Loop
t[1]                              = 1.73                                         
x1[1] (closed_form)               = 2.0003191119379457800480601789497            
x1[1] (numeric)                   = 2.0002977716573332638010475711474            
absolute error                    = 2.1340280612516247012607802290520e-05        
relative error                    = 0.0010668438093280722809287390211973       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0064165806259245015866393892681            
x2[1] (numeric)                   = 1.0064309298307496227404163421071            
absolute error                    = 1.4349204825121153776952838937083e-05        
relative error                    = 0.0014257719021478062399043381090163       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=2876.9MB, alloc=40.3MB, time=32.14
memory used=2916.3MB, alloc=40.3MB, time=32.57
memory used=2955.7MB, alloc=40.3MB, time=33.00
 
TOP MAIN SOLVE Loop
memory used=2995.0MB, alloc=40.3MB, time=33.44
t[1]                              = 1.74                                         
x1[1] (closed_form)               = 2.0003159367211105943690597492498            
x1[1] (numeric)                   = 2.0002926913288347607106765938597            
absolute error                    = 2.3245392275833658383155390134989e-05        
relative error                    = 0.00116208604096496748731961499138         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0065446005353578585070014540056            
x2[1] (numeric)                   = 1.0065604267600982470852024288725            
absolute error                    = 1.5826224740388578200974866956486e-05        
relative error                    = 0.0015723321879597758778793438323863       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3034.5MB, alloc=40.3MB, time=33.88
memory used=3073.8MB, alloc=40.3MB, time=34.32
 
TOP MAIN SOLVE Loop
memory used=3113.2MB, alloc=40.3MB, time=34.75
t[1]                              = 1.75                                         
x1[1] (closed_form)               = 2.0003127930982108012280252910656            
x1[1] (numeric)                   = 2.0002875599421860052036161194432            
absolute error                    = 2.5233156024796024409171622401827e-05        
relative error                    = 0.0012614605131687089066181597877952       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0066752225747735962881348650477            
x2[1] (numeric)                   = 1.0066926170578888539572199959867            
absolute error                    = 1.7394483115257669085130939010568e-05        
relative error                    = 0.0017279141003160674863590223135889       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3152.6MB, alloc=40.3MB, time=35.19
memory used=3192.0MB, alloc=40.3MB, time=35.63
memory used=3231.4MB, alloc=40.3MB, time=36.06
 
TOP MAIN SOLVE Loop
t[1]                              = 1.76                                         
x1[1] (closed_form)               = 2.0003096807548814909511605719075            
x1[1] (numeric)                   = 2.0002823769842440562345209378538            
absolute error                    = 2.7303770637434716639634053724170e-05        
relative error                    = 0.001364977178290251365729206637363        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0068084991519168259349449636972            
x2[1] (numeric)                   = 1.0068275559112233271903989251387            
absolute error                    = 1.9056759306501255453961441487427e-05        
relative error                    = 0.0018927888791715285934504645699316       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3270.8MB, alloc=40.3MB, time=36.50
memory used=3310.2MB, alloc=40.3MB, time=36.94
memory used=3349.6MB, alloc=40.3MB, time=37.38
 
TOP MAIN SOLVE Loop
t[1]                              = 1.77                                         
x1[1] (closed_form)               = 2.0003065993798857369793513998311            
x1[1] (numeric)                   = 2.0002771419367088004624787205389            
absolute error                    = 2.9457443176936516872679292193039e-05        
relative error                    = 0.0014726464026099102637127643760911       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.006944483734819100066543734031             
x2[1] (numeric)                   = 1.0069652996298704649734435562762            
absolute error                    = 2.0815895051364906899822245209454e-05        
relative error                    = 0.0020672336347836645636035546822132       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3389.2MB, alloc=40.3MB, time=37.81
memory used=3428.5MB, alloc=40.3MB, time=38.25
memory used=3467.9MB, alloc=40.3MB, time=38.68
 
TOP MAIN SOLVE Loop
t[1]                              = 1.78                                         
x1[1] (closed_form)               = 2.0003035486650834719161447420031            
x1[1] (numeric)                   = 2.0002718542760711218077577283623            
absolute error                    = 3.1694389012350108387013640774879e-05        
relative error                    = 0.0015844789673798049304356358439411       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.00708323087320190094863760886              
x2[1] (numeric)                   = 1.0071059056690238829453027660458            
absolute error                    = 2.2674795821981996665157185735314e-05        
relative error                    = 0.0022515314650132324328551206862787       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3507.3MB, alloc=40.3MB, time=39.12
memory used=3546.7MB, alloc=40.3MB, time=39.56
memory used=3586.1MB, alloc=40.3MB, time=40.00
 
TOP MAIN SOLVE Loop
t[1]                              = 1.79                                         
x1[1] (closed_form)               = 2.0003005283054006732642248339551            
x1[1] (numeric)                   = 2.000266513473560550103939787503             
absolute error                    = 3.4014831840123160285046452142644e-05        
relative error                    = 0.0017004860699076846106188712843479       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0072247962203126640710885972565            
x2[1] (numeric)                   = 1.0072494326525204466390573133783            
absolute error                    = 2.4636432207782567968716121772302e-05        
relative error                    = 0.0024459715745911583803297061358752       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3625.7MB, alloc=40.3MB, time=40.44
memory used=3665.0MB, alloc=40.3MB, time=40.87
memory used=3704.4MB, alloc=40.3MB, time=41.31
 
TOP MAIN SOLVE Loop
memory used=3743.8MB, alloc=40.3MB, time=41.75
t[1]                              = 1.8                                          
x1[1] (closed_form)               = 2.0002975379987988557689342484968            
x1[1] (numeric)                   = 2.0002611189950923836102601203564            
absolute error                    = 3.6419003706472158674128140367172e-05        
relative error                    = 0.0018206793246822477296276494276664       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.007369236555202073512007994596             
x2[1] (numeric)                   = 1.0073959403965285445158733758359            
absolute error                    = 2.6703841326471003865381239982813e-05        
relative error                    = 0.0026508493963730130280688583589311       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3783.3MB, alloc=40.3MB, time=42.19
memory used=3822.7MB, alloc=40.3MB, time=42.62
 
TOP MAIN SOLVE Loop
memory used=3862.1MB, alloc=40.3MB, time=43.06
t[1]                              = 1.81                                         
x1[1] (closed_form)               = 2.0002945774462448673180488532632            
x1[1] (numeric)                   = 2.0002556703012142800963612007018            
absolute error                    = 3.8907145030587221687652561392896e-05        
relative error                    = 0.0019450707645400692017768026553992       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0075166098054515418290092603443            
x2[1] (numeric)                   = 1.0075454899337157010099446237175            
absolute error                    = 2.8880128264159180935363373235706e-05        
relative error                    = 0.0028664667146019406799264681406951       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=3901.6MB, alloc=40.3MB, time=43.50
memory used=3941.0MB, alloc=40.3MB, time=43.94
memory used=3980.4MB, alloc=40.3MB, time=44.38
 
TOP MAIN SOLVE Loop
t[1]                              = 1.82                                         
x1[1] (closed_form)               = 2.0002916463516809853773714642261            
x1[1] (numeric)                   = 2.0002501668470523111585246009433            
absolute error                    = 4.1479504628674218846863282844752e-05        
relative error                    = 0.0020736728418742546587157501948059       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0076669750703599672828816077678            
x2[1] (numeric)                   = 1.0076981435379052209868932377908            
absolute error                    = 3.1168467545253704011630022950378e-05        
relative error                    = 0.0030931317902005647744909468133294       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4019.8MB, alloc=40.3MB, time=44.82
memory used=4059.3MB, alloc=40.3MB, time=45.26
memory used=4098.7MB, alloc=40.3MB, time=45.70
 
TOP MAIN SOLVE Loop
t[1]                              = 1.83                                         
x1[1] (closed_form)               = 2.0002887444219953109717628348128            
x1[1] (numeric)                   = 2.0002446080822564743727674997227            
absolute error                    = 4.4136339738836598995335090045185e-05        
relative error                    = 0.0022064984298849446050052388698347       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0078203926445990449009751803877            
x2[1] (numeric)                   = 1.0078539647492317528787420653408            
absolute error                    = 3.3572104632707977766884953135021e-05        
relative error                    = 0.0033311594881119805246396436099013       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4138.3MB, alloc=40.3MB, time=46.13
memory used=4177.6MB, alloc=40.3MB, time=46.58
memory used=4216.9MB, alloc=40.3MB, time=47.01
 
TOP MAIN SOLVE Loop
t[1]                              = 1.84                                         
x1[1] (closed_form)               = 2.0002858713669924572509834119675            
x1[1] (numeric)                   = 2.0002389934509456578359737528654            
absolute error                    = 4.6877916046799415009659102120227e-05        
relative error                    = 0.0023435608238717956507007996465728       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0079769240423465953004941506983            
x2[1] (numeric)                   = 1.0080130183998058575766766519981            
absolute error                    = 3.6094357459262276182501299767359e-05        
relative error                    = 0.0035808714067094951728945451432534       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4256.4MB, alloc=40.3MB, time=47.45
memory used=4295.8MB, alloc=40.3MB, time=47.89
memory used=4335.2MB, alloc=40.3MB, time=48.32
 
TOP MAIN SOLVE Loop
t[1]                              = 1.85                                         
x1[1] (closed_form)               = 2.0002830268993645297091780170548            
x1[1] (numeric)                   = 2.0002333223916520515914677777294            
absolute error                    = 4.9704507712478117710239325420854e-05        
relative error                    = 0.002484873742568570127011648893638        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0081366320219075663906418406903            
x2[1] (numeric)                   = 1.0081753706398978740183414890049            
absolute error                    = 3.8738617990307627699648314578312e-05        
relative error                    = 0.003842596009294284668726135055202        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4374.7MB, alloc=40.3MB, time=48.76
memory used=4414.1MB, alloc=40.3MB, time=49.20
memory used=4453.5MB, alloc=40.3MB, time=49.64
 
TOP MAIN SOLVE Loop
t[1]                              = 1.86                                         
x1[1] (closed_form)               = 2.0002802107346623951560012168411            
x1[1] (numeric)                   = 2.0002275943372650003801274843818            
absolute error                    = 5.2616397397394775873732459309629e-05        
relative error                    = 0.0026304513295199695613080215818756       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0082995806108325581336326065058            
x2[1] (numeric)                   = 1.0083410889646515803809290493057            
absolute error                    = 4.1508353819022247296442799931263e-05        
relative error                    = 0.0041166687576996009671945210594487       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4493.0MB, alloc=40.3MB, time=50.08
memory used=4532.5MB, alloc=40.3MB, time=50.52
memory used=4571.9MB, alloc=40.3MB, time=50.96
 
TOP MAIN SOLVE Loop
memory used=4611.3MB, alloc=40.3MB, time=51.39
t[1]                              = 1.87                                         
x1[1] (closed_form)               = 2.0002774225912672365662565544882            
x1[1] (numeric)                   = 2.0002218087149742921022645753637            
absolute error                    = 5.5613876292944463991979124459825e-05        
relative error                    = 0.0027803081545008516723054654376184       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0084658351315439195460043218896            
x2[1] (numeric)                   = 1.0085102422413383619680405212846            
absolute error                    = 4.4407109794442422036199394997172e-05        
relative error                    = 0.0044034322480195845863833060005504       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4650.8MB, alloc=40.3MB, time=51.83
memory used=4690.1MB, alloc=40.3MB, time=52.27
 
TOP MAIN SOLVE Loop
memory used=4729.5MB, alloc=40.3MB, time=52.70
t[1]                              = 1.88                                         
x1[1] (closed_form)               = 2.0002746621903623909635109001106            
x1[1] (numeric)                   = 2.0002159649462128763190711423021            
absolute error                    = 5.8697244149514644439757808440168e-05        
relative error                    = 0.0029344592149779747455640501106995       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0086354622274796701430346141597            
x2[1] (numeric)                   = 1.0086829007371628133421222449109            
absolute error                    = 4.7438509683143199087630751253081e-05        
relative error                    = 0.0047032363484801105035964807174108       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4769.0MB, alloc=40.3MB, time=53.14
memory used=4808.5MB, alloc=40.3MB, time=53.58
memory used=4847.9MB, alloc=40.3MB, time=54.02
 
TOP MAIN SOLVE Loop
t[1]                              = 1.89                                         
x1[1] (closed_form)               = 2.0002719292559054675214488138234            
x1[1] (numeric)                   = 2.0002100624465990070654349692868            
absolute error                    = 6.1866809306460456013844536673493e-05        
relative error                    = 0.0030929199376144174639081413953068       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.008808529889765705151593377472             
x2[1] (numeric)                   = 1.0088591361476309230918255220545            
absolute error                    = 5.0606257865217940232144582546792e-05        
relative error                    = 0.0050164383394684198062998846332423       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=4887.5MB, alloc=40.3MB, time=54.45
memory used=4927.0MB, alloc=40.3MB, time=54.89
memory used=4966.4MB, alloc=40.3MB, time=55.33
 
TOP MAIN SOLVE Loop
t[1]                              = 1.9                                          
x1[1] (closed_form)               = 2.0002692235146007430947538217244            
x1[1] (numeric)                   = 2.0002041006258778041883566100593            
absolute error                    = 6.5122888722938906397211665117117e-05        
relative error                    = 0.0032557061798168264974045673197342       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0089851074844269551233038693665            
x2[1] (numeric)                   = 1.0090390216254922149232633222884            
absolute error                    = 5.3914141065259799959452921835906e-05        
relative error                    = 0.0053434030557375625601357733430891       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5005.9MB, alloc=40.3MB, time=55.77
memory used=5045.2MB, alloc=40.3MB, time=56.20
memory used=5084.6MB, alloc=40.3MB, time=56.64
 
TOP MAIN SOLVE Loop
t[1]                              = 1.91                                         
x1[1] (closed_form)               = 2.0002665446958718324190466891352            
x1[1] (numeric)                   = 2.0001980788878622273670533816746            
absolute error                    = 6.8465808009605051993307460581662e-05        
relative error                    = 0.0034228342313256484035417271683919       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0091652657801483861549589201677            
x2[1] (numeric)                   = 1.0092226318102674486159941992777            
absolute error                    = 5.7366030119062461035279110020515e-05        
relative error                    = 0.0056845030308008968560324146522446       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5124.2MB, alloc=40.3MB, time=57.08
memory used=5163.6MB, alloc=40.3MB, time=57.52
memory used=5202.9MB, alloc=40.3MB, time=57.95
 
TOP MAIN SOLVE Loop
t[1]                              = 1.92                                         
x1[1] (closed_form)               = 2.0002638925318346302468779100226            
x1[1] (numeric)                   = 2.0001919966303734569121030965547            
absolute error                    = 7.1895901461173334774813467886681e-05        
relative error                    = 0.0035943208158485066506394245840365       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0093490769765969468529789676193            
x2[1] (numeric)                   = 1.0094100428583737188806214459623            
absolute error                    = 6.0965881776772027642478343017980e-05        
relative error                    = 0.0060401186435310526190501525688333       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5242.4MB, alloc=40.3MB, time=58.39
memory used=5281.8MB, alloc=40.3MB, time=58.82
memory used=5321.2MB, alloc=40.3MB, time=59.26
 
TOP MAIN SOLVE Loop
memory used=5360.6MB, alloc=40.3MB, time=59.70
t[1]                              = 1.93                                         
x1[1] (closed_form)               = 2.0002612667572705227139654635506            
x1[1] (numeric)                   = 2.0001858532451806753816577644732            
absolute error                    = 7.5413512089847332307699077412035e-05        
relative error                    = 0.0037701830927368888567008270951326       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0095366147333157925512782662579            
x2[1] (numeric)                   = 1.0096013324738590293889821295598            
absolute error                    = 6.4717740543236837703863301852782e-05        
relative error                    = 0.006410638266976874093720221190642        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5400.1MB, alloc=40.3MB, time=60.14
memory used=5439.5MB, alloc=40.3MB, time=60.58
 
TOP MAIN SOLVE Loop
memory used=5478.8MB, alloc=40.3MB, time=61.01
t[1]                              = 1.94                                         
x1[1] (closed_form)               = 2.0002586671095998652567921376056            
x1[1] (numeric)                   = 2.0001796481179402439928387036892            
absolute error                    = 7.9018991659621263953433916382398e-05        
relative error                    = 0.003950438658706313632307814418205        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.009727954199202346196975376248             
x2[1] (numeric)                   = 1.0097965799397586633157396807076            
absolute error                    = 6.8625740556317118764304459643353e-05        
relative error                    = 0.0067964584194108994762500235745468       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5518.2MB, alloc=40.3MB, time=61.45
memory used=5557.6MB, alloc=40.3MB, time=61.88
memory used=5597.1MB, alloc=40.3MB, time=62.32
 
TOP MAIN SOLVE Loop
t[1]                              = 1.95                                         
x1[1] (closed_form)               = 2.000256093328855724429332077216             
x1[1] (numeric)                   = 2.000173380628134267745903514247             
absolute error                    = 8.2712700721456683428562968907922e-05        
relative error                    = 0.004135105549600150730174922635166        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0099231720425819888475076435109            
x2[1] (numeric)                   = 1.0099958661500859207294425192926            
absolute error                    = 7.2694107503931881934875781715085e-05        
relative error                    = 0.0071979839176189173750169087666225       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5636.5MB, alloc=40.3MB, time=62.76
memory used=5675.9MB, alloc=40.3MB, time=63.19
memory used=5715.2MB, alloc=40.3MB, time=63.63
 
TOP MAIN SOLVE Loop
t[1]                              = 1.96                                         
x1[1] (closed_form)               = 2.00025354515765788099306634863              
x1[1] (numeric)                   = 2.0001670501490085431176461342395            
absolute error                    = 8.6495008649337875420214390472590e-05        
relative error                    = 0.0043242022421972725360330011493865       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0101223464818894109693002723608            
x2[1] (numeric)                   = 1.010199273642470047201400037825             
absolute error                    = 7.6927160580636232099765464200371e-05        
relative error                    = 0.0076156280324420549976247662894483       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5754.8MB, alloc=40.3MB, time=64.07
memory used=5794.1MB, alloc=40.3MB, time=64.50
memory used=5833.4MB, alloc=40.3MB, time=64.94
 
TOP MAIN SOLVE Loop
t[1]                              = 1.97                                         
x1[1] (closed_form)               = 2.0002510223411870916805748564442            
x1[1] (numeric)                   = 2.0001606560475098821187476086125            
absolute error                    = 9.0366293677209561827247831651965e-05        
relative error                    = 0.004517747656063719286031525301667        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.010325557316969898787499256969             
x2[1] (numeric)                   = 1.0104068866314544371636991435554            
absolute error                    = 8.1329314484538376199886586396973e-05        
relative error                    = 0.0080498126465806994528434390652942       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5872.9MB, alloc=40.3MB, time=65.38
memory used=5912.3MB, alloc=40.3MB, time=65.81
memory used=5951.6MB, alloc=40.3MB, time=66.25
 
TOP MAIN SOLVE Loop
t[1]                              = 1.98                                         
x1[1] (closed_form)               = 2.0002485246271596070588595243716            
x1[1] (numeric)                   = 2.0001541976842228064474310754613            
absolute error                    = 9.4326942936800611428448910365226e-05        
relative error                    = 0.0047157611554485647652503083616695       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0105328859610130779056295566856            
x2[1] (numeric)                   = 1.0106187910424684599470359129778            
absolute error                    = 8.5905081455382041406356292164843e-05        
relative error                    = 0.0085009684146683285020226517928054       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=5991.1MB, alloc=40.3MB, time=66.68
memory used=6030.5MB, alloc=40.3MB, time=67.12
memory used=6069.9MB, alloc=40.3MB, time=67.56
 
TOP MAIN SOLVE Loop
memory used=6109.3MB, alloc=40.3MB, time=67.99
t[1]                              = 1.99                                         
x1[1] (closed_form)               = 2.0002460517658019429441638367841            
x1[1] (numeric)                   = 2.0001476744133056054087835802689            
absolute error                    = 9.8377352496337535380256515231557e-05        
relative error                    = 0.004918262551224173630621335614278        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0107444154731318893925752262717            
x2[1] (numeric)                   = 1.0108350745464865261705590678585            
absolute error                    = 9.0659073354636777983841586799443e-05        
relative error                    = 0.0089695349256220275944358466340873       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=6148.7MB, alloc=40.3MB, time=68.43
memory used=6188.1MB, alloc=40.3MB, time=68.86
 
TOP MAIN SOLVE Loop
memory used=6227.5MB, alloc=40.3MB, time=69.31
t[1]                              = 2                                            
x1[1] (closed_form)               = 2.000243603509825902845409199091             
x1[1] (numeric)                   = 2.0001410855824257512054833650244            
absolute error                    = 0.00010251792740015163992583406654697        
relative error                    = 0.0051252721028710459100059857560925       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0109602305915998316231902520891            
x2[1] (numeric)                   = 1.0110558265953882873475434930148            
absolute error                    = 9.5596003788455724353240925689345e-05        
relative error                    = 0.0094559608672750930849264678124492       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=6266.9MB, alloc=40.3MB, time=69.75
memory used=6306.3MB, alloc=40.3MB, time=70.19
memory used=6345.6MB, alloc=40.3MB, time=70.62
 
TOP MAIN SOLVE Loop
t[1]                              = 2.01                                         
x1[1] (closed_form)               = 2.0002411796144038489384716458907            
x1[1] (numeric)                   = 2.0001344305326946651414078841781            
absolute error                    = 0.00010674908170918379706376171261858        
relative error                    = 0.0053368105205074486577806158348608       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0111804177677597644613753374967            
x2[1] (numeric)                   = 1.0112811384580341423225418326013            
absolute error                    = 0.00010072069027437786116649510466863        
relative error                    = 0.0099607041932956640826000072445002       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
memory used=6385.0MB, alloc=40.3MB, time=71.06
memory used=6424.3MB, alloc=40.3MB, time=71.50
memory used=6463.7MB, alloc=40.3MB, time=71.93
 
TOP MAIN SOLVE Loop
t[1]                              = 2.02                                         
x1[1] (closed_form)               = 2.0002387798371442190983757169765            
x1[1] (numeric)                   = 2.0001277085986018282146885465578            
absolute error                    = 0.00011107123854239088368717041874667        
relative error                    = 0.0055528989669640391964852282584742       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.01140506520061784099592009124              
x2[1] (numeric)                   = 1.011511103257070510580033718708             
absolute error                    = 0.00010603805645266958411362746806153        
relative error                    = 0.010484232292393784249402587082545        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=6503.2MB, alloc=40.3MB, time=72.37
memory used=6542.5MB, alloc=40.3MB, time=72.80
memory used=6581.9MB, alloc=40.3MB, time=73.24
 
TOP MAIN SOLVE Loop
t[1]                              = 2.03                                         
x1[1] (closed_form)               = 2.0002364039380672875410883180418            
x1[1] (numeric)                   = 2.0001209191079482295112165806985            
absolute error                    = 0.00011548483011905802987173734323066        
relative error                    = 0.0057735590599036888443188707863678       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.011634262872136406087262926132             
x2[1] (numeric)                   = 1.011745816006479624676108181656             
absolute error                    = 0.0001115531343432185888452555240298         
relative error                    = 0.011027022159817666800432629716684        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=6621.3MB, alloc=40.3MB, time=73.68
memory used=6660.7MB, alloc=40.3MB, time=74.12
memory used=6700.0MB, alloc=40.3MB, time=74.55
 
TOP MAIN SOLVE Loop
t[1]                              = 2.04                                         
x1[1] (closed_form)               = 2.0002340516795811666509565459387            
x1[1] (numeric)                   = 2.0001140613817791457433839143144            
absolute error                    = 0.00011999029780202090757263162437762        
relative error                    = 0.0059988128739867205199570364328882       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0118681025832399805671840366238            
x2[1] (numeric)                   = 1.0119853736498888921602932720652            
absolute error                    = 0.00011727106664891159310923544135706        
relative error                    = 0.011589560571138217605984665948608        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=6739.4MB, alloc=40.3MB, time=74.99
memory used=6778.8MB, alloc=40.3MB, time=75.42
memory used=6818.2MB, alloc=40.3MB, time=75.86
 
TOP MAIN SOLVE Loop
t[1]                              = 2.05                                         
x1[1] (closed_form)               = 2.0002317228264580475939522237301            
x1[1] (numeric)                   = 2.0001071347343162452119569247631            
absolute error                    = 0.00012458809214180238199529896706803        
relative error                    = 0.0062286829430817781297584971044882       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0121066779905487351651561478966            
x2[1] (numeric)                   = 1.0122298750996551814935678973331            
absolute error                    = 0.00012319710910644632841174943640652        
relative error                    = 0.012172344258319059219191524823935        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=6857.6MB, alloc=40.3MB, time=76.30
memory used=6896.9MB, alloc=40.3MB, time=76.73
memory used=6936.3MB, alloc=40.3MB, time=77.16
 
TOP MAIN SOLVE Loop
memory used=6975.6MB, alloc=40.3MB, time=77.60
t[1]                              = 2.06                                         
x1[1] (closed_form)               = 2.0002294171458106773407646704313            
x1[1] (numeric)                   = 2.0001001384728890094014226676586            
absolute error                    = 0.00012927867292166793934200277274863        
relative error                    = 0.0064631922625225501783620028243574       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0123500846438541492287285967562            
x2[1] (numeric)                   = 1.0124794212767396967525440632167            
absolute error                    = 0.00012933663288554752381546646049335        
relative error                    = 0.012775880088067389321020457305092        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7015.0MB, alloc=40.3MB, time=78.04
memory used=7054.4MB, alloc=40.3MB, time=78.48
memory used=7093.7MB, alloc=40.3MB, time=78.91
 
TOP MAIN SOLVE Loop
t[1]                              = 2.07                                         
x1[1] (closed_form)               = 2.000227134407069069747424412174             
x1[1] (numeric)                   = 2.0000930718978654653509099693921            
absolute error                    = 0.00013406250920360439651444278190811        
relative error                    = 0.0067023642914105746023898404929733       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0125984200243518461773128622039            
x2[1] (numeric)                   = 1.0127341151513894224629412356737            
absolute error                    = 0.00013569512703757628562837346977081        
relative error                    = 0.013400685242458996861897531864953        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7133.3MB, alloc=40.3MB, time=79.35
memory used=7172.6MB, alloc=40.3MB, time=79.78
memory used=7212.0MB, alloc=40.3MB, time=80.22
 
TOP MAIN SOLVE Loop
t[1]                              = 2.08                                         
x1[1] (closed_form)               = 2.0002248743819574483645464896661            
x1[1] (numeric)                   = 2.000085934302582221873864752456             
absolute error                    = 0.00013894007937522649068173721003771        
relative error                    = 0.0069462229549643564089205978468336       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.012851783583646900497823484353             
x2[1] (numeric)                   = 1.0129940617846414428544445811979            
absolute error                    = 0.00014227820099454235662109684483729        
relative error                    = 0.01404728740182864436901551300963         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7251.5MB, alloc=40.3MB, time=80.66
memory used=7290.8MB, alloc=40.3MB, time=81.09
memory used=7330.3MB, alloc=40.3MB, time=81.53
 
TOP MAIN SOLVE Loop
t[1]                              = 2.09                                         
x1[1] (closed_form)               = 2.0002226368444714186694550718867            
x1[1] (numeric)                   = 2.0000787249732738026300432577564            
absolute error                    = 0.00014391187119761603941181413022651        
relative error                    = 0.0071947926469150343060153781041807       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0131102767835472200779578966481            
x2[1] (numeric)                   = 1.0132593683706667693030603162941            
absolute error                    = 0.00014909158711954922510241964599011        
relative error                    = 0.014716224929914801669986497078532        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7369.6MB, alloc=40.3MB, time=81.97
memory used=7409.1MB, alloc=40.3MB, time=82.41
memory used=7448.4MB, alloc=40.3MB, time=82.84
 
TOP MAIN SOLVE Loop
t[1]                              = 2.1                                          
x1[1] (closed_form)               = 2.0002204215708553674383935652769            
x1[1] (numeric)                   = 2.0000714431890012689830714739357            
absolute error                    = 0.00014897838185409845532209134119253        
relative error                    = 0.0074480982319488371423304907997978       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0133740031366609229020699411436            
x2[1] (numeric)                   = 1.0135301442799706458579796284734            
absolute error                    = 0.00015614114330972295590968732982252        
relative error                    = 0.015408047061245380753526605590807        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7487.8MB, alloc=40.3MB, time=83.28
memory used=7527.2MB, alloc=40.3MB, time=83.72
memory used=7566.6MB, alloc=40.3MB, time=84.15
 
TOP MAIN SOLVE Loop
t[1]                              = 2.11                                         
x1[1] (closed_form)               = 2.0002182283395800869987386055161            
x1[1] (numeric)                   = 2.0000640882215801255057970484964            
absolute error                    = 0.00015414011799996149294155701976942        
relative error                    = 0.0077061650481965756271782511455276       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0136430682478139487316994643526            
x2[1] (numeric)                   = 1.013806501103466645672226106554             
absolute error                    = 0.00016343285565269694052664220143987        
relative error                    = 0.016123314090748669650246492642538        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7606.1MB, alloc=40.3MB, time=84.59
memory used=7645.6MB, alloc=40.3MB, time=85.02
memory used=7685.0MB, alloc=40.3MB, time=85.46
 
TOP MAIN SOLVE Loop
memory used=7724.4MB, alloc=40.3MB, time=85.90
t[1]                              = 2.12                                         
x1[1] (closed_form)               = 2.0002160569313206221236245067648            
x1[1] (numeric)                   = 2.0000566593355075009239241369717            
absolute error                    = 0.00015939759581312119970036979307321        
relative error                    = 0.0079690189097704194817615564257057       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.013917579856304474486506397187             
x2[1] (numeric)                   = 1.014088552697442221007195776104             
absolute error                    = 0.00017097284113774652068937891696715        
relative error                    = 0.016862597565571090983199233528527        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7763.8MB, alloc=40.3MB, time=86.34
memory used=7803.2MB, alloc=40.3MB, time=86.77
 
TOP MAIN SOLVE Loop
memory used=7842.5MB, alloc=40.3MB, time=87.21
t[1]                              = 2.13                                         
x1[1] (closed_form)               = 2.0002139071289343373536491698366            
x1[1] (numeric)                   = 2.0000491557878885972159648708797            
absolute error                    = 0.00016475134104574013768429895692034        
relative error                    = 0.0082366861093482148771656735111069       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0141976478790110367628628313787            
x2[1] (numeric)                   = 1.0143764152294337264005809574416            
absolute error                    = 0.00017876735042268963771812606287947        
relative error                    = 0.017626480479080714029122081680471        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=7881.9MB, alloc=40.3MB, time=87.65
memory used=7921.4MB, alloc=40.3MB, time=88.09
memory used=7960.8MB, alloc=40.3MB, time=88.53
 
TOP MAIN SOLVE Loop
t[1]                              = 2.14                                         
x1[1] (closed_form)               = 2.0002117787174392025523753425972            
x1[1] (numeric)                   = 2.0000415768283623995143561469845            
absolute error                    = 0.00017020188907680303801919561269804        
relative error                    = 0.0085091934208056017455032061736697       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0144833844543716064105727682695            
x2[1] (numeric)                   = 1.0146702072250292987179043674475            
absolute error                    = 0.00018682277065769230733159917800949        
relative error                    = 0.018415557467032623477565095544817        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8000.2MB, alloc=40.3MB, time=88.96
memory used=8039.6MB, alloc=40.3MB, time=89.40
memory used=8079.0MB, alloc=40.3MB, time=89.84
 
TOP MAIN SOLVE Loop
t[1]                              = 2.15                                         
x1[1] (closed_form)               = 2.0002096714839922945241646872855            
x1[1] (numeric)                   = 2.0000339216990266393786699409244            
absolute error                    = 0.00017574978496565514549474636116503        
relative error                    = 0.0087865681018961953078393360483587       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0147749039872512084697131714484            
x2[1] (numeric)                   = 1.0149700496156183492956682563893            
absolute error                    = 0.00019514562836714082595508494090268        
relative error                    = 0.019230435005869289217695367664269        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8118.5MB, alloc=40.3MB, time=90.28
memory used=8158.0MB, alloc=40.3MB, time=90.71
memory used=8197.3MB, alloc=40.3MB, time=91.15
 
TOP MAIN SOLVE Loop
t[1]                              = 2.16                                         
x1[1] (closed_form)               = 2.0002075852178685125444885227851            
x1[1] (numeric)                   = 2.0000261896343620039371819354207            
absolute error                    = 0.00018139558350650860730658736445615        
relative error                    = 0.0090688378969801009466407929899216       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0150723231947160361887778658907            
x2[1] (numeric)                   = 1.0152760657871068023775782371978            
absolute error                    = 0.0002037425923907661888003713070698         
relative error                    = 0.020071731613125984975638287288097        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8236.8MB, alloc=40.3MB, time=91.58
memory used=8276.2MB, alloc=40.3MB, time=92.02
memory used=8315.6MB, alloc=40.3MB, time=92.46
 
TOP MAIN SOLVE Loop
t[1]                              = 2.17                                         
x1[1] (closed_form)               = 2.0002055197104395056742505358041            
x1[1] (numeric)                   = 2.0000183798611555833176494606744            
absolute error                    = 0.00018713984928392235660107512972245        
relative error                    = 0.0093560310398010363619631230800434       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0153757611527323704443290268073            
x2[1] (numeric)                   = 1.0155883816296176006960688623661            
absolute error                    = 0.00021262047688523025173983555881907        
relative error                    = 0.020940078049908064937677623309621        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8355.0MB, alloc=40.3MB, time=92.90
memory used=8394.4MB, alloc=40.3MB, time=93.33
memory used=8433.8MB, alloc=40.3MB, time=93.77
 
TOP MAIN SOLVE Loop
memory used=8473.2MB, alloc=40.3MB, time=94.21
t[1]                              = 2.18                                         
x1[1] (closed_form)               = 2.0002034747551528097508353326035            
x1[1] (numeric)                   = 2.0000104915984235487119780307216            
absolute error                    = 0.00019298315672926103885730188188337        
relative error                    = 0.0096481762563123397898891106446572       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0156853393438089858062628657252            
x2[1] (numeric)                   = 1.0159071255881963935141373328596            
absolute error                    = 0.00022178624438740770787446713437552        
relative error                    = 0.021836117525403522012530857380677        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8512.7MB, alloc=40.3MB, time=94.65
memory used=8552.1MB, alloc=40.3MB, time=95.08
 
TOP MAIN SOLVE Loop
memory used=8591.4MB, alloc=40.3MB, time=95.52
t[1]                              = 2.19                                         
x1[1] (closed_form)               = 2.0002014501475111919695645502313            
x1[1] (numeric)                   = 2.0000025240573330533425185072421            
absolute error                    = 0.00019892609017813862704604298917731        
relative error                    = 0.0099453027675521479293320542375023       % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 5                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.01600118170560210188955008355              
x2[1] (numeric)                   = 1.0162324287145427248751076341307            
absolute error                    = 0.00023124700894062298555755058073736        
relative error                    = 0.02276050590339071441517650856992         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8630.9MB, alloc=40.3MB, time=95.96
memory used=8670.1MB, alloc=40.3MB, time=96.40
memory used=8709.6MB, alloc=40.3MB, time=96.84
 
TOP MAIN SOLVE Loop
t[1]                              = 2.2                                          
x1[1] (closed_form)               = 2.0001994456850522009900014599665            
x1[1] (numeric)                   = 1.9999944764411233485200264377914            
absolute error                    = 0.00020496924392885246997502217511804        
relative error                    = 0.010247440292568032119699374583104        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.016323414680502323653880405673             
x2[1] (numeric)                   = 1.0165644247197874503714129219367            
absolute error                    = 0.00024101003928512671753251626368501        
relative error                    = 0.023713911910697454024313738790346        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8749.0MB, alloc=40.3MB, time=97.27
memory used=8788.4MB, alloc=40.3MB, time=97.71
memory used=8827.7MB, alloc=40.3MB, time=98.14
 
TOP MAIN SOLVE Loop
t[1]                              = 2.21                                         
x1[1] (closed_form)               = 2.0001974611673279205220976517994            
x1[1] (numeric)                   = 1.9999863479450261069048236275535            
absolute error                    = 0.00021111322230181361727402424598293        
relative error                    = 0.010554619051391386237556167466246        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0166521672662234071110363657655            
x2[1] (numeric)                   = 1.0169032500283375296020649568025            
absolute error                    = 0.00025108276211412249102859103702223        
relative error                    = 0.024697017347563795631107231808946        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8867.2MB, alloc=40.3MB, time=98.60
memory used=8906.5MB, alloc=40.3MB, time=99.03
memory used=8945.9MB, alloc=40.3MB, time=99.47
 
TOP MAIN SOLVE Loop
t[1]                              = 2.22                                         
x1[1] (closed_form)               = 2.000195496395884924367523542548             
x1[1] (numeric)                   = 1.999978137756184945003421663267             
absolute error                    = 0.00021735863969997936410187928101118        
relative error                    = 0.010866869768061864735819317473013        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0169875710674130876331680307776            
x2[1] (numeric)                   = 1.0172490438328097688097601505396            
absolute error                    = 0.00026147276539668117659211976199243        
relative error                    = 0.025710517299856845844758749715085        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=8985.4MB, alloc=40.3MB, time=99.91
memory used=9024.9MB, alloc=40.3MB, time=100.35
memory used=9064.3MB, alloc=40.3MB, time=100.78
 
TOP MAIN SOLVE Loop
t[1]                              = 2.23                                         
x1[1] (closed_form)               = 2.0001935511742444309116701364738            
x1[1] (numeric)                   = 1.9999698450535741368527899868683            
absolute error                    = 0.00022370612067029405888014960552197        
relative error                    = 0.011184223673702174234638304005793        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0173297603483066168837352241901            
x2[1] (numeric)                   = 1.0176019481500755241435222288628            
absolute error                    = 0.00027218780176890725978700467267503        
relative error                    = 0.026755120353081719072291177486547        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9103.8MB, alloc=40.3MB, time=101.22
memory used=9143.3MB, alloc=40.3MB, time=101.66
memory used=9182.6MB, alloc=40.3MB, time=102.10
 
TOP MAIN SOLVE Loop
t[1]                              = 2.24                                         
x1[1] (closed_form)               = 2.0001916253078826550817547005949            
x1[1] (numeric)                   = 1.9999614690079165107635692068355            
absolute error                    = 0.00023015629996614431818549375943042        
relative error                    = 0.011506712509643527089469683127542        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0176788720864440714802628894828            
x2[1] (numeric)                   = 1.0179621078784388207558254600391            
absolute error                    = 0.00028323579199474927556257055628409        
relative error                    = 0.027831548808128400607771268282536        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9222.2MB, alloc=40.3MB, time=102.54
memory used=9261.6MB, alloc=40.3MB, time=102.98
memory used=9301.0MB, alloc=40.3MB, time=103.42
 
TOP MAIN SOLVE Loop
memory used=9340.5MB, alloc=40.3MB, time=103.86
t[1]                              = 2.25                                         
x1[1] (closed_form)               = 2.0001897186042113558062097918406            
x1[1] (numeric)                   = 1.9999530087816005209118355489572            
absolute error                    = 0.00023670982261083489437424288345551        
relative error                    = 0.011834368530602070409422466908235        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0180350460274729220110580566559            
x2[1] (numeric)                   = 1.0183296708559707966922273968518            
absolute error                    = 0.00029462482849787468116934019591568        
relative error                    = 0.028940538898689728358145663153712        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9379.8MB, alloc=40.3MB, time=104.30
memory used=9419.2MB, alloc=40.3MB, time=104.73
 
TOP MAIN SOLVE Loop
memory used=9458.6MB, alloc=40.3MB, time=105.17
t[1]                              = 2.26                                         
x1[1] (closed_form)               = 2.0001878308725585770300853644456            
x1[1] (numeric)                   = 1.9999444635285964854865065157322            
absolute error                    = 0.00024336734396209154357884871333449        
relative error                    = 0.012167224507906609078238567166782        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0183984247410577851368733188052            
x2[1] (numeric)                   = 1.0187047879200238434482085762348            
absolute error                    = 0.00030636317896605831133525742963294        
relative error                    = 0.030082841010280969959378321710148        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9498.0MB, alloc=40.3MB, time=105.61
memory used=9537.4MB, alloc=40.3MB, time=106.05
memory used=9576.8MB, alloc=40.3MB, time=106.48
 
TOP MAIN SOLVE Loop
t[1]                              = 2.27                                         
x1[1] (closed_form)               = 2.0001859619241495803605494485876            
x1[1] (numeric)                   = 1.9999358323943719830161326931916            
absolute error                    = 0.00025012952977759734441675539601517        
relative error                    = 0.012505313732777946441776762472396        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0187691536779197243868201384209            
x2[1] (numeric)                   = 1.0190876129679492873373785910926            
absolute error                    = 0.00031845929002956295055845267166751        
relative error                    = 0.031259219900786545817369333790944        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9616.4MB, alloc=40.3MB, time=106.92
memory used=9655.7MB, alloc=40.3MB, time=107.36
memory used=9695.1MB, alloc=40.3MB, time=107.81
 
TOP MAIN SOLVE Loop
t[1]                              = 2.28                                         
x1[1] (closed_form)               = 2.0001841115720879674357360608217            
x1[1] (numeric)                   = 1.9999271145158063984146378810257            
absolute error                    = 0.00025699705628156902109817979597734        
relative error                    = 0.01284867001966017147009429133965         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0191473812280279170827919489146            
x2[1] (numeric)                   = 1.0194783030190429376264149807436            
absolute error                    = 0.00033092179101502054362303182897607        
relative error                    = 0.032470454922454325729759427433231        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9734.6MB, alloc=40.3MB, time=108.25
memory used=9774.0MB, alloc=40.3MB, time=108.68
memory used=9813.4MB, alloc=40.3MB, time=109.12
 
TOP MAIN SOLVE Loop
t[1]                              = 2.29                                         
x1[1] (closed_form)               = 2.0001822796313369901291614996888            
x1[1] (numeric)                   = 1.9999183090211046102005409081649            
absolute error                    = 0.00026397061023237992862059152390502        
relative error                    = 0.013197327709604226379674589336676        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0195332587799669657789869447521            
x2[1] (numeric)                   = 1.0198770182777433189378222709781            
absolute error                    = 0.00034375949777635315883532622601574        
relative error                    = 0.03371734024525260196887586684567         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9853.0MB, alloc=40.3MB, time=109.56
memory used=9892.4MB, alloc=40.3MB, time=110.00
memory used=9931.8MB, alloc=40.3MB, time=110.44
 
TOP MAIN SOLVE Loop
t[1]                              = 2.3                                          
x1[1] (closed_form)               = 2.0001804659187010467207138932488            
x1[1] (numeric)                   = 1.9999094150297098102583091284376            
absolute error                    = 0.00027105088899123646240476481121628        
relative error                    = 0.013551321673704093912543753169577        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0199269407815036028672097929057            
x2[1] (numeric)                   = 1.0202839221981079068984963388527            
absolute error                    = 0.00035698141660430403128654594704521        
relative error                    = 0.035000685081499309778641873790407        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=9971.3MB, alloc=40.3MB, time=110.87
memory used=10010.7MB, alloc=40.3MB, time=111.31
memory used=10050.1MB, alloc=40.3MB, time=111.75
 
TOP MAIN SOLVE Loop
memory used=10089.5MB, alloc=40.3MB, time=112.19
t[1]                              = 2.31                                         
x1[1] (closed_form)               = 2.000178670252807362183817677582             
x1[1] (numeric)                   = 1.9999004316522154474237470812143            
absolute error                    = 0.00027823860059191476007059636776969        
relative error                    = 0.013910687316585948714466420142403        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0203285848013770167625912159095            
x2[1] (numeric)                   = 1.0206991815495931976207901757568            
absolute error                    = 0.00037059674821618085819895984728909        
relative error                    = 0.036321313911667321899183825846147        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10129.0MB, alloc=40.3MB, time=112.63
memory used=10168.3MB, alloc=40.3MB, time=113.06
 
TOP MAIN SOLVE Loop
memory used=10207.7MB, alloc=40.3MB, time=113.50
t[1]                              = 2.32                                         
x1[1] (closed_form)               = 2.0001768924540878507567864562299            
x1[1] (numeric)                   = 1.9998913579902762860877054753135            
absolute error                    = 0.00028553446381156466908098091639293        
relative error                    = 0.014275460579950622534631844513395        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0207383515923375175401055435668            
x2[1] (numeric)                   = 1.0211229664841649635479904184486            
absolute error                    = 0.00038461489182744600788487488185327        
relative error                    = 0.037680066711263681726789542471382        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10247.2MB, alloc=40.3MB, time=113.94
memory used=10286.7MB, alloc=40.3MB, time=114.38
memory used=10326.0MB, alloc=40.3MB, time=114.81
 
TOP MAIN SOLVE Loop
t[1]                              = 2.33                                         
x1[1] (closed_form)               = 2.0001751323447611589846062612862            
x1[1] (numeric)                   = 1.9998821931365185709238967489914            
absolute error                    = 0.00029293920824258806070951229483495        
relative error                    = 0.014645677946169738284754588500356        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.021156405155458759235576808298             
x2[1] (numeric)                   = 1.0215554506047655806866541862276            
absolute error                    = 0.00039904544930682145107737792960121        
relative error                    = 0.039077799178674454804760314601708        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10365.4MB, alloc=40.3MB, time=115.25
memory used=10404.8MB, alloc=40.3MB, time=115.69
memory used=10444.2MB, alloc=40.3MB, time=116.12
 
TOP MAIN SOLVE Loop
t[1]                              = 2.34                                         
x1[1] (closed_form)               = 2.0001733897488148874354384302831            
x1[1] (numeric)                   = 1.9998729361744492887572151245932            
absolute error                    = 0.0003004535743655986782233056898872         
relative error                    = 0.01502137644193587334684663747853         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0215829128057492454554868389719            
x2[1] (numeric)                   = 1.0219968110351658554971659453987            
absolute error                    = 0.00041389822941661004167910642680847        
relative error                    = 0.040515382963860465312325023261692        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10483.7MB, alloc=40.3MB, time=116.56
memory used=10523.1MB, alloc=40.3MB, time=117.00
memory used=10562.6MB, alloc=40.3MB, time=117.44
 
TOP MAIN SOLVE Loop
t[1]                              = 2.35                                         
x1[1] (closed_form)               = 2.0001716644919879893139989338742            
x1[1] (numeric)                   = 1.9998635861783645184986723745122            
absolute error                    = 0.00030807831362347081532655936204974        
relative error                    = 0.015402593641967117906597815836024        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0220180452390893646616122290701            
x2[1] (numeric)                   = 1.0224472284912293339385013536039            
absolute error                    = 0.0004291832521399692768891245338037         
relative error                    = 0.041993705897782537906192280603153        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10602.0MB, alloc=40.3MB, time=117.88
memory used=10641.5MB, alloc=40.3MB, time=118.32
memory used=10681.0MB, alloc=40.3MB, time=118.76
 
TOP MAIN SOLVE Loop
t[1]                              = 2.36                                         
x1[1] (closed_form)               = 2.0001699564017533442116608243761            
x1[1] (numeric)                   = 1.9998541422132568599818664167215            
absolute error                    = 0.00031581418849648422979440765464183        
relative error                    = 0.015789367672766399513861799127361        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0224619766005207317172157388726            
x2[1] (numeric)                   = 1.0229068873536176405852671878057            
absolute error                    = 0.00044491075309690886805144893316482        
relative error                    = 0.043513672222427980561332245827075        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10720.5MB, alloc=40.3MB, time=119.20
memory used=10759.8MB, alloc=40.3MB, time=119.63
memory used=10799.2MB, alloc=40.3MB, time=120.07
 
TOP MAIN SOLVE Loop
t[1]                              = 2.37                                         
x1[1] (closed_form)               = 2.0001682653073005052506402934904            
x1[1] (numeric)                   = 1.9998446033347219324437892438476            
absolute error                    = 0.00032366197257857280685104964275589        
relative error                    = 0.016181737216435950533722275116344        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0229148845539151532132961026616            
x2[1] (numeric)                   = 1.0233759757419659725808409416897            
absolute error                    = 0.00046109118805081936754483902814735        
relative error                    = 0.045076202821302915915385476101402        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10838.6MB, alloc=40.3MB, time=120.51
memory used=10878.0MB, alloc=40.3MB, time=120.95
memory used=10917.4MB, alloc=40.3MB, time=121.39
 
TOP MAIN SOLVE Loop
memory used=10956.9MB, alloc=40.3MB, time=121.83
t[1]                              = 2.38                                         
x1[1] (closed_form)               = 2.0001665910395186178969663803834            
x1[1] (numeric)                   = 1.9998349685888639332997443483838            
absolute error                    = 0.00033162245065468459722203199953685        
relative error                    = 0.016579741514547300651548246221486        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0233769503530510859526373988824            
x2[1] (numeric)                   = 1.0238546855905584616906479356758            
absolute error                    = 0.00047773523750737573801053679347853        
relative error                    = 0.046682235450247692094928486303756        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=10996.4MB, alloc=40.3MB, time=122.26
memory used=11035.7MB, alloc=40.3MB, time=122.70
 
TOP MAIN SOLVE Loop
memory used=11075.2MB, alloc=40.3MB, time=123.14
t[1]                              = 2.39                                         
x1[1] (closed_form)               = 2.0001649334309795087341013927256            
x1[1] (numeric)                   = 1.9998252370122002477681724345043            
absolute error                    = 0.00033969641877926096592895822133982        
relative error                    = 0.016983420372067182133883345352398        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0238483589141260209768452898533            
x2[1] (numeric)                   = 1.0243432127255337181097376161737            
absolute error                    = 0.00049485381140769713289232632036281        
relative error                    = 0.048332724968424974248850716940247        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11114.7MB, alloc=40.3MB, time=123.58
memory used=11154.1MB, alloc=40.3MB, time=124.01
memory used=11193.7MB, alloc=40.3MB, time=124.45
 
TOP MAIN SOLVE Loop
t[1]                              = 2.4                                          
x1[1] (closed_form)               = 2.0001632923159209425060753099961            
x1[1] (numeric)                   = 1.9998154076315650998062684068048            
absolute error                    = 0.00034788468435584269980690319134881        
relative error                    = 0.01739281416133974112449957626679         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0243292988897337999024221749256            
x2[1] (numeric)                   = 1.0248417569436514821990604739017            
absolute error                    = 0.00051245805391768229663829897606322        
relative error                    = 0.050028643569322230317513531114837        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11233.1MB, alloc=40.3MB, time=124.89
memory used=11272.6MB, alloc=40.3MB, time=125.33
memory used=11312.0MB, alloc=40.3MB, time=125.76
 
TOP MAIN SOLVE Loop
t[1]                              = 2.41                                         
x1[1] (closed_form)               = 2.0001616675302300457558245299824            
x1[1] (numeric)                   = 1.9998054794640122347214029065153            
absolute error                    = 0.00035618806621781103442162346717244        
relative error                    = 0.017807963826125453872033324617357        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0248199627443364563159757815122            
x2[1] (numeric)                   = 1.0253505220926519352202616608516            
absolute error                    = 0.00053055934831547890428587933938115        
relative error                    = 0.051770981011602174355782406599377        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11351.5MB, alloc=40.3MB, time=126.20
memory used=11390.9MB, alloc=40.3MB, time=126.64
memory used=11430.3MB, alloc=40.3MB, time=127.08
 
TOP MAIN SOLVE Loop
t[1]                              = 2.42                                         
x1[1] (closed_form)               = 2.0001600589114268954010849786693            
x1[1] (numeric)                   = 1.9997954515167166237265284392425            
absolute error                    = 0.00036460739471027167455653942682403        
relative error                    = 0.018228910885697152442867122180731        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0253205468312607728002765309717            
x2[1] (numeric)                   = 1.0258697161532398576594065729025            
absolute error                    = 0.00054916932197908485913004193078666        
relative error                    = 0.053560744849626313601195886538398        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11469.8MB, alloc=40.3MB, time=127.52
memory used=11509.2MB, alloc=40.3MB, time=127.95
memory used=11548.7MB, alloc=40.3MB, time=128.39
 
TOP MAIN SOLVE Loop
t[1]                              = 2.43                                         
x1[1] (closed_form)               = 2.0001584662986482706066834965958            
x1[1] (numeric)                   = 1.9997853227868751806099437217133            
absolute error                    = 0.00037314351177308999673977488249589        
relative error                    = 0.018655697438993570170884912387341        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0258312514712503540612139473036            
x2[1] (numeric)                   = 1.0263995513227264741308977069954            
absolute error                    = 0.00056829985147612006968375969180266        
relative error                    = 0.055398960663468057224446346377513        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11588.3MB, alloc=40.3MB, time=128.84
memory used=11627.7MB, alloc=40.3MB, time=129.27
memory used=11667.1MB, alloc=40.3MB, time=129.71
 
TOP MAIN SOLVE Loop
t[1]                              = 2.44                                         
x1[1] (closed_form)               = 2.0001568895326315663284011906667            
x1[1] (numeric)                   = 1.9997750922616064805910004875679            
absolute error                    = 0.00038179727102508573740070309884862        
relative error                    = 0.019088366168830822834976064795822        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0263522810326046388447180673305            
x2[1] (numeric)                   = 1.0269402441003624873941440226484            
absolute error                    = 0.00058796306775784854942595531791758        
relative error                    = 0.057286672288222881322774890372955        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11706.6MB, alloc=40.3MB, time=130.15
memory used=11745.9MB, alloc=40.3MB, time=130.58
memory used=11785.2MB, alloc=40.3MB, time=131.02
 
TOP MAIN SOLVE Loop
memory used=11824.6MB, alloc=40.3MB, time=131.46
t[1]                              = 2.45                                         
x1[1] (closed_form)               = 2.0001553284556988669197497323297            
x1[1] (numeric)                   = 1.9997647589178494713335547549853            
absolute error                    = 0.00039056953784939558619497734442231        
relative error                    = 0.019526960346172247336262955143261        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0268838440129369081213033476098            
x2[1] (numeric)                   = 1.0274920153743964809627736625853            
absolute error                    = 0.00060817136145957284147031497549637        
relative error                    = 0.059224942042413802464438494328363        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11864.2MB, alloc=40.3MB, time=131.90
memory used=11903.6MB, alloc=40.3MB, time=132.33
 
TOP MAIN SOLVE Loop
memory used=11943.0MB, alloc=40.3MB, time=132.77
t[1]                              = 2.46                                         
x1[1] (closed_form)               = 2.0001537829117411782090080077086            
x1[1] (numeric)                   = 1.9997543217222611659881794934978            
absolute error                    = 0.00039946118948001222082851421078082        
relative error                    = 0.019971523834457025470551687449021        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0274261531225839946279830379304            
x2[1] (numeric)                   = 1.0280550905108935604101710382003            
absolute error                    = 0.00062893738830956578218800026991164        
relative error                    = 0.061214850955280887480139015249138        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=11982.6MB, alloc=40.3MB, time=133.21
memory used=12022.1MB, alloc=40.3MB, time=133.65
memory used=12061.5MB, alloc=40.3MB, time=134.09
 
TOP MAIN SOLVE Loop
t[1]                              = 2.47                                         
x1[1] (closed_form)               = 2.0001522527462028164697136833785            
x1[1] (numeric)                   = 1.9997437796311133080323576551781            
absolute error                    = 0.00040847311508950843735602820046125        
relative error                    = 0.020422101093988026258032947911264        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0279794253697010595519440746666            
x2[1] (numeric)                   = 1.02862969944434980805217412214              
absolute error                    = 0.000650274074648748500230047473371          
relative error                    = 0.063257498992733717039896063187427        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12101.0MB, alloc=40.3MB, time=134.52
memory used=12140.4MB, alloc=40.3MB, time=134.96
memory used=12179.9MB, alloc=40.3MB, time=135.40
 
TOP MAIN SOLVE Loop
t[1]                              = 2.48                                         
x1[1] (closed_form)               = 2.0001507378060659527234937277056            
x1[1] (numeric)                   = 1.9997331315901879975750534765828            
absolute error                    = 0.00041760621587795514844025112278104        
relative error                    = 0.020878737186379306202371906530078        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0285438821470754761818521133203            
x2[1] (numeric)                   = 1.029216076770138844499773339882             
absolute error                    = 0.00067219462306336831792122656170468        
relative error                    = 0.065354005281735621995484400231836        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12219.4MB, alloc=40.3MB, time=135.84
memory used=12258.7MB, alloc=40.3MB, time=136.28
memory used=12298.2MB, alloc=40.3MB, time=136.71
 
TOP MAIN SOLVE Loop
t[1]                              = 2.49                                         
x1[1] (closed_form)               = 2.0001492379398353108296512910108            
x1[1] (numeric)                   = 1.9997223765346722686882055302125            
absolute error                    = 0.00042686140516304214144576079831995        
relative error                    = 0.021341477779063712805608834280252        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0291197493206945480105981629308            
x2[1] (numeric)                   = 1.0298144618388275239091903727331            
absolute error                    = 0.00069471251813297589859220980230178        
relative error                    = 0.067505508332878122015500222389853        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12337.7MB, alloc=40.3MB, time=137.15
memory used=12377.1MB, alloc=40.3MB, time=137.59
memory used=12416.6MB, alloc=40.3MB, time=138.02
 
TOP MAIN SOLVE Loop
t[1]                              = 2.5                                          
x1[1] (closed_form)               = 2.000147752997523017831305151614             
x1[1] (numeric)                   = 1.999711513389051607222786822277             
absolute error                    = 0.00043623960847141060851832933702806        
relative error                    = 0.021810369149861042664336504006744        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0297072573201024903227739746105            
x2[1] (numeric)                   = 1.0304250988523985379071738052914            
absolute error                    = 0.0007178415322960475843998306809662         
relative error                    = 0.069713166260893313595036198753128        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12456.0MB, alloc=40.3MB, time=138.46
memory used=12495.6MB, alloc=40.3MB, time=138.90
memory used=12535.0MB, alloc=40.3MB, time=139.34
 
TOP MAIN SOLVE Loop
t[1]                              = 2.51                                         
x1[1] (closed_form)               = 2.0001462828306336050431037169473            
x1[1] (numeric)                   = 1.9997005410670023984611248073271            
absolute error                    = 0.00044574176363120658197890962022223        
relative error                    = 0.02228545819160721151702188204948         % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0303066412305828200218012476873            
x2[1] (numeric)                   = 1.0310482369624184664350462361891            
absolute error                    = 0.00074159573183564641324498850183129        
relative error                    = 0.071978157002840977420053158687892        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12574.5MB, alloc=40.3MB, time=139.77
memory used=12614.0MB, alloc=40.3MB, time=140.22
memory used=12653.3MB, alloc=40.3MB, time=140.65
 
TOP MAIN SOLVE Loop
memory used=12692.7MB, alloc=40.3MB, time=141.09
t[1]                              = 2.52                                         
x1[1] (closed_form)               = 2.0001448272921491583806098520027            
x1[1] (numeric)                   = 1.9996894584712832938501569244977            
absolute error                    = 0.00045536882086586453045292750504077        
relative error                    = 0.022766792416844899702698109943909        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0309181408872030286317372867347            
x2[1] (numeric)                   = 1.0316841303701905924413383585147            
absolute error                    = 0.00076598948298756380960107177995951        
relative error                    = 0.074301678533695902113615376690189        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12732.3MB, alloc=40.3MB, time=141.53
memory used=12771.7MB, alloc=40.3MB, time=141.97
 
TOP MAIN SOLVE Loop
memory used=12811.1MB, alloc=40.3MB, time=142.41
t[1]                              = 2.53                                         
x1[1] (closed_form)               = 2.0001433862365146164463770988317            
x1[1] (numeric)                   = 1.9996782644936254859522044528938            
absolute error                    = 0.00046512174288913049417264593786163        
relative error                    = 0.023254419962576142628173019653597        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0315420009707591583394179922855            
x2[1] (numeric)                   = 1.0323330384289325917712826684633            
absolute error                    = 0.00079103745817343343186467617775218        
relative error                    = 0.076684949079049351903449924507242        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12850.7MB, alloc=40.3MB, time=142.85
memory used=12890.1MB, alloc=40.3MB, time=143.28
memory used=12929.5MB, alloc=40.3MB, time=143.72
 
TOP MAIN SOLVE Loop
t[1]                              = 2.54                                         
x1[1] (closed_form)               = 2.0001419595196232149025136430807            
x1[1] (numeric)                   = 1.9996669580146218806406683256575            
absolute error                    = 0.00047500150500133426184531742313432        
relative error                    = 0.023748389595077342024991861920675        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0321784711056586609217594388637            
x2[1] (numeric)                   = 1.0329952257480200200698394885203            
absolute error                    = 0.00081675464236135914808004965665532        
relative error                    = 0.079129207324626739596358647184316        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=12969.1MB, alloc=40.3MB, time=144.16
memory used=13008.5MB, alloc=40.3MB, time=144.60
memory used=13047.9MB, alloc=40.3MB, time=145.04
 
TOP MAIN SOLVE Loop
t[1]                              = 2.55                                         
x1[1] (closed_form)               = 2.0001405469988020756741591542312            
x1[1] (numeric)                   = 1.9996555379036151554577741154868            
absolute error                    = 0.00048500909518692021638503874435235        
relative error                    = 0.024248750714777180009268796956977        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0328278059597806947347228446323            
x2[1] (numeric)                   = 1.0336709622993373453575381939074            
absolute error                    = 0.00084315633955665062281534927510702        
relative error                    = 0.081635712622311403889565797853412        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=13087.4MB, alloc=40.3MB, time=145.48
memory used=13126.9MB, alloc=40.3MB, time=145.91
memory used=13166.2MB, alloc=40.3MB, time=146.35
 
TOP MAIN SOLVE Loop
t[1]                              = 2.56                                         
x1[1] (closed_form)               = 2.0001391485327979395427828381899            
x1[1] (numeric)                   = 1.9996440030185846929401086810915            
absolute error                    = 0.00049514551421324660267415709833422        
relative error                    = 0.024755553361197924237783102335489        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0334902653463538059347967473061            
x2[1] (numeric)                   = 1.0343605235257791184860346033793            
absolute error                    = 0.00087025817942531255123785607321552        
relative error                    = 0.084205745192351932598841462581697        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=13205.7MB, alloc=40.3MB, time=146.79
memory used=13245.1MB, alloc=40.3MB, time=147.23
memory used=13284.6MB, alloc=40.3MB, time=147.67
 
TOP MAIN SOLVE Loop
t[1]                              = 2.57                                         
x1[1] (closed_form)               = 2.0001377639817630407025501424895            
x1[1] (numeric)                   = 1.9996323522060323776051868057085            
absolute error                    = 0.00050541177573066309736333678100381        
relative error                    = 0.025268848217960618783046018359478        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0341661143278917470772722331457            
x2[1] (numeric)                   = 1.0350641904519447342703918576392            
absolute error                    = 0.00089807612405298719311962449342997        
relative error                    = 0.086840606321417722634821489783719        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=13324.1MB, alloc=40.3MB, time=148.10
memory used=13363.6MB, alloc=40.3MB, time=148.54
memory used=13403.1MB, alloc=40.3MB, time=148.98
 
TOP MAIN SOLVE Loop
memory used=13442.5MB, alloc=40.3MB, time=149.42
t[1]                              = 2.58                                         
x1[1] (closed_form)               = 2.0001363932072411218672019795289            
x1[1] (numeric)                   = 1.9996205843008672451786513148448            
absolute error                    = 0.00051580890637387668855066468416585        
relative error                    = 0.025788686617854661729011682264977        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0348556233222290095108815314645            
x2[1] (numeric)                   = 1.0357822497970711140719849068554            
absolute error                    = 0.00092662647484210456110337539082767        
relative error                    = 0.089541618556154426048846746526596        % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=13481.9MB, alloc=40.3MB, time=149.86
memory used=13521.3MB, alloc=40.3MB, time=150.30
 
TOP MAIN SOLVE Loop
memory used=13560.7MB, alloc=40.3MB, time=150.74
t[1]                              = 2.59                                         
x1[1] (closed_form)               = 2.0001350360721535885289455016576            
x1[1] (numeric)                   = 1.9996086981262889725269332672958            
absolute error                    = 0.00052633794586461600201223436179754        
relative error                    = 0.026315120547972276918364748666969        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0355590682106984858948575712173            
x2[1] (numeric)                   = 1.0365149940902485363208615644626            
absolute error                    = 0.00095592587955005042600399324530046        
relative error                    = 0.092310125891877602526307098899308        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=13600.3MB, alloc=40.3MB, time=151.17
memory used=13639.7MB, alloc=40.3MB, time=151.61
memory used=13679.1MB, alloc=40.3MB, time=152.05
 
TOP MAIN SOLVE Loop
t[1]                              = 2.6                                          
x1[1] (closed_form)               = 2.0001336924407858009847707790263            
x1[1] (numeric)                   = 1.9995966924936701966442683934117            
absolute error                    = 0.00053699994711560434050238561463447        
relative error                    = 0.026848202654908393762507209317183        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0362767304484945360381252899357            
x2[1] (numeric)                   = 1.0372627217879657552777155255215            
absolute error                    = 0.000985991339471219239590235585733          
relative error                    = 0.095147493956029286503445728755093        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=13718.6MB, alloc=40.3MB, time=152.49
memory used=13758.0MB, alloc=40.3MB, time=152.93
memory used=13797.5MB, alloc=40.3MB, time=153.36
 
TOP MAIN SOLVE Loop
t[1]                              = 2.61                                         
x1[1] (closed_form)               = 2.000132362178773502759384588523             
x1[1] (numeric)                   = 1.9995845662024376509258704144177            
absolute error                    = 0.00054779597633585183351417410524043        
relative error                    = 0.027387986250026455557131932852801        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0370088971772656034439147791413            
x2[1] (numeric)                   = 1.0380257373940314806089276785501            
absolute error                    = 0.0010168402167658771650128994088388         
relative error                    = 0.098055110186008286699788678088025        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
memory used=13837.0MB, alloc=40.3MB, time=153.80
memory used=13876.4MB, alloc=40.3MB, time=154.24
memory used=13915.8MB, alloc=40.3MB, time=154.68
 
TOP MAIN SOLVE Loop
t[1]                              = 2.62                                         
x1[1] (closed_form)               = 2.0001310451530893840675922974857            
x1[1] (numeric)                   = 1.9995723180399521068407895066846            
absolute error                    = 0.00055872711313727722680279080113515        
relative error                    = 0.027934525314790683330260097816914        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0377558613399814217862761431891            
x2[1] (numeric)                   = 1.0388043515819202414563859059666            
absolute error                    = 0.0010484902419388196701097627775314         
relative error                    = 0.10103438400097087333051025676342         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=13955.4MB, alloc=40.3MB, time=155.12
memory used=13994.7MB, alloc=40.3MB, time=155.56
memory used=14034.2MB, alloc=40.3MB, time=156.00
 
TOP MAIN SOLVE Loop
t[1]                              = 2.63                                         
x1[1] (closed_form)               = 2.0001297412320297789724628832313            
x1[1] (numeric)                   = 1.999559946781387108998523147856             
absolute error                    = 0.00056979445064266997393973537536569        
relative error                    = 0.028487874506165328886488837058066        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0385179217981207604045247255734            
x2[1] (numeric)                   = 1.039598881319591629007509578031             
absolute error                    = 0.0010809595214708686029848524575941         
relative error                    = 0.10408674696718408065006605648969         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14073.7MB, alloc=40.3MB, time=156.44
memory used=14113.1MB, alloc=40.3MB, time=156.87
memory used=14152.4MB, alloc=40.3MB, time=157.30
 
TOP MAIN SOLVE Loop
t[1]                              = 2.64                                         
x1[1] (closed_form)               = 2.0001284502852014949089818191613            
x1[1] (numeric)                   = 1.9995474511896064914827849514699            
absolute error                    = 0.00058099909559500342619686769138541        
relative error                    = 0.029048089162081457401604254170875        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0392953834512265861415083939609            
x2[1] (numeric)                   = 1.0404096499968329014982792823837            
absolute error                    = 0.0011142665456063153567708884227567         
relative error                    = 0.10721365295649916792304973068601         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14191.9MB, alloc=40.3MB, time=157.74
memory used=14231.4MB, alloc=40.3MB, time=158.18
memory used=14270.8MB, alloc=40.3MB, time=158.62
 
TOP MAIN SOLVE Loop
memory used=14310.2MB, alloc=40.3MB, time=159.06
t[1]                              = 2.65                                         
x1[1] (closed_form)               = 2.0001271721835087732561332173007            
x1[1] (numeric)                   = 1.9995348300150406632039627968948            
absolute error                    = 0.00059234216846811005217042040594047        
relative error                    = 0.029615225306971806666329141329297        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0400885573588764658430735260112            
x2[1] (numeric)                   = 1.0412369875551759455091434448778            
absolute error                    = 0.0011484301962994796660699188666008         
relative error                    = 0.11041657829749784971156148006263         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14349.7MB, alloc=40.3MB, time=159.49
memory used=14389.2MB, alloc=40.3MB, time=159.94
 
TOP MAIN SOLVE Loop
memory used=14428.6MB, alloc=40.3MB, time=160.37
t[1]                              = 2.66                                         
x1[1] (closed_form)               = 2.0001259067991403796534575692593            
x1[1] (numeric)                   = 1.999522081995561649898698404511             
absolute error                    = 0.00060382480357872975475916474834249        
relative error                    = 0.030189339657374276877465339202246        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0408977608651169999580217612353            
x2[1] (numeric)                   = 1.0420812306204406177444805274384            
absolute error                    = 0.0011834697553236177864587662030735         
relative error                    = 0.11369702191884873701647773573728         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14468.1MB, alloc=40.3MB, time=160.81
memory used=14507.5MB, alloc=40.3MB, time=161.25
memory used=14546.9MB, alloc=40.3MB, time=161.68
 
TOP MAIN SOLVE Loop
t[1]                              = 2.67                                         
x1[1] (closed_form)               = 2.000124654005556822771105983281             
x1[1] (numeric)                   = 1.9995092058563568802806841820796            
absolute error                    = 0.00061544814919994249042180120143293        
relative error                    = 0.0307704896276046117297344040284          % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.041723317725412063316656472424             
x2[1] (numeric)                   = 1.0429427226379575426330398928161            
absolute error                    = 0.0012194049125454793163834203921634         
relative error                    = 0.11705650548439603610242391863183         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14586.4MB, alloc=40.3MB, time=162.12
memory used=14625.8MB, alloc=40.3MB, time=162.56
memory used=14665.3MB, alloc=40.3MB, time=162.99
 
TOP MAIN SOLVE Loop
t[1]                              = 2.68                                         
x1[1] (closed_form)               = 2.0001234136774777002552572717478            
x1[1] (numeric)                   = 1.9994962003098017037211872434267            
absolute error                    = 0.0006272133676759965340700283211129         
relative error                    = 0.031358733335498838472899375011371        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.042565558236155634715984279575             
x2[1] (numeric)                   = 1.0438218140105245134699948712576            
absolute error                    = 0.0012562557743688787540105916825676         
relative error                    = 0.12049657351948694491638238546405         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14704.8MB, alloc=40.3MB, time=163.43
memory used=14744.2MB, alloc=40.3MB, time=163.87
memory used=14783.7MB, alloc=40.3MB, time=164.31
 
TOP MAIN SOLVE Loop
t[1]                              = 2.69                                         
x1[1] (closed_form)               = 2.0001221856908691705834818857643            
x1[1] (numeric)                   = 1.9994830640553306267109624162233            
absolute error                    = 0.00063912163553854387251946954103244        
relative error                    = 0.031954129608226041566952944823085        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0434248193668010228029955315253            
x2[1] (numeric)                   = 1.0447188622391517388699421491169            
absolute error                    = 0.0012940428723507160669466175916117         
relative error                    = 0.12401879352802838244715686200903         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14823.2MB, alloc=40.3MB, time=164.75
memory used=14862.5MB, alloc=40.3MB, time=165.18
memory used=14902.0MB, alloc=40.3MB, time=165.63
 
TOP MAIN SOLVE Loop
t[1]                              = 2.7                                          
x1[1] (closed_form)               = 2.0001209699229315495772277930615            
x1[1] (numeric)                   = 1.9994697957793072552270931268557            
absolute error                    = 0.00065117414362429435013466620587212        
relative error                    = 0.032556737988172051593976959757018        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0443014448946593423345569015331            
x2[1] (numeric)                   = 1.0456342320666522924520634760455            
absolute error                    = 0.0013327871719929501175065745123646         
relative error                    = 0.12762475609974770023668467168857         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=14941.5MB, alloc=40.3MB, time=166.07
memory used=14980.8MB, alloc=40.3MB, time=166.50
memory used=15020.3MB, alloc=40.3MB, time=166.94
 
TOP MAIN SOLVE Loop
t[1]                              = 2.71                                         
x1[1] (closed_form)               = 2.0001197662520870303310692115344            
x1[1] (numeric)                   = 1.9994563941548929299988884647537            
absolute error                    = 0.00066337209719410033218074678070875        
relative error                    = 0.033166618738894638169414469421665        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0451957855424211626219572516615            
x2[1] (numeric)                   = 1.0465682956241352623802621483167            
absolute error                    = 0.0013725100817140997583048966552274         
relative error                    = 0.13131607500711587518904673838084         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15059.8MB, alloc=40.3MB, time=167.38
memory used=15099.2MB, alloc=40.3MB, time=167.81
memory used=15138.6MB, alloc=40.3MB, time=168.25
 
TOP MAIN SOLVE Loop
memory used=15178.0MB, alloc=40.3MB, time=168.69
t[1]                              = 2.72                                         
x1[1] (closed_form)               = 2.0001185745579675253307008898587            
x1[1] (numeric)                   = 1.9994428578419140415362535449051            
absolute error                    = 0.00067571671605348379444734495363697        
relative error                    = 0.033783832851150802738653955908483        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0461081991184563392671601334367            
x2[1] (numeric)                   = 1.0475214325804602590879518297278            
absolute error                    = 0.0014132334620039198207916962911176         
relative error                    = 0.13509438729137538812569170947141         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15217.5MB, alloc=40.3MB, time=169.13
memory used=15257.0MB, alloc=40.3MB, time=169.56
 
TOP MAIN SOLVE Loop
memory used=15296.3MB, alloc=40.3MB, time=170.00
t[1]                              = 2.73                                         
x1[1] (closed_form)               = 2.0001173947214026295438796030143            
x1[1] (numeric)                   = 1.9994291854867280116519254344147            
absolute error                    = 0.00068820923467461789195416859960845        
relative error                    = 0.034408442048996774347717307203185        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0470390506599481516020662208654            
x2[1] (numeric)                   = 1.0484940302947131246940660765367            
absolute error                    = 0.0014549796347649730919998556713            
relative error                    = 0.13896135333709857423278123820724         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15335.9MB, alloc=40.3MB, time=170.44
memory used=15375.3MB, alloc=40.3MB, time=170.88
memory used=15414.7MB, alloc=40.3MB, time=171.32
 
TOP MAIN SOLVE Loop
t[1]                              = 2.74                                         
x1[1] (closed_form)               = 2.0001162266244077032806119260732            
x1[1] (numeric)                   = 1.9994153757220879280756151842648            
absolute error                    = 0.00070085090231977520499674180847775        
relative error                    = 0.035040508795961318740185998307352        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0479887125789190019961125230614            
x2[1] (numeric)                   = 1.0494864839717638967379194115822            
absolute error                    = 0.0014977713928448947418068885207522         
relative error                    = 0.14291865693468571247496014366278         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15454.1MB, alloc=40.3MB, time=171.76
memory used=15493.4MB, alloc=40.3MB, time=172.19
memory used=15532.9MB, alloc=40.3MB, time=172.63
 
TOP MAIN SOLVE Loop
t[1]                              = 2.75                                         
x1[1] (closed_form)               = 2.000115070150172073630864374046             
x1[1] (numeric)                   = 1.9994014271670058186234045756133            
absolute error                    = 0.00071364298316625500745979843274155        
relative error                    = 0.035680096301292978457017346756906        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.04895756481120608985484851891              
x2[1] (numeric)                   = 1.0504991968209693124095095026975            
absolute error                    = 0.0015416320097632225546609837874198         
relative error                    = 0.14696800533019552593494995843255         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15572.4MB, alloc=40.3MB, time=173.07
memory used=15611.9MB, alloc=40.3MB, time=173.50
memory used=15651.3MB, alloc=40.3MB, time=173.94
 
TOP MAIN SOLVE Loop
t[1]                              = 2.76                                         
x1[1] (closed_form)               = 2.0001139251830473532999298466339            
x1[1] (numeric)                   = 1.9993873384266145512497005817356            
absolute error                    = 0.00072658675643280205022926489827453        
relative error                    = 0.036327268526281869002324330448811        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0499459949684466531554101441361            
x2[1] (numeric)                   = 1.0515325802180833979222015866875            
absolute error                    = 0.0015865852496367447667914425513525         
relative error                    = 0.1511111292618841205759560388498          % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15690.8MB, alloc=40.3MB, time=174.38
memory used=15730.2MB, alloc=40.3MB, time=174.82
memory used=15769.5MB, alloc=40.3MB, time=175.25
 
TOP MAIN SOLVE Loop
t[1]                              = 2.77                                         
x1[1] (closed_form)               = 2.0001127916085358756733241801936            
x1[1] (numeric)                   = 1.9993731080920283461716376573799            
absolute error                    = 0.00073968351650752950168652281368351        
relative error                    = 0.036982090190656663587254253106884        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0509543984931335742260852950776            
x2[1] (numeric)                   = 1.0525870538704409715699468860192            
absolute error                    = 0.0016326553773073973438615909415368         
relative error                    = 0.15534978298281172486096629492194         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15809.1MB, alloc=40.3MB, time=175.69
memory used=15848.5MB, alloc=40.3MB, time=176.13
memory used=15887.9MB, alloc=40.3MB, time=176.57
 
TOP MAIN SOLVE Loop
memory used=15927.3MB, alloc=40.3MB, time=177.00
t[1]                              = 2.78                                         
x1[1] (closed_form)               = 2.0001116693132792449547096590927            
x1[1] (numeric)                   = 1.9993587347402018861170240554824            
absolute error                    = 0.00075293457307735883768560361029465        
relative error                    = 0.037644626779057406476545791752484        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0519831788168033746579891671908            
x2[1] (numeric)                   = 1.0536630459854801988448934324416            
absolute error                    = 0.0016798671686768241869042652507927         
relative error                    = 0.15968574426885993787901528098632         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=15966.8MB, alloc=40.3MB, time=177.44
memory used=16006.2MB, alloc=40.3MB, time=177.88
 
TOP MAIN SOLVE Loop
memory used=16045.7MB, alloc=40.3MB, time=178.32
t[1]                              = 2.79                                         
x1[1] (closed_form)               = 2.0001105581850470002318497372226            
x1[1] (numeric)                   = 1.9993442169337880106067395573558            
absolute error                    = 0.00076634125125898962511017986677462        
relative error                    = 0.038314944547584802538919327027015        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0530327475214198772285324444596            
x2[1] (numeric)                   = 1.0547609934426716742874638472044            
absolute error                    = 0.0017282459212517970589314027447908         
relative error                    = 0.16412081441148558221623539301809         % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=16085.1MB, alloc=40.3MB, time=178.76
memory used=16124.6MB, alloc=40.3MB, time=179.19
memory used=16164.0MB, alloc=40.3MB, time=179.63
 
TOP MAIN SOLVE Loop
t[1]                              = 2.8                                          
x1[1] (closed_form)               = 2.0001094581127253923369921184987            
x1[1] (numeric)                   = 1.9993295532209939800408942676311            
absolute error                    = 0.00077990489173141229609785086762114        
relative error                    = 0.038993110530426638243917071219771        % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 4                                   
h                                 = 0.001                                        
x2[1] (closed_form)               = 1.0541035245040180910200828957228            
x2[1] (numeric)                   = 1.0558813419689228680342996229586            
absolute error                    = 0.0017778174649047770142167272358436         
relative error                    = 0.1686568181945207251557857458967          % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 3                                   
h                                 = 0.001                                        
memory used=16203.5MB, alloc=40.3MB, time=180.07
Finished!
Maximum Time Reached before Solution Completed!
diff  ( x1 , t , 1 )   =  4.0  *  x2  -   2.0  *  diff  ( x2 , t  , 1 )   -  2.0  *  x1 ; 
diff  ( x2 , t , 2 )   =  3.0  *  diff ( x2 , t , 1 )   -  2.0  *  x2  -  diff ( x1 , t , 2 )   -  diff  ( x1 , t , 1 )   +  x1 ; 
Iterations                       = 1305                                
Total Elapsed Time               = 3 Minutes 0 Seconds
Elapsed Time(since restart)      = 3 Minutes 0 Seconds
Expected Time Remaining          = 11 Minutes 56 Seconds
Optimized Time Remaining         = 11 Minutes 56 Seconds
Expected Total Time              = 14 Minutes 57 Seconds
Time to Timeout                  0.0 Seconds
Percent Done                     = 20.09                                      % 
> quit
memory used=16226.6MB, alloc=40.3MB, time=180.31