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

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

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

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

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

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

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

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

# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
>     global MAX_TERMS;
>     local iii;
>     iii  := 1;
>     while (iii <= MAX_TERMS) do # do number 1
>         arr_a [iii] := 0.0;
>         iii  :=  iii + 1;
>     od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global MAX_TERMS;
    iii := 1;
    while iii <= MAX_TERMS do arr_a[iii] := 0.; iii := iii + 1 end do
end proc

# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
>     global MAX_TERMS;
>     local iii_ats, lll_ats,ma_ats, ret_ats;
>     ret_ats  :=  0.0;
>     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 <= MAX_TERMS  and (iii_ats <= MAX_TERMS) ))  then # if number 7
>                 ret_ats  :=  ret_ats + arr_a[iii_ats]*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 MAX_TERMS;
    ret_ats := 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 <= MAX_TERMS and iii_ats <= MAX_TERMS then
                ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]
            end if;
            iii_ats := iii_ats + 1
        end do
    end if;
    ret_ats
end proc

# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
>     global MAX_TERMS;
>     local al_att, iii_att,lll_att, ma_att, ret_att;
>     ret_att  :=  0.0;
>     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 <= MAX_TERMS) )   do # do number 1
>             lll_att  :=  ma_att - iii_att;
>             al_att  :=  (lll_att - 1);
>             if ((lll_att <= MAX_TERMS  and (iii_att <= MAX_TERMS) ))  then # if number 7
>                 ret_att  :=   ret_att + arr_aa[iii_att]*arr_bb[lll_att]* (al_att);
>             fi;# end if 7;
>             iii_att  :=  iii_att + 1;
>         od;# end do number 1;
>         ret_att  :=  ret_att / (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 MAX_TERMS;
    ret_att := 0.;
    if jjj_att < mmm_att then
        ma_att := mmm_att + 2;
        iii_att := jjj_att;
        while iii_att < mmm_att and iii_att <= MAX_TERMS do
            lll_att := ma_att - iii_att;
            al_att := lll_att - 1;
            if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS then
                ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*al_att
            end if;
            iii_att := iii_att + 1
        end do;
        ret_att := ret_att/mmm_att
    end if;
    ret_att
end proc

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

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

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

# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
>     global glob_small_float,glob_prec;
>     local good_digits;
>     fprintf(file,"<td>");
>     if (rel_error <> -1.0) then # if number 6
>         if (rel_error > glob_prec) then # if number 7
>             good_digits := 3-int_trunc(log10(rel_error));
>             fprintf(file,"%d",good_digits);
>         else
>             good_digits := Digits;
>             fprintf(file,"%d",good_digits);
>         fi;# end if 7;
>     else
>         fprintf(file,"Unknown");
>     fi;# end if 6;
>     fprintf(file,"</td>");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
    fprintf(file, "<td>");
    if rel_error <> -1.0 then
        if glob_prec < rel_error then
            good_digits := 3 - int_trunc(log10(rel_error));
            fprintf(file, "%d", good_digits)
        else good_digits := Digits; fprintf(file, "%d", good_digits)
        end if
    else fprintf(file, "Unknown")
    end if;
    fprintf(file, "</td>")
end proc

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

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

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

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

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

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

# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
>     global glob_small_float;
>     local ms2, rrr, sec_left, sub1, sub2;
>     ;
>     ms2 := clock_sec2;
>     sub1 := (t_end2-t_start2);
>     sub2 := (t2-t_start2);
>     if (sub1 = 0.0)  then # if number 12
>         sec_left := 0.0;
>     else
>         if (sub2 > 0.0)  then # if number 13
>             rrr := (sub1/sub2);
>             sec_left  := rrr * ms2 - ms2;
>         else
>             sec_left  := 0.0;
>         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 := clock_sec2;
    sub1 := t_end2 - t_start2;
    sub2 := t2 - t_start2;
    if sub1 = 0. then sec_left := 0.
    else
        if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
        else sec_left := 0.
        end if
    end if;
    sec_left
end proc

# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
>     global glob_small_float;
>     local rrr, sub1, sub2;
>     sub1  :=  (t_end2-t_start2);
>     sub2  :=  (t2-t_start2);
>     if (sub2 > glob_small_float)  then # if number 12
>         rrr  :=  (100.0*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 := 100.0*sub2/sub1
    else rrr := 0.
    end if;
    rrr
end proc

# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (term2 > 0.0)  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 0. < term2 then ret := float_abs(term1*glob_h/term2)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
>     #TOP TWO TERM ORDER ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret;
>     if (term2 > 0.0)  then # if number 12
>         ret := 1.0 +  float_abs(term2) * convfloat(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(convfloat(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 0. < term2 then ret := 1.0 + float_abs(term2)*convfloat(last_no)*
        ln(float_abs(term1*glob_h/term2))/ln(convfloat(last_no))
    else ret := glob_larger_float
    end if;
    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*convfloat(last_no)-2.0*term2*term2-term1*term3*convfloat(last_no)+term1*term3);
>     if (temp > 0.0)  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*convfloat(last_no) - 2.0*term2*term2
         - term1*term3*convfloat(last_no) + term1*term3);
    if 0. < 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((4.0*term1*term3*convfloat(last_no)-3.0*term1*term3-4.0*term2*term2*convfloat(last_no)+4.0*term2*term2+term2*term2*convfloat(last_no*last_no)-term1*term3*convfloat(last_no*last_no))/(term2*term2*convfloat(last_no)-2.0*term2*term2-term1*term3*convfloat(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((4.0*term1*term3*convfloat(last_no) - 3.0*term1*term3
         - 4.0*term2*term2*convfloat(last_no) + 4.0*term2*term2
         + term2*term2*convfloat(last_no*last_no)
         - term1*term3*convfloat(last_no*last_no))/(
        term2*term2*convfloat(last_no) - 2.0*term2*term2
         - term1*term3*convfloat(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  <> 0.0) and (term4  <> 0.0) and (term3  <> 0.0) and  (term2  <> 0.0) and (term1  <> 0.0)) then # if number 12
>         rm0 := term6/term5;
>         rm1 := term5/term4;
>         rm2 := term4/term3;
>         rm3 := term3/term2;
>         rm4 := term2/term1;
>         nr1 :=  convfloat(last_no-1)*rm0 - 2.0*convfloat(last_no-2)*rm1 + convfloat(last_no-3)*rm2;
>         nr2 :=  convfloat(last_no-2)*rm1 - 2.0*convfloat(last_no-3)*rm2 + convfloat(last_no-4)*rm3;
>         dr1 :=  (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
>         dr2 :=  (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
>         ds1 :=  3.0/rm1 - 8.0/rm2 + 5.0/rm3;
>         ds2 :=  3.0/rm2 - 8.0/rm3 + 5.0/rm4;
>         if ((float_abs(nr1 * dr2 - nr2 * dr1)  =  0.0)  or  (float_abs(dr1) = 0.0))  then # if number 13
>             rad_c :=  glob_larger_float;
>             ord_no :=  glob_larger_float;
>         else
>             if (float_abs(nr1*dr2 - nr2 * dr1) <> 0.0)  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)/(2.0*dr1) -convfloat(last_no)/2.0;
>                 if (float_abs(rcs)  <> 0.0)  then # if number 15
>                     if (rcs > 0.0)  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 <> 0. and term4 <> 0. and term3 <> 0. and term2 <> 0. and
    term1 <> 0. then
        rm0 := term6/term5;
        rm1 := term5/term4;
        rm2 := term4/term3;
        rm3 := term3/term2;
        rm4 := term2/term1;
        nr1 := convfloat(last_no - 1)*rm0 - 2.0*convfloat(last_no - 2)*rm1
             + convfloat(last_no - 3)*rm2;
        nr2 := convfloat(last_no - 2)*rm1 - 2.0*convfloat(last_no - 3)*rm2
             + convfloat(last_no - 4)*rm3;
        dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
        dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
        ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
        ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
        if float_abs(nr1*dr2 - nr2*dr1) = 0. or float_abs(dr1) = 0. then
            rad_c := glob_larger_float; ord_no := glob_larger_float
        else
            if float_abs(nr1*dr2 - nr2*dr1) <> 0. then
                rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
                ord_no :=
                    (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(last_no)/2.0;
                if float_abs(rcs) <> 0. then
                    if 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 MAX_TERMS,array_fact_1;
>     local ret;
>     if (nnn <= 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 MAX_TERMS, array_fact_1;
    if nnn <= 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 MAX_TERMS,array_fact_2;
>     local ret;
>     if ((nnn <= MAX_TERMS)  and  (mmm <= 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 MAX_TERMS, array_fact_2;
    if nnn <= MAX_TERMS and mmm <= 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
> int_trunc := proc(xxx)
>     trunc(xxx);
> end;
                   int_trunc := proc(xxx) trunc(xxx) end proc

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

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

# End Function number 38
# Begin Function number 39
> 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,MAX_TERMS;
>     omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
>     desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * float_abs(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 := (float_abs(desired_abs_gbl_error /sqrt( estimated_steps)/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, MAX_TERMS;
    omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
        glob_desired_digits_correct, 32, "");
    desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*
        float_abs(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 :=
        float_abs(desired_abs_gbl_error/(sqrt(estimated_steps)*MAX_TERMS));
    omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
    step_error
end proc

# End Function number 39
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(  - cos(x));
> end;
                exact_soln_y1 := proc(x) return -cos(x) end proc

> exact_soln_y2 := proc(x)
> return( - sin(x));
> end;
                exact_soln_y2 := proc(x) return -sin(x) end proc

> exact_soln_y2p := proc(x)
> return( - cos(x));
> end;
               exact_soln_y2p := proc(x) return -cos(x) end proc

#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
>     local rad_given;
>     global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 1
>         rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) +  array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
>         omniout_float(ALWAYS,"Radius of convergence (given) for eq  1           ",4,rad_given,4," ");
>         omniout_float(ALWAYS,"Order of pole (given)                             ",4,array_given_ord_poles[1,1],4," ");
>         if (rad_given < glob_least_given_sing)  then # if number 2
>             glob_least_given_sing :=  rad_given;
>         fi;# end if 2;
>     elif
>     (glob_type_given_pole = 3) then # if number 2
>         omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
>     elif
>     (glob_type_given_pole = 5) then # if number 3
>         omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
>     else
>         omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
>     fi;# end if 3;
>     if (array_rad_test_poles[1,1] < glob_large_float)  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq  1      ",4,array_rad_test_poles[1,1],4," ");
>         if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
>             glob_least_ratio_sing := array_rad_test_poles[1,1];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (ratio test)                        ",4, array_ord_test_poles[1,1],4," ");
>     else
>         omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
>     fi;# end if 3;
>     if ((array_rad_test_poles[1,2] >  0.0) 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] >  0.0) and (array_rad_test_poles[1,3] < glob_large_float))  then # if number 3
>         omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1    ",4,array_rad_test_poles[1,3],4," ");
>         if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
>             glob_least_6_sing := array_rad_test_poles[1,3];
>         fi;# end if 4;
>         omniout_float(ALWAYS,"Order of pole (six term test)                     ",4, array_ord_test_poles[1,3],4," ");
>     else
>         omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
>     fi;# end if 3
>     ;
>     if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2))  then # if number 3
>         rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) +  array_given_rad_poles[2,2] * array_given_rad_poles[2,2]);
>         omniout_float(ALWAYS,"Radius of convergence (given) for eq  2           ",4,rad_given,4," ");
>         omniout_float(ALWAYS,"Order of pole (given)                             ",4,array_given_ord_poles[2,1],4," ");
>         if (rad_given < glob_least_given_sing)  then # if number 4
>             glob_least_given_sing :=  rad_given;
>         fi;# end if 4;
>     elif
>     (glob_type_given_pole = 3) then # if number 4
>         omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
>     elif
>     (glob_type_given_pole = 5) then # if number 5
>         omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
>     else
>         omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
>     fi;# end if 5;
>     if (array_rad_test_poles[2,1] < glob_large_float)  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq  2      ",4,array_rad_test_poles[2,1],4," ");
>         if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6
>             glob_least_ratio_sing := array_rad_test_poles[2,1];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (ratio test)                        ",4, array_ord_test_poles[2,1],4," ");
>     else
>         omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
>     fi;# end if 5;
>     if ((array_rad_test_poles[2,2] >  0.0) 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] >  0.0) and (array_rad_test_poles[2,3] < glob_large_float))  then # if number 5
>         omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2    ",4,array_rad_test_poles[2,3],4," ");
>         if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6
>             glob_least_6_sing := array_rad_test_poles[2,3];
>         fi;# end if 6;
>         omniout_float(ALWAYS,"Order of pole (six term test)                     ",4, array_ord_test_poles[2,3],4," ");
>     else
>         omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
>     fi;# end if 5
>     ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
    if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
        rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
            (array_x[1] - array_given_rad_poles[1, 1])
             + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
        omniout_float(ALWAYS,
            "Radius of convergence (given) for eq  1           ", 4,
            rad_given, 4, " ");
        omniout_float(ALWAYS,
            "Order of pole (given)                             ", 4,
            array_given_ord_poles[1, 1], 4, " ");
        if rad_given < glob_least_given_sing then
            glob_least_given_sing := rad_given
        end if
    elif glob_type_given_pole = 3 then
        omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
    elif glob_type_given_pole = 5 then
        omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
    else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
    end if;
    if array_rad_test_poles[1, 1] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (ratio test) for eq  1      ", 4,
            array_rad_test_poles[1, 1], 4, " ");
        if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
            glob_least_ratio_sing := array_rad_test_poles[1, 1]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (ratio test)                        ", 4,
            array_ord_test_poles[1, 1], 4, " ")
    else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
    end if;
    if 0. < 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 0. < array_rad_test_poles[1, 3] and
    array_rad_test_poles[1, 3] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (six term test) for eq 1    ", 4,
            array_rad_test_poles[1, 3], 4, " ");
        if array_rad_test_poles[1, 3] < glob_least_6_sing then
            glob_least_6_sing := array_rad_test_poles[1, 3]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (six term test)                     ", 4,
            array_ord_test_poles[1, 3], 4, " ")
    else omniout_str(ALWAYS,
        "NO COMPLEX POLE (six term test) for Equation 1")
    end if;
    if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
        rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])*
            (array_x[1] - array_given_rad_poles[2, 1])
             + array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]);
        omniout_float(ALWAYS,
            "Radius of convergence (given) for eq  2           ", 4,
            rad_given, 4, " ");
        omniout_float(ALWAYS,
            "Order of pole (given)                             ", 4,
            array_given_ord_poles[2, 1], 4, " ");
        if rad_given < glob_least_given_sing then
            glob_least_given_sing := rad_given
        end if
    elif glob_type_given_pole = 3 then
        omniout_str(ALWAYS, "NO POLE (given) for Equation 2")
    elif glob_type_given_pole = 5 then
        omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
    else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
    end if;
    if array_rad_test_poles[2, 1] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (ratio test) for eq  2      ", 4,
            array_rad_test_poles[2, 1], 4, " ");
        if array_rad_test_poles[2, 1] < glob_least_ratio_sing then
            glob_least_ratio_sing := array_rad_test_poles[2, 1]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (ratio test)                        ", 4,
            array_ord_test_poles[2, 1], 4, " ")
    else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
    end if;
    if 0. < 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 0. < 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 := 1.0;
>     else
>         ret := -1.0;
>     fi;# end if 5;
>     ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
    if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc

# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> MAX_TERMS,
> glob_last;
>     local min_size;
>     min_size := glob_estimated_size_answer;
>     if (float_abs(array_y1[1]) < min_size) then # if number 5
>         min_size := float_abs(array_y1[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     if (float_abs(array_y2[1]) < min_size) then # if number 5
>         min_size := float_abs(array_y2[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     if (min_size < 1.0) then # if number 5
>         min_size := 1.0;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     min_size;
> end;
est_size_answer := proc()
local min_size;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    min_size := glob_estimated_size_answer;
    if float_abs(array_y1[1]) < min_size then
        min_size := float_abs(array_y1[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if float_abs(array_y2[1]) < min_size then
        min_size := float_abs(array_y2[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if min_size < 1.0 then
        min_size := 1.0;
        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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> 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  := 0.0;
>     no_terms := MAX_TERMS;
>     hn_div_ho := 0.5;
>     hn_div_ho_2 := 0.25;
>     hn_div_ho_3 := 0.125;
>     omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
>     est_tmp := float_abs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 5
>         max_estimated_step_error := est_tmp;
>     fi;# end if 5;
>     est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 5
>         max_estimated_step_error := est_tmp;
>     fi;# end if 5;
>     omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
>     max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    max_estimated_step_error := 0.;
    no_terms := MAX_TERMS;
    hn_div_ho := 0.5;
    hn_div_ho_2 := 0.25;
    hn_div_ho_3 := 0.125;
    omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
    est_tmp := float_abs(array_y1[no_terms - 3]
         + array_y1[no_terms - 2]*hn_div_ho
         + array_y1[no_terms - 1]*hn_div_ho_2
         + array_y1[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    est_tmp := float_abs(array_y2[no_terms - 3]
         + array_y2[no_terms - 2]*hn_div_ho
         + array_y2[no_terms - 1]*hn_div_ho_2
         + array_y2[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    omniout_float(ALWAYS, "max_estimated_step_error", 32,
        max_estimated_step_error, 32, "");
    max_estimated_step_error
end proc

# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> MAX_TERMS,
> glob_last;
>     local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     no_terms := MAX_TERMS;
>     hn_div_ho := 0.5;
>     hn_div_ho_2 := 0.25;
>     hn_div_ho_3 := 0.125;
>     est_tmp := float_abs(array_y1[no_terms-3]) + float_abs(array_y1[no_terms - 2]) * hn_div_ho + float_abs(array_y1[no_terms - 1]) * hn_div_ho_2 + float_abs(array_y1[no_terms]) * hn_div_ho_3;
>     if (glob_prec * float_abs(array_y1[1]) > est_tmp) then # if number 5
>         est_tmp := glob_prec * float_abs(array_y1[1]);
>     fi;# end if 5;
>     if (est_tmp >= array_max_est_error[1]) then # if number 5
>         array_max_est_error[1] := est_tmp;
>     fi;# end if 5
>     ;
>     est_tmp := float_abs(array_y2[no_terms-3]) + float_abs(array_y2[no_terms - 2]) * hn_div_ho + float_abs(array_y2[no_terms - 1]) * hn_div_ho_2 + float_abs(array_y2[no_terms]) * hn_div_ho_3;
>     if (glob_prec * float_abs(array_y2[1]) > est_tmp) then # if number 5
>         est_tmp := glob_prec * float_abs(array_y2[1]);
>     fi;# end if 5;
>     if (est_tmp >= array_max_est_error[2]) then # if number 5
>         array_max_est_error[2] := 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 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    no_terms := MAX_TERMS;
    hn_div_ho := 0.5;
    hn_div_ho_2 := 0.25;
    hn_div_ho_3 := 0.125;
    est_tmp := float_abs(array_y1[no_terms - 3])
         + float_abs(array_y1[no_terms - 2])*hn_div_ho
         + float_abs(array_y1[no_terms - 1])*hn_div_ho_2
         + float_abs(array_y1[no_terms])*hn_div_ho_3;
    if est_tmp < glob_prec*float_abs(array_y1[1]) then
        est_tmp := glob_prec*float_abs(array_y1[1])
    end if;
    if array_max_est_error[1] <= est_tmp then
        array_max_est_error[1] := est_tmp
    end if;
    est_tmp := float_abs(array_y2[no_terms - 3])
         + float_abs(array_y2[no_terms - 2])*hn_div_ho
         + float_abs(array_y2[no_terms - 1])*hn_div_ho_2
         + float_abs(array_y2[no_terms])*hn_div_ho_3;
    if est_tmp < glob_prec*float_abs(array_y2[1]) then
        est_tmp := glob_prec*float_abs(array_y2[1])
    end if;
    if array_max_est_error[2] <= est_tmp then
        array_max_est_error[2] := est_tmp
    end if
end proc

# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> MAX_TERMS,
> glob_last;
>     local ret;
>     if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/10.0)) then # if number 5
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 5;
>     return(ret);
> end;
reached_interval := proc()
local ret;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    if glob_check_sign*glob_next_display - glob_h/10.0 <=
    glob_check_sign*array_x[1] then ret := true
    else ret := false
    end if;
    return ret
end proc

# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> MAX_TERMS,
> glob_last;
>     local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
>     #TOP DISPLAY ALOT
>     if (reached_interval())  then # if number 5
>         if (iter >= 0)  then # if number 6
>             ind_var := array_x[1];
>             omniout_float(ALWAYS,"x[1]                             ",33,ind_var,20," ");
>             closed_form_val_y := evalf(exact_soln_y1(ind_var));
>             omniout_float(ALWAYS,"y1[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y1[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y1[1] (numeric)                  ",33,numeric_val,20," ");
>             if (evalf(float_abs(closed_form_val_y)) >  glob_prec)  then # if number 7
>                 relerr := abserr*100.0/float_abs(closed_form_val_y);
>                 if (relerr > glob_prec) then # if number 8
>                     glob_good_digits := -int_trunc(log10(relerr)) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  -1.0  ;
>                 glob_good_digits := -16;
>             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)*35*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 :=  -1.0  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[1] := glob_est_digits;
>             array_good_digits[1] := glob_good_digits;
>             if (glob_iter  = 1) then # if number 7
>                 array_1st_rel_error[1] := relerr;
>             else
>                 array_last_rel_error[1] := relerr;
>             fi;# end if 7;
>             array_est_rel_error[1] := est_rel_err;
>             omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>             omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>             omniout_int(INFO,"Desired digits                   ",32,glob_desired_digits_correct,4," ");
>             omniout_int(INFO,"Estimated correct digits         ",32,glob_est_digits,4," ");
>             omniout_int(INFO,"Correct digits                   ",32,glob_good_digits,4," ")
>             ;
>             omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>             ;
>             closed_form_val_y := evalf(exact_soln_y2(ind_var));
>             omniout_float(ALWAYS,"y2[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y2[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y2[1] (numeric)                  ",33,numeric_val,20," ");
>             if (evalf(float_abs(closed_form_val_y)) >  glob_prec)  then # if number 7
>                 relerr := abserr*100.0/float_abs(closed_form_val_y);
>                 if (relerr > glob_prec) then # if number 8
>                     glob_good_digits := -int_trunc(log10(relerr)) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  -1.0  ;
>                 glob_good_digits := -16;
>             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)*35*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 :=  -1.0  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[2] := glob_est_digits;
>             array_good_digits[2] := glob_good_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 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    if reached_interval() then
        if 0 <= iter then
            ind_var := array_x[1];
            omniout_float(ALWAYS, "x[1]                             ", 33,
                ind_var, 20, " ");
            closed_form_val_y := evalf(exact_soln_y1(ind_var));
            omniout_float(ALWAYS, "y1[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y1[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y1[1] (numeric)                  ", 33,
                numeric_val, 20, " ");
            if glob_prec < evalf(float_abs(closed_form_val_y)) then
                relerr := abserr*100.0/float_abs(closed_form_val_y);
                if glob_prec < relerr then
                    glob_good_digits := -int_trunc(log10(relerr)) + 3
                else glob_good_digits := Digits
                end if
            else relerr := -1.0; glob_good_digits := -16
            end if;
            if evalf(glob_prec < float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[1]*100.0*
                    sqrt(glob_iter)*35*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 := -1.0; glob_est_digits := -16
            end if;
            array_est_digits[1] := glob_est_digits;
            array_good_digits[1] := glob_good_digits;
            if glob_iter = 1 then array_1st_rel_error[1] := relerr
            else array_last_rel_error[1] := relerr
            end if;
            array_est_rel_error[1] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ");
            closed_form_val_y := evalf(exact_soln_y2(ind_var));
            omniout_float(ALWAYS, "y2[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y2[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y2[1] (numeric)                  ", 33,
                numeric_val, 20, " ");
            if glob_prec < evalf(float_abs(closed_form_val_y)) then
                relerr := abserr*100.0/float_abs(closed_form_val_y);
                if glob_prec < relerr then
                    glob_good_digits := -int_trunc(log10(relerr)) + 3
                else glob_good_digits := Digits
                end if
            else relerr := -1.0; glob_good_digits := -16
            end if;
            if evalf(glob_prec < float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[2]*100.0*
                    sqrt(glob_iter)*35*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 := -1.0; glob_est_digits := -16
            end if;
            array_est_digits[2] := glob_est_digits;
            array_good_digits[2] := glob_good_digits;
            if glob_iter = 1 then array_1st_rel_error[2] := relerr
            else array_last_rel_error[2] := relerr
            end if;
            array_est_rel_error[2] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ")
        end if
    end if
end proc

# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> MAX_TERMS,
> glob_last;
>     local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>     #TOP PROGRESS REPORT
>     clock_sec1   := elapsed_time_seconds();
>     total_clock_sec   :=  (clock_sec1) - (glob_orig_start_sec);
>     glob_clock_sec   :=  (clock_sec1) - (glob_clock_start_sec);
>     left_sec   :=  (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
>     expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h)  ,( clock_sec1) - (glob_orig_start_sec));
>     opt_clock_sec   := ( clock_sec1) - (glob_optimal_clock_start_sec);
>     glob_optimal_expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
>     glob_total_exp_sec   := glob_optimal_expect_sec + total_clock_sec;
>     percent_done   :=  comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
>     glob_percent_done := percent_done;
>     omniout_str_noeol(INFO,"Total Elapsed Time              ");
>     omniout_timestr((total_clock_sec));
>     omniout_str_noeol(INFO,"Elapsed Time(since restart)     ");
>     omniout_timestr((glob_clock_sec));
>     if ((percent_done) < (100.0))  then # if number 5
>         omniout_str_noeol(INFO,"Expected Time Remaining         ");
>         omniout_timestr((expect_sec));
>         omniout_str_noeol(INFO,"Optimized Time Remaining        ");
>         omniout_timestr((glob_optimal_expect_sec));
>         omniout_str_noeol(INFO,"Expected Total Time             ");
>         omniout_timestr((glob_total_exp_sec));
>     fi;# end if 5;
>     omniout_str_noeol(INFO,"Time to Timeout                 ");
>     omniout_timestr((left_sec));
>     omniout_float(INFO,    "Percent Done                    ",33,percent_done,4,"%");
>     #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    clock_sec1 := elapsed_time_seconds();
    total_clock_sec := clock_sec1 - glob_orig_start_sec;
    glob_clock_sec := clock_sec1 - glob_clock_start_sec;
    left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
    expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
        clock_sec1 - glob_orig_start_sec);
    opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
    glob_optimal_expect_sec :=
        comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
        ;
    glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
    percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
    glob_percent_done := percent_done;
    omniout_str_noeol(INFO, "Total Elapsed Time              ");
    omniout_timestr(total_clock_sec);
    omniout_str_noeol(INFO, "Elapsed Time(since restart)     ");
    omniout_timestr(glob_clock_sec);
    if percent_done < 100.0 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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> 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 :=  MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 6
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 7
>             found_sing := 0;
>         fi;# end if 7;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 7
>         if (rad_c  < array_rad_test_poles[1,1]) then # if number 8
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[1,1] := rad_c;
>             array_ord_test_poles[1,1] := tmp_ord;
>         fi;# end if 8;
>     fi;# end if 7;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,1] :=  glob_larger_float;
>     array_ord_test_poles[2,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  MAX_TERMS - 2 - 10;
>     cnt :=  0;
>     while (last_no < MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 8
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 9
>             found_sing := 0;
>         fi;# end if 9;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 9
>         if (rad_c  < array_rad_test_poles[2,1]) then # if number 10
>             array_rad_test_poles[2,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[2,1] := rad_c;
>             array_ord_test_poles[2,1] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test2
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,2] :=  glob_larger_float;
>     array_ord_test_poles[1,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 10
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 11
>             found_sing := 0;
>         fi;# end if 11;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 11
>         if (rad_c  < array_rad_test_poles[1,2]) then # if number 12
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 13
>                 glob_min_pole_est := rad_c;
>             fi;# end if 13;
>             array_ord_test_poles[1,2] := tmp_ord;
>         fi;# end if 12;
>     fi;# end if 11;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,2] :=  glob_larger_float;
>     array_ord_test_poles[2,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  MAX_TERMS - 2 - 10;
>     cnt :=  0;
>     while (last_no < MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 12
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 13
>             found_sing := 0;
>         fi;# end if 13;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 13
>         if (rad_c  < array_rad_test_poles[2,2]) then # if number 14
>             array_rad_test_poles[2,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[2,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 15
>                 glob_min_pole_est := rad_c;
>             fi;# end if 15;
>             array_ord_test_poles[2,2] := tmp_ord;
>         fi;# end if 14;
>     fi;# end if 13;
>     #BOTTOM general radius test2
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,3] :=  glob_larger_float;
>     array_ord_test_poles[1,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 14
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 15
>             found_sing := 0;
>         fi;# end if 15;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 15
>         if (rad_c  < array_rad_test_poles[1,3]) then # if number 16
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 17
>                 glob_min_pole_est := rad_c;
>             fi;# end if 17;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 16;
>     fi;# end if 15;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,3] :=  glob_larger_float;
>     array_ord_test_poles[2,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  MAX_TERMS - 2 - 10;
>     cnt :=  0;
>     while (last_no < MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 16
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 17
>             found_sing := 0;
>         fi;# end if 17;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 17
>         if (rad_c  < array_rad_test_poles[2,3]) then # if number 18
>             array_rad_test_poles[2,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[2,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 19
>                 glob_min_pole_est := rad_c;
>             fi;# end if 19;
>             array_ord_test_poles[2,3] := tmp_ord;
>         fi;# end if 18;
>     fi;# end if 17;
>     #BOTTOM general radius test2
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
>         h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
>         omniout_str(ALWAYS,"SETTING H FOR POLE");
>         glob_h_reason := 6;
>         if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 18;
>         term := 1;
>         ratio := 1.0;
>         while (term <= MAX_TERMS)  do # do number 1
>             array_y1[term] := array_y1[term]* ratio;
>             array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             array_y2[term] := array_y2[term]* ratio;
>             array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             ratio := ratio * h_new / float_abs(glob_h);
>             term := term + 1;
>         od;# end do number 1;
>         glob_h := h_new;
>     fi;# end if 17;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 17
>         display_poles();
>     fi;# end if 17
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, 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 := MAX_TERMS - 11;
    cnt := 0;
    while last_no < MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y1_higher[1, last_no - 1],
            array_y1_higher[1, last_no], last_no);
        tmp_ratio := tmp_rad/prev_tmp_rad;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 1] then
            array_rad_test_poles[1, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y1_higher[1, last_no - 1],
                array_y1_higher[1, last_no], last_no);
            array_rad_test_poles[1, 1] := rad_c;
            array_ord_test_poles[1, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 1] := glob_larger_float;
    array_ord_test_poles[2, 1] := glob_larger_float;
    found_sing := 1;
    last_no := MAX_TERMS - 12;
    cnt := 0;
    while last_no < MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
            array_y2_higher[1, last_no], last_no);
        tmp_ratio := tmp_rad/prev_tmp_rad;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 1] then
            array_rad_test_poles[2, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[2, 1] := rad_c;
            array_ord_test_poles[2, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 2] := glob_larger_float;
    array_ord_test_poles[1, 2] := glob_larger_float;
    found_sing := 1;
    last_no := MAX_TERMS - 11;
    cnt := 0;
    while last_no < MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
            last_no);
        tmp_ratio := tmp_rad/prev_tmp_rad;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 2] then
            array_rad_test_poles[1, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y1_higher[1, last_no - 2],
                array_y1_higher[1, last_no - 1],
                array_y1_higher[1, last_no], last_no);
            array_rad_test_poles[1, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 2] := glob_larger_float;
    array_ord_test_poles[2, 2] := glob_larger_float;
    found_sing := 1;
    last_no := MAX_TERMS - 12;
    cnt := 0;
    while last_no < MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
            last_no);
        tmp_ratio := tmp_rad/prev_tmp_rad;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 2] then
            array_rad_test_poles[2, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y2_higher[1, last_no - 2],
                array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[2, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 3] := glob_larger_float;
    array_ord_test_poles[1, 3] := glob_larger_float;
    found_sing := 1;
    last_no := MAX_TERMS - 11;
    cnt := 0;
    while last_no < MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y1_higher[1, last_no - 5],
            array_y1_higher[1, last_no - 4],
            array_y1_higher[1, last_no - 3],
            array_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
            last_no);
        tmp_ratio := tmp_rad/prev_tmp_rad;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 3] then
            array_rad_test_poles[1, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y1_higher[1, last_no - 5],
                array_y1_higher[1, last_no - 4],
                array_y1_higher[1, last_no - 3],
                array_y1_higher[1, last_no - 2],
                array_y1_higher[1, last_no - 1],
                array_y1_higher[1, last_no], last_no);
            array_rad_test_poles[1, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 3] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 3] := glob_larger_float;
    array_ord_test_poles[2, 3] := glob_larger_float;
    found_sing := 1;
    last_no := MAX_TERMS - 12;
    cnt := 0;
    while last_no < MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
            array_y2_higher[1, last_no - 4],
            array_y2_higher[1, last_no - 3],
            array_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
            last_no);
        tmp_ratio := tmp_rad/prev_tmp_rad;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 3] then
            array_rad_test_poles[2, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y2_higher[1, last_no - 5],
                array_y2_higher[1, last_no - 4],
                array_y2_higher[1, last_no - 3],
                array_y2_higher[1, last_no - 2],
                array_y2_higher[1, last_no - 1],
                array_y2_higher[1, last_no], last_no);
            array_rad_test_poles[2, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 3] := tmp_ord
        end if
    end if;
    if
    float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
    then
        h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
        omniout_str(ALWAYS, "SETTING H FOR POLE");
        glob_h_reason := 6;
        if glob_check_sign*h_new < glob_check_sign*glob_min_h then
            omniout_str(ALWAYS, "SETTING H FOR MIN H");
            h_new := glob_min_h;
            glob_h_reason := 5
        end if;
        term := 1;
        ratio := 1.0;
        while term <= MAX_TERMS do
            array_y1[term] := array_y1[term]*ratio;
            array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            array_y2[term] := array_y2[term]*ratio;
            array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            ratio := ratio*h_new/float_abs(glob_h);
            term := term + 1
        end do;
        glob_h := h_new
    end if;
    if reached_interval() then display_poles() end if
end proc

# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_good_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> 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 FULL FULL $eq_no = 1 i = 1
>     array_tmp1[1] :=  (array_m1[1] * (array_y2[1]));
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,2]) then # if number 1
>         if (1 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1);
>             if (2 <= MAX_TERMS) then # if number 3
>                 array_y1[2] := temporary;
>                 array_y1_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (1.0);
>             array_y1_higher[2,1] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #emit pre diff $eq_no = 2 i = 1 order_d = 1
>     array_tmp4[1] := array_y1_higher[2,1];
>     #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,3]) then # if number 1
>         if (1 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp4[1] * expt(glob_h , (2)) * factorial_3(0,2);
>             if (3 <= MAX_TERMS) then # if number 3
>                 array_y2[3] := temporary;
>                 array_y2_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (2.0);
>             array_y2_higher[2,2] := temporary;
>             temporary := temporary / glob_h * (1.0);
>             array_y2_higher[3,1] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     # emit pre mult FULL FULL $eq_no = 1 i = 2
>     array_tmp1[2] :=  ats(2,array_m1,array_y2,1);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp2[2] := array_tmp1[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,3]) then # if number 1
>         if (2 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2);
>             if (3 <= MAX_TERMS) then # if number 3
>                 array_y1[3] := temporary;
>                 array_y1_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (2.0);
>             array_y1_higher[2,2] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #emit pre diff $eq_no = 2 i = 2 order_d = 1
>     array_tmp4[2] := array_y1_higher[2,2];
>     #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,4]) then # if number 1
>         if (2 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp4[2] * expt(glob_h , (2)) * factorial_3(1,3);
>             if (4 <= MAX_TERMS) then # if number 3
>                 array_y2[4] := temporary;
>                 array_y2_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (3.0);
>             array_y2_higher[2,3] := temporary;
>             temporary := temporary / glob_h * (2.0);
>             array_y2_higher[3,2] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     # emit pre mult FULL FULL $eq_no = 1 i = 3
>     array_tmp1[3] :=  ats(3,array_m1,array_y2,1);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp2[3] := array_tmp1[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,4]) then # if number 1
>         if (3 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3);
>             if (4 <= MAX_TERMS) then # if number 3
>                 array_y1[4] := temporary;
>                 array_y1_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (3.0);
>             array_y1_higher[2,3] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #emit pre diff $eq_no = 2 i = 3 order_d = 1
>     array_tmp4[3] := array_y1_higher[2,3];
>     #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,5]) then # if number 1
>         if (3 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp4[3] * expt(glob_h , (2)) * factorial_3(2,4);
>             if (5 <= MAX_TERMS) then # if number 3
>                 array_y2[5] := temporary;
>                 array_y2_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (4.0);
>             array_y2_higher[2,4] := temporary;
>             temporary := temporary / glob_h * (3.0);
>             array_y2_higher[3,3] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     # emit pre mult FULL FULL $eq_no = 1 i = 4
>     array_tmp1[4] :=  ats(4,array_m1,array_y2,1);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp2[4] := array_tmp1[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,5]) then # if number 1
>         if (4 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4);
>             if (5 <= MAX_TERMS) then # if number 3
>                 array_y1[5] := temporary;
>                 array_y1_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (4.0);
>             array_y1_higher[2,4] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #emit pre diff $eq_no = 2 i = 4 order_d = 1
>     array_tmp4[4] := array_y1_higher[2,4];
>     #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,6]) then # if number 1
>         if (4 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp4[4] * expt(glob_h , (2)) * factorial_3(3,5);
>             if (6 <= MAX_TERMS) then # if number 3
>                 array_y2[6] := temporary;
>                 array_y2_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (5.0);
>             array_y2_higher[2,5] := temporary;
>             temporary := temporary / glob_h * (4.0);
>             array_y2_higher[3,4] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     # emit pre mult FULL FULL $eq_no = 1 i = 5
>     array_tmp1[5] :=  ats(5,array_m1,array_y2,1);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp2[5] := array_tmp1[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_y1_set_initial[1,6]) then # if number 1
>         if (5 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5);
>             if (6 <= MAX_TERMS) then # if number 3
>                 array_y1[6] := temporary;
>                 array_y1_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (5.0);
>             array_y1_higher[2,5] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #emit pre diff $eq_no = 2 i = 5 order_d = 1
>     array_tmp4[5] := array_y1_higher[2,5];
>     #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
>     if ( not  array_y2_set_initial[2,7]) then # if number 1
>         if (5 <= MAX_TERMS) then # if number 2
>             temporary := array_tmp4[5] * expt(glob_h , (2)) * factorial_3(4,6);
>             if (7 <= MAX_TERMS) then # if number 3
>                 array_y2[7] := temporary;
>                 array_y2_higher[1,7] := temporary;
>             fi;# end if 3;
>             temporary := temporary / glob_h * (6.0);
>             array_y2_higher[2,6] := temporary;
>             temporary := temporary / glob_h * (5.0);
>             array_y2_higher[3,5] := temporary;
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #END ATOMHDR5
>     #BEGIN OUTFILE3
>     #Top Atomall While Loop-- outfile3
>     while (kkk <= MAX_TERMS) do # do number 1
>         #END OUTFILE3
>         #BEGIN OUTFILE4
>         #emit mult FULL FULL $eq_no = 1
>         array_tmp1[kkk] :=  ats(kkk,array_m1,array_y2,1);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp2[kkk] := array_tmp1[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 1;
>         if (kkk + order_d <= MAX_TERMS) then # if number 1
>             if ( not  array_y1_set_initial[1,kkk + order_d]) then # if number 2
>                 temporary :=  array_tmp2[kkk] * expt(glob_h , (order_d))  * factorial_3((kkk - 1),(kkk + order_d - 1));
>                 array_y1[kkk + order_d] := temporary;
>                 array_y1_higher[1,kkk + order_d] := temporary;
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= 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 := temporary / glob_h * (adj2);
>                         else
>                             temporary := temporary;
>                         fi;# end if 4;
>                         array_y1_higher[adj3,term] := 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 <= MAX_TERMS) then # if number 1
>             array_tmp4[kkk] :=  array_y1_higher[2,kkk];
>         fi;# end if 1;
>         #emit assign $eq_no = 2
>         order_d  := 2;
>         if (kkk + order_d <= MAX_TERMS) then # if number 1
>             if ( not  array_y2_set_initial[2,kkk + order_d]) then # if number 2
>                 temporary :=  array_tmp4[kkk] * expt(glob_h , (order_d))  * factorial_3((kkk - 1),(kkk + order_d - 1));
>                 array_y2[kkk + order_d] := temporary;
>                 array_y2_higher[1,kkk + order_d] := temporary;
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= 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 := temporary / glob_h * (adj2);
>                         else
>                             temporary := temporary;
>                         fi;# end if 4;
>                         array_y2_higher[adj3,term] := 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 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    array_tmp1[1] := array_m1[1]*array_y2[1];
    array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
    if not array_y1_set_initial[1, 2] then
        if 1 <= MAX_TERMS then
            temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1);
            if 2 <= MAX_TERMS then
                array_y1[2] := temporary;
                array_y1_higher[1, 2] := temporary
            end if;
            temporary := temporary*1.0/glob_h;
            array_y1_higher[2, 1] := temporary
        end if
    end if;
    kkk := 2;
    array_tmp4[1] := array_y1_higher[2, 1];
    if not array_y2_set_initial[2, 3] then
        if 1 <= MAX_TERMS then
            temporary := array_tmp4[1]*expt(glob_h, 2)*factorial_3(0, 2);
            if 3 <= MAX_TERMS then
                array_y2[3] := temporary;
                array_y2_higher[1, 3] := temporary
            end if;
            temporary := temporary*2.0/glob_h;
            array_y2_higher[2, 2] := temporary;
            temporary := temporary*1.0/glob_h;
            array_y2_higher[3, 1] := temporary
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := ats(2, array_m1, array_y2, 1);
    array_tmp2[2] := array_tmp1[2];
    if not array_y1_set_initial[1, 3] then
        if 2 <= MAX_TERMS then
            temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2);
            if 3 <= MAX_TERMS then
                array_y1[3] := temporary;
                array_y1_higher[1, 3] := temporary
            end if;
            temporary := temporary*2.0/glob_h;
            array_y1_higher[2, 2] := temporary
        end if
    end if;
    kkk := 3;
    array_tmp4[2] := array_y1_higher[2, 2];
    if not array_y2_set_initial[2, 4] then
        if 2 <= MAX_TERMS then
            temporary := array_tmp4[2]*expt(glob_h, 2)*factorial_3(1, 3);
            if 4 <= MAX_TERMS then
                array_y2[4] := temporary;
                array_y2_higher[1, 4] := temporary
            end if;
            temporary := temporary*3.0/glob_h;
            array_y2_higher[2, 3] := temporary;
            temporary := temporary*2.0/glob_h;
            array_y2_higher[3, 2] := temporary
        end if
    end if;
    kkk := 3;
    array_tmp1[3] := ats(3, array_m1, array_y2, 1);
    array_tmp2[3] := array_tmp1[3];
    if not array_y1_set_initial[1, 4] then
        if 3 <= MAX_TERMS then
            temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3);
            if 4 <= MAX_TERMS then
                array_y1[4] := temporary;
                array_y1_higher[1, 4] := temporary
            end if;
            temporary := temporary*3.0/glob_h;
            array_y1_higher[2, 3] := temporary
        end if
    end if;
    kkk := 4;
    array_tmp4[3] := array_y1_higher[2, 3];
    if not array_y2_set_initial[2, 5] then
        if 3 <= MAX_TERMS then
            temporary := array_tmp4[3]*expt(glob_h, 2)*factorial_3(2, 4);
            if 5 <= MAX_TERMS then
                array_y2[5] := temporary;
                array_y2_higher[1, 5] := temporary
            end if;
            temporary := temporary*4.0/glob_h;
            array_y2_higher[2, 4] := temporary;
            temporary := temporary*3.0/glob_h;
            array_y2_higher[3, 3] := temporary
        end if
    end if;
    kkk := 4;
    array_tmp1[4] := ats(4, array_m1, array_y2, 1);
    array_tmp2[4] := array_tmp1[4];
    if not array_y1_set_initial[1, 5] then
        if 4 <= MAX_TERMS then
            temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4);
            if 5 <= MAX_TERMS then
                array_y1[5] := temporary;
                array_y1_higher[1, 5] := temporary
            end if;
            temporary := temporary*4.0/glob_h;
            array_y1_higher[2, 4] := temporary
        end if
    end if;
    kkk := 5;
    array_tmp4[4] := array_y1_higher[2, 4];
    if not array_y2_set_initial[2, 6] then
        if 4 <= MAX_TERMS then
            temporary := array_tmp4[4]*expt(glob_h, 2)*factorial_3(3, 5);
            if 6 <= MAX_TERMS then
                array_y2[6] := temporary;
                array_y2_higher[1, 6] := temporary
            end if;
            temporary := temporary*5.0/glob_h;
            array_y2_higher[2, 5] := temporary;
            temporary := temporary*4.0/glob_h;
            array_y2_higher[3, 4] := temporary
        end if
    end if;
    kkk := 5;
    array_tmp1[5] := ats(5, array_m1, array_y2, 1);
    array_tmp2[5] := array_tmp1[5];
    if not array_y1_set_initial[1, 6] then
        if 5 <= MAX_TERMS then
            temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5);
            if 6 <= MAX_TERMS then
                array_y1[6] := temporary;
                array_y1_higher[1, 6] := temporary
            end if;
            temporary := temporary*5.0/glob_h;
            array_y1_higher[2, 5] := temporary
        end if
    end if;
    kkk := 6;
    array_tmp4[5] := array_y1_higher[2, 5];
    if not array_y2_set_initial[2, 7] then
        if 5 <= MAX_TERMS then
            temporary := array_tmp4[5]*expt(glob_h, 2)*factorial_3(4, 6);
            if 7 <= MAX_TERMS then
                array_y2[7] := temporary;
                array_y2_higher[1, 7] := temporary
            end if;
            temporary := temporary*6.0/glob_h;
            array_y2_higher[2, 6] := temporary;
            temporary := temporary*5.0/glob_h;
            array_y2_higher[3, 5] := temporary
        end if
    end if;
    kkk := 6;
    while kkk <= MAX_TERMS do
        array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1);
        array_tmp2[kkk] := array_tmp1[kkk];
        order_d := 1;
        if kkk + order_d <= MAX_TERMS then
            if not array_y1_set_initial[1, kkk + order_d] then
                temporary := array_tmp2[kkk]*expt(glob_h, order_d)*
                    factorial_3(kkk - 1, kkk + order_d - 1);
                array_y1[kkk + order_d] := temporary;
                array_y1_higher[1, kkk + order_d] := temporary;
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= MAX_TERMS and adj3 < order_d + 1 do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then temporary := temporary*adj2/glob_h
                        else temporary := temporary
                        end if;
                        array_y1_higher[adj3, term] := temporary
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        if kkk <= MAX_TERMS then array_tmp4[kkk] := array_y1_higher[2, kkk]
        end if;
        order_d := 2;
        if kkk + order_d <= MAX_TERMS then
            if not array_y2_set_initial[2, kkk + order_d] then
                temporary := array_tmp4[kkk]*expt(glob_h, order_d)*
                    factorial_3(kkk - 1, kkk + order_d - 1);
                array_y2[kkk + order_d] := temporary;
                array_y2_higher[1, kkk + order_d] := temporary;
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= MAX_TERMS and adj3 < order_d + 1 do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then temporary := temporary*adj2/glob_h
                        else temporary := temporary
                        end if;
                        array_y2_higher[adj3, term] := temporary
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        kkk := kkk + 1
    end do
end proc

# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
>     #BEGIN OUTFIEMAIN
>     local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
>     term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
>     rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
>     x_start,x_end
>     ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
>     global
>     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,
>     ALWAYS,
>     INFO,
>     DEBUGL,
>     DEBUGMASSIVE,
>     #Top Generate Globals Decl
>     MAX_UNCHANGED,
>     glob_prec,
>     glob_est_digits,
>     glob_check_sign,
>     glob_desired_digits_correct,
>     glob_max_estimated_step_error,
>     glob_ratio_of_radius,
>     glob_percent_done,
>     glob_subiter_method,
>     glob_total_exp_sec,
>     glob_optimal_expect_sec,
>     glob_estimated_size_answer,
>     glob_html_log,
>     glob_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_almost_1,
>     glob_clock_sec,
>     glob_clock_start_sec,
>     glob_not_yet_finished,
>     glob_initial_pass,
>     glob_not_yet_start_msg,
>     glob_reached_optimal_h,
>     glob_optimal_done,
>     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_max_h,
>     glob_min_h,
>     glob_type_given_pole,
>     glob_large_float,
>     glob_larger_float,
>     glob_least_given_sing,
>     glob_least_ratio_sing,
>     glob_least_3_sing,
>     glob_least_6_sing,
>     glob_last_good_h,
>     glob_look_poles,
>     glob_display_interval,
>     glob_next_display,
>     glob_dump_closed_form,
>     glob_abserr,
>     glob_relerr,
>     glob_min_pole_est,
>     glob_max_hours,
>     glob_max_iter,
>     glob_max_rel_trunc_err,
>     glob_max_trunc_err,
>     glob_no_eqs,
>     glob_optimal_clock_start_sec,
>     glob_optimal_start,
>     glob_upper_ratio_limit,
>     glob_lower_ratio_limit,
>     glob_small_float,
>     glob_smallish_float,
>     glob_unchanged_h_cnt,
>     glob_warned,
>     glob_warned2,
>     glob_max_sec,
>     glob_orig_start_sec,
>     glob_start,
>     glob_iter,
>     glob_normmax,
>     glob_max_minutes,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_1,
>     array_const_0D0,
>     array_const_2,
>     #END CONST
>     array_y1_init,
>     array_y2_init,
>     array_norms,
>     array_fact_1,
>     array_1st_rel_error,
>     array_last_rel_error,
>     array_est_rel_error,
>     array_max_est_error,
>     array_type_pole,
>     array_type_real_pole,
>     array_type_complex_pole,
>     array_est_digits,
>     array_good_digits,
>     array_y1,
>     array_x,
>     array_y2,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_m1,
>     array_y1_higher,
>     array_y1_higher_work,
>     array_y1_higher_work2,
>     array_y1_set_initial,
>     array_y2_higher,
>     array_y2_higher_work,
>     array_y2_higher_work2,
>     array_y2_set_initial,
>     array_given_rad_poles,
>     array_given_ord_poles,
>     array_rad_test_poles,
>     array_ord_test_poles,
>     array_fact_2,
>     MAX_TERMS,
>     glob_last;
>     MAX_TERMS := 30;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=30;
>     #END BLOCK 1
>     #END FIRST INPUT BLOCK
>     #START OF INITS AFTER INPUT BLOCK
>     glob_html_log := true;
>     #END OF INITS AFTER INPUT BLOCK
>     # before generate arrays
>     array_y1_init:= Array(0..(MAX_TERMS),[]);
>     array_y2_init:= Array(0..(MAX_TERMS),[]);
>     array_norms:= Array(0..(MAX_TERMS),[]);
>     array_fact_1:= Array(0..(MAX_TERMS),[]);
>     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_good_digits:= Array(0..(3),[]);
>     array_y1:= Array(0..(MAX_TERMS),[]);
>     array_x:= Array(0..(MAX_TERMS),[]);
>     array_y2:= Array(0..(MAX_TERMS),[]);
>     array_tmp0:= Array(0..(MAX_TERMS),[]);
>     array_tmp1:= Array(0..(MAX_TERMS),[]);
>     array_tmp2:= Array(0..(MAX_TERMS),[]);
>     array_tmp3:= Array(0..(MAX_TERMS),[]);
>     array_tmp4:= Array(0..(MAX_TERMS),[]);
>     array_m1:= Array(0..(MAX_TERMS),[]);
>     array_y1_higher := Array(0..(2) ,(0..MAX_TERMS+ 1),[]);
>     array_y1_higher_work := Array(0..(2) ,(0..MAX_TERMS+ 1),[]);
>     array_y1_higher_work2 := Array(0..(2) ,(0..MAX_TERMS+ 1),[]);
>     array_y1_set_initial := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
>     array_y2_higher := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
>     array_y2_higher_work := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
>     array_y2_higher_work2 := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
>     array_y2_set_initial := Array(0..(3) ,(0..MAX_TERMS+ 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..(MAX_TERMS) ,(0..MAX_TERMS+ 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 <= MAX_TERMS) do # do number 1
>         array_y1_init[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_y2_init[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_norms[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_fact_1[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_1st_rel_error[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_last_rel_error[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_est_rel_error[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_max_est_error[term] := 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 <= 3) do # do number 1
>         array_good_digits[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_y1[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_x[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_y2[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_tmp0[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_tmp1[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_tmp2[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_tmp3[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_tmp4[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= MAX_TERMS) do # do number 1
>         array_m1[term] := 0.0;
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= MAX_TERMS) do # do number 2
>             array_y1_higher[ord,term] := 0.0;
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= MAX_TERMS) do # do number 2
>             array_y1_higher_work[ord,term] := 0.0;
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= MAX_TERMS) do # do number 2
>             array_y1_higher_work2[ord,term] := 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 <= MAX_TERMS) do # do number 2
>             array_y1_set_initial[ord,term] := 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 <= MAX_TERMS) do # do number 2
>             array_y2_higher[ord,term] := 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 <= MAX_TERMS) do # do number 2
>             array_y2_higher_work[ord,term] := 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 <= MAX_TERMS) do # do number 2
>             array_y2_higher_work2[ord,term] := 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 <= MAX_TERMS) do # do number 2
>             array_y2_set_initial[ord,term] := 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] := 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] := 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] := 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] := 0.0;
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=MAX_TERMS) do # do number 1
>         term := 1;
>         while (term <= MAX_TERMS) do # do number 2
>             array_fact_2[ord,term] := 0.0;
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y1);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_m1);
>     zero_ats_ar(array_y2);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := 1;
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := 0.0;
>     zero_ats_ar(array_const_2);
>     array_const_2[1]   := 2;
>     zero_ats_ar(array_m1);
>     array_m1[1]   :=  -1.0;
>     #END SYMBOLS INITIALIZATED
>     # before generate factorials init
>     #Initing Factorial Tables
>     iiif := 0;
>     while (iiif <= MAX_TERMS) do # do number 1
>         jjjf := 0;
>         while (jjjf <= 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
>     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(10.0);
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     MAX_UNCHANGED := 10;
>     glob_prec := 1.0e-16;
>     glob_est_digits := 1;
>     glob_check_sign := 1.0;
>     glob_desired_digits_correct := 8.0;
>     glob_max_estimated_step_error := 0.0;
>     glob_ratio_of_radius := 0.1;
>     glob_percent_done := 0.0;
>     glob_subiter_method := 3;
>     glob_total_exp_sec := 0.1;
>     glob_optimal_expect_sec := 0.1;
>     glob_estimated_size_answer := 100.0;
>     glob_html_log := true;
>     glob_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 := 60.0;
>     glob_hours_in_day := 24.0;
>     glob_days_in_year := 365;
>     glob_sec_in_hour := 3600;
>     glob_sec_in_day := 86400;
>     glob_sec_in_year := 31536000;
>     glob_almost_1 := 0.9990;
>     glob_clock_sec := 0.0;
>     glob_clock_start_sec := 0.0;
>     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_disp_incr := 0.1;
>     glob_h := 0.1;
>     glob_diff_rc_fm := 0.1;
>     glob_diff_rc_fmm1 := 0.1;
>     glob_diff_rc_fmm2 := 0.1;
>     glob_diff_ord_fm := 0.1;
>     glob_diff_ord_fmm1 := 0.1;
>     glob_diff_ord_fmm2 := 0.1;
>     glob_six_term_ord_save := 0.1;
>     glob_guess_error_rc := 0.1;
>     glob_guess_error_ord := 0.1;
>     glob_max_h := 0.1;
>     glob_min_h := 0.000001;
>     glob_type_given_pole := 0;
>     glob_large_float := 1.0e100;
>     glob_larger_float := 1.1e100;
>     glob_least_given_sing := 9.9e100;
>     glob_least_ratio_sing := 9.9e100;
>     glob_least_3_sing := 9.9e100;
>     glob_least_6_sing := 9.9e100;
>     glob_last_good_h := 0.1;
>     glob_look_poles := false;
>     glob_display_interval := 0.1;
>     glob_next_display := 0.0;
>     glob_dump_closed_form := false;
>     glob_abserr := 0.1e-10;
>     glob_relerr := 0.1e-10;
>     glob_min_pole_est := 0.1e+10;
>     glob_max_hours := 0.0;
>     glob_max_iter := 1000;
>     glob_max_rel_trunc_err := 0.1e-10;
>     glob_max_trunc_err := 0.1e-10;
>     glob_no_eqs := 0;
>     glob_optimal_clock_start_sec := 0.0;
>     glob_optimal_start := 0.0;
>     glob_upper_ratio_limit := 1.0001;
>     glob_lower_ratio_limit := 0.9999;
>     glob_small_float := 0.0;
>     glob_smallish_float := 0.0;
>     glob_unchanged_h_cnt := 0;
>     glob_warned := false;
>     glob_warned2 := false;
>     glob_max_sec := 10000.0;
>     glob_orig_start_sec := 0.0;
>     glob_start := 0;
>     glob_iter := 0;
>     glob_normmax := 0.0;
>     glob_max_minutes := 0.0;
>     # before generate set diff initial
>     array_y1_set_initial[1,1] := true;
>     array_y1_set_initial[1,2] := false;
>     array_y1_set_initial[1,3] := false;
>     array_y1_set_initial[1,4] := false;
>     array_y1_set_initial[1,5] := false;
>     array_y1_set_initial[1,6] := false;
>     array_y1_set_initial[1,7] := false;
>     array_y1_set_initial[1,8] := false;
>     array_y1_set_initial[1,9] := false;
>     array_y1_set_initial[1,10] := false;
>     array_y1_set_initial[1,11] := false;
>     array_y1_set_initial[1,12] := false;
>     array_y1_set_initial[1,13] := false;
>     array_y1_set_initial[1,14] := false;
>     array_y1_set_initial[1,15] := false;
>     array_y1_set_initial[1,16] := false;
>     array_y1_set_initial[1,17] := false;
>     array_y1_set_initial[1,18] := false;
>     array_y1_set_initial[1,19] := false;
>     array_y1_set_initial[1,20] := false;
>     array_y1_set_initial[1,21] := false;
>     array_y1_set_initial[1,22] := false;
>     array_y1_set_initial[1,23] := false;
>     array_y1_set_initial[1,24] := false;
>     array_y1_set_initial[1,25] := false;
>     array_y1_set_initial[1,26] := false;
>     array_y1_set_initial[1,27] := false;
>     array_y1_set_initial[1,28] := false;
>     array_y1_set_initial[1,29] := false;
>     array_y1_set_initial[1,30] := false;
>     array_y2_set_initial[2,1] := true;
>     array_y2_set_initial[2,2] := true;
>     array_y2_set_initial[2,3] := false;
>     array_y2_set_initial[2,4] := false;
>     array_y2_set_initial[2,5] := false;
>     array_y2_set_initial[2,6] := false;
>     array_y2_set_initial[2,7] := false;
>     array_y2_set_initial[2,8] := false;
>     array_y2_set_initial[2,9] := false;
>     array_y2_set_initial[2,10] := false;
>     array_y2_set_initial[2,11] := false;
>     array_y2_set_initial[2,12] := false;
>     array_y2_set_initial[2,13] := false;
>     array_y2_set_initial[2,14] := false;
>     array_y2_set_initial[2,15] := false;
>     array_y2_set_initial[2,16] := false;
>     array_y2_set_initial[2,17] := false;
>     array_y2_set_initial[2,18] := false;
>     array_y2_set_initial[2,19] := false;
>     array_y2_set_initial[2,20] := false;
>     array_y2_set_initial[2,21] := false;
>     array_y2_set_initial[2,22] := false;
>     array_y2_set_initial[2,23] := false;
>     array_y2_set_initial[2,24] := false;
>     array_y2_set_initial[2,25] := false;
>     array_y2_set_initial[2,26] := false;
>     array_y2_set_initial[2,27] := false;
>     array_y2_set_initial[2,28] := false;
>     array_y2_set_initial[2,29] := false;
>     array_y2_set_initial[2,30] := false;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     MAX_TERMS := 30;
>     glob_iolevel := INFO;
>     # set default block
>     #Write Set Defaults
>     glob_orig_start_sec   :=  elapsed_time_seconds();
>     glob_display_flag   :=   true;
>     glob_no_eqs   := 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/mtest5postode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; ");
>     omniout_str(ALWAYS,"diff  (  y2  ,  x  ,  2  )   =  diff  (  y1 ,  x  ,  1 )   ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=30;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := 0.5;");
>     omniout_str(ALWAYS,"x_end := 5.0;");
>     omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
>     omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
>     omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 3;");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=16;");
>     omniout_str(ALWAYS,"glob_max_minutes:=3.0;");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000000;");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
>     omniout_str(ALWAYS,"return(  - cos(x));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
>     omniout_str(ALWAYS,"return( - sin(x));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
>     omniout_str(ALWAYS,"return( - cos(x));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := 0.0;
>     glob_smallish_float   := 0.0;
>     glob_large_float   :=  1.0e100;
>     glob_larger_float   :=  1.1e100;
>     glob_almost_1   :=  0.99;
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := 0.5;
>     x_end := 5.0;
>     array_y1_init[0 + 1] := exact_soln_y1(x_start);
>     array_y2_init[0 + 1] := exact_soln_y2(x_start);
>     array_y2_init[1 + 1] := exact_soln_y2p(x_start);
>     glob_look_poles := true;
>     glob_type_given_pole := 3;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=16;
>     glob_max_minutes:=3.0;
>     glob_subiter_method:=3;
>     glob_max_iter:=100000000;
>     #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
>     #BEGIN OPTIMIZE CODE
>     omniout_str(ALWAYS,"START of Optimize");
>     #Start Series -- INITIALIZE FOR OPTIMIZE
>     glob_check_sign := my_check_sign(x_start,x_end);
>     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 := float_abs(glob_display_interval) * glob_check_sign;
>     display_max := (x_end - x_start)/10.0;
>     if (glob_display_interval > display_max) then # if number 17
>         glob_display_interval := display_max;
>     fi;# end if 17;
>     chk_data();
>     min_value := glob_larger_float;
>     est_answer := est_size_answer();
>     opt_iter := 1;
>     glob_prec = expt(10.0,-Digits);
>     est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>     omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>     estimated_step_error  := glob_small_float;
>     while ((opt_iter <= 100) and ( not found_h)) do # do number 1
>         omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
>         array_x[1]   := x_start;
>         array_x[2]   :=  glob_h;
>         glob_next_display := x_start;
>         order_diff := 1;
>         #Start Series array_y1
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 2
>             array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / 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 < MAX_TERMS) then # if number 17
>                     array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
>                 fi;# end if 17;
>                 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_y2
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 2
>             array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / 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 < MAX_TERMS) then # if number 17
>                     array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
>                 fi;# end if 17;
>                 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 17
>             atomall();
>         elif
>         (glob_subiter_method  =  2 ) then # if number 18
>             subiter := 1;
>             while (subiter <= 3) do # do number 2
>                 atomall();
>                 subiter := subiter + 1;
>             od;# end do number 2;
>         else
>             subiter := 1;
>             while (subiter <= 3 + MAX_TERMS) do # do number 2
>                 atomall();
>                 subiter := subiter + 1;
>             od;# end do number 2;
>         fi;# end if 18;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 18
>             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 18;
>         if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 18
>             omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>             glob_h_reason := 2;
>             glob_h := glob_display_interval;
>             found_h := true;
>         fi;# end if 18;
>         if (glob_look_poles)  then # if number 18
>             check_for_pole();
>             if ((opt_iter > 2) and ( not  found_h) and ((glob_min_pole_est < 0.999 * last_min_pole_est) or (glob_min_pole_est > 1.111 * last_min_pole_est))) then # if number 19
>                 omniout_str(ALWAYS,"SETTING H FOR POLE ACCURACY");
>                 glob_h_reason := 4;
>                 found_h := true;
>                 glob_h := glob_h/2.0;
>                 last_min_pole_est :=  glob_min_pole_est;
>             else
>                 last_min_pole_est :=  glob_min_pole_est;
>             fi;# end if 19;
>         fi;# end if 18;
>         if ( not found_h) then # if number 18
>             est_answer := est_size_answer();
>             est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>             omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>             estimated_step_error := test_suggested_h();
>             omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
>             if (estimated_step_error < est_needed_step_err) then # if number 19
>                 omniout_str(ALWAYS,"Double H and LOOP");
>                 glob_h := glob_h*2.0;
>             else
>                 omniout_str(ALWAYS,"Found H for OPTIMAL");
>                 found_h := true;
>                 glob_h_reason := 3;
>                 glob_h := glob_h/2.0;
>             fi;# end if 19;
>         fi;# end if 18;
>         opt_iter := opt_iter + 1;
>     od;# end do number 1;
>     if (( not found_h) and (opt_iter = 1)) then # if number 18
>         omniout_str(ALWAYS,"Beginning glob_h too large.");
>         found_h := false;
>     fi;# end if 18;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 18
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 18;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 18
>         omniout_str(ALWAYS,"START of Soultion");
>         #Start Series -- INITIALIZE FOR SOLUTION
>         array_x[1]   := x_start;
>         array_x[2]   :=  glob_h;
>         glob_next_display := x_start;
>         glob_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         order_diff := 1;
>         #Start Series array_y1
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / 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 < MAX_TERMS) then # if number 19
>                     array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((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_y2
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / 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 < MAX_TERMS) then # if number 19
>                     array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
>                 fi;# end if 19;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         current_iter   :=  1;
>         glob_clock_start_sec   := elapsed_time_seconds();
>         glob_clock_sec   :=  elapsed_time_seconds();
>         glob_iter   :=  0;
>         omniout_str(DEBUGL," ");
>         glob_reached_optimal_h   :=  true;
>         glob_optimal_clock_start_sec := elapsed_time_seconds();
>         while ((glob_iter < glob_max_iter)  and (glob_check_sign * array_x[1] < glob_check_sign * x_end )  and  (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
>             #left paren 0001C
>             if (reached_interval()) then # if number 19
>                 omniout_str(INFO," ");
>                 omniout_str(INFO,"TOP MAIN SOLVE Loop");
>             fi;# end if 19;
>             glob_iter   :=  glob_iter + 1;
>             glob_clock_sec   := elapsed_time_seconds();
>             track_estimated_error();
>             if (glob_subiter_method  =  1 ) then # if number 19
>                 atomall();
>             elif
>             (glob_subiter_method  =  2 ) then # if number 20
>                 subiter := 1;
>                 while (subiter <= 3) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 3 + 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);
>             check_for_pole();
>             if (reached_interval()) then # if number 20
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 20;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y1;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y1
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y1
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y1
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y1
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y1
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y1
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (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 := MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_y1[term_no] := array_y1_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
>                     ord := ord + 1;
>                 od;# end do number 3;
>                 term_no   :=  term_no - 1;
>             od;# end do number 2;
>             #END PART 2 HEVE MOVED TERMS to REGULAR Array
>             #Jump Series array_y2;
>             order_diff  := 3;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =2
>             #sum_and_adjust array_y2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 3;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 3;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 2;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 2;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 3;
>             #adjust_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 1;
>             calc_term := 3;
>             #sum_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (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 := MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_y2[term_no] := array_y2_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
>                     ord := ord + 1;
>                 od;# end do number 3;
>                 term_no   :=  term_no - 1;
>             od;# end do number 2;
>             #END PART 2 HEVE MOVED TERMS to REGULAR Array
>             ;
>         od;# end do number 1;#right paren 0001C
>         omniout_str(ALWAYS,"Finished!");
>         if (glob_iter >= glob_max_iter)  then # if number 20
>             omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
>         fi;# end if 20;
>         if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec  )) then # if number 20
>             omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
>         fi;# end if 20;
>         glob_clock_sec   := elapsed_time_seconds();
>         omniout_str(INFO,"diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; ");
>         omniout_str(INFO,"diff  (  y2  ,  x  ,  2  )   =  diff  (  y1 ,  x  ,  1 )   ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(x_start,x_end);
>         if (glob_html_log)  then # if number 20
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2014-09-23T14:50:42-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"mtest5.ode.txt\">mtest5</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; ")
>             ;
>             logitem_float(html_log_file,x_start)
>             ;
>             logitem_float(html_log_file,x_end)
>             ;
>             logitem_float(html_log_file,array_x[1])
>             ;
>             logitem_float(html_log_file,glob_h)
>             ;
>             logitem_h_reason(html_log_file)
>             ;
>             logitem_integer(html_log_file,Digits)
>             ;
>             ;
>             logitem_float(html_log_file,glob_desired_digits_correct)
>             ;
>             if (array_est_digits[1] <> -16) then # if number 21
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             if (array_good_digits[1] <> -16) then # if number 21
>                 logitem_integer(html_log_file,array_good_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             logitem_integer(html_log_file,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 (glob_percent_done < 100.0)  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> 269 </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.mtest5.mxt.txt\">mtest5 diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.mtest5.mxt.txt\">mtest5 maple results</a>")
>             ;
>             logitem_str(html_log_file,"OK")
>             ;
>             logend(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logitem_str(html_log_file,"diff  (  y2  ,  x  ,  2  )   =  diff  (  y1 ,  x  ,  1 )   ; ")
>             ;
>             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 (array_good_digits[2] <> -16) then # if number 26
>                 logitem_integer(html_log_file,array_good_digits[2])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             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 (glob_percent_done < 100.0)  then # if number 31
>                 logditto(html_log_file)
>                 ;
>                 0;
>             else
>                 logditto(html_log_file)
>                 ;
>                 0;
>             fi;# end if 31;
>             logditto(html_log_file);
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logend(html_log_file)
>             ;
>             ;
>         fi;# end if 30;
>         if (glob_html_log)  then # if number 30
>             fclose(html_log_file);
>         fi;# end if 30
>         ;
>         ;;
>     fi;# end if 29
>     #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_good_digits, array_y1,
array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, MAX_TERMS, glob_last;
    MAX_TERMS := 30;
    Digits := 32;
    max_terms := 30;
    glob_html_log := true;
    array_y1_init := Array(0 .. MAX_TERMS, []);
    array_y2_init := Array(0 .. MAX_TERMS, []);
    array_norms := Array(0 .. MAX_TERMS, []);
    array_fact_1 := Array(0 .. MAX_TERMS, []);
    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_good_digits := Array(0 .. 3, []);
    array_y1 := Array(0 .. MAX_TERMS, []);
    array_x := Array(0 .. MAX_TERMS, []);
    array_y2 := Array(0 .. MAX_TERMS, []);
    array_tmp0 := Array(0 .. MAX_TERMS, []);
    array_tmp1 := Array(0 .. MAX_TERMS, []);
    array_tmp2 := Array(0 .. MAX_TERMS, []);
    array_tmp3 := Array(0 .. MAX_TERMS, []);
    array_tmp4 := Array(0 .. MAX_TERMS, []);
    array_m1 := Array(0 .. MAX_TERMS, []);
    array_y1_higher := Array(0 .. 2, 0 .. MAX_TERMS + 1, []);
    array_y1_higher_work := Array(0 .. 2, 0 .. MAX_TERMS + 1, []);
    array_y1_higher_work2 := Array(0 .. 2, 0 .. MAX_TERMS + 1, []);
    array_y1_set_initial := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
    array_y2_higher := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
    array_y2_higher_work := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
    array_y2_higher_work2 := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
    array_y2_set_initial := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
    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 .. MAX_TERMS, 0 .. MAX_TERMS + 1, []);
    term := 1;
    while term <= MAX_TERMS do array_y1_init[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_y2_init[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_norms[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_fact_1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_1st_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_last_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_est_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_max_est_error[term] := 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 <= 3 do array_good_digits[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_y1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_x[term] := 0.; term := term + 1 end do
    ;
    term := 1;
    while term <= MAX_TERMS do array_y2[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_tmp0[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_tmp1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_tmp2[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_tmp3[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_tmp4[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= MAX_TERMS do array_m1[term] := 0.; term := term + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= MAX_TERMS do
            array_y1_higher[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= MAX_TERMS do
            array_y1_higher_work[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= MAX_TERMS do
            array_y1_higher_work2[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= MAX_TERMS do
            array_y1_set_initial[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= MAX_TERMS do
            array_y2_higher[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= MAX_TERMS do
            array_y2_higher_work[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= MAX_TERMS do
            array_y2_higher_work2[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= MAX_TERMS do
            array_y2_set_initial[ord, term] := 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] := 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] := 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] := 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] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= MAX_TERMS do
        term := 1;
        while term <= MAX_TERMS do
            array_fact_2[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y1);
    zero_ats_ar(array_x);
    zero_ats_ar(array_m1);
    zero_ats_ar(array_y2);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_const_1);
    array_const_1[1] := 1;
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := 0.;
    zero_ats_ar(array_const_2);
    array_const_2[1] := 2;
    zero_ats_ar(array_m1);
    array_m1[1] := -1.0;
    iiif := 0;
    while iiif <= MAX_TERMS do
        jjjf := 0;
        while jjjf <= MAX_TERMS do
            array_fact_1[iiif] := 0;
            array_fact_2[iiif, jjjf] := 0;
            jjjf := jjjf + 1
        end do;
        iiif := iiif + 1
    end do;
    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(10.0);
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    MAX_UNCHANGED := 10;
    glob_prec := 0.10*10^(-15);
    glob_est_digits := 1;
    glob_check_sign := 1.0;
    glob_desired_digits_correct := 8.0;
    glob_max_estimated_step_error := 0.;
    glob_ratio_of_radius := 0.1;
    glob_percent_done := 0.;
    glob_subiter_method := 3;
    glob_total_exp_sec := 0.1;
    glob_optimal_expect_sec := 0.1;
    glob_estimated_size_answer := 100.0;
    glob_html_log := true;
    glob_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 := 60.0;
    glob_hours_in_day := 24.0;
    glob_days_in_year := 365;
    glob_sec_in_hour := 3600;
    glob_sec_in_day := 86400;
    glob_sec_in_year := 31536000;
    glob_almost_1 := 0.9990;
    glob_clock_sec := 0.;
    glob_clock_start_sec := 0.;
    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_disp_incr := 0.1;
    glob_h := 0.1;
    glob_diff_rc_fm := 0.1;
    glob_diff_rc_fmm1 := 0.1;
    glob_diff_rc_fmm2 := 0.1;
    glob_diff_ord_fm := 0.1;
    glob_diff_ord_fmm1 := 0.1;
    glob_diff_ord_fmm2 := 0.1;
    glob_six_term_ord_save := 0.1;
    glob_guess_error_rc := 0.1;
    glob_guess_error_ord := 0.1;
    glob_max_h := 0.1;
    glob_min_h := 0.1*10^(-5);
    glob_type_given_pole := 0;
    glob_large_float := 0.10*10^101;
    glob_larger_float := 0.11*10^101;
    glob_least_given_sing := 0.99*10^101;
    glob_least_ratio_sing := 0.99*10^101;
    glob_least_3_sing := 0.99*10^101;
    glob_least_6_sing := 0.99*10^101;
    glob_last_good_h := 0.1;
    glob_look_poles := false;
    glob_display_interval := 0.1;
    glob_next_display := 0.;
    glob_dump_closed_form := false;
    glob_abserr := 0.1*10^(-10);
    glob_relerr := 0.1*10^(-10);
    glob_min_pole_est := 0.1*10^10;
    glob_max_hours := 0.;
    glob_max_iter := 1000;
    glob_max_rel_trunc_err := 0.1*10^(-10);
    glob_max_trunc_err := 0.1*10^(-10);
    glob_no_eqs := 0;
    glob_optimal_clock_start_sec := 0.;
    glob_optimal_start := 0.;
    glob_upper_ratio_limit := 1.0001;
    glob_lower_ratio_limit := 0.9999;
    glob_small_float := 0.;
    glob_smallish_float := 0.;
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_max_sec := 10000.0;
    glob_orig_start_sec := 0.;
    glob_start := 0;
    glob_iter := 0;
    glob_normmax := 0.;
    glob_max_minutes := 0.;
    array_y1_set_initial[1, 1] := true;
    array_y1_set_initial[1, 2] := false;
    array_y1_set_initial[1, 3] := false;
    array_y1_set_initial[1, 4] := false;
    array_y1_set_initial[1, 5] := false;
    array_y1_set_initial[1, 6] := false;
    array_y1_set_initial[1, 7] := false;
    array_y1_set_initial[1, 8] := false;
    array_y1_set_initial[1, 9] := false;
    array_y1_set_initial[1, 10] := false;
    array_y1_set_initial[1, 11] := false;
    array_y1_set_initial[1, 12] := false;
    array_y1_set_initial[1, 13] := false;
    array_y1_set_initial[1, 14] := false;
    array_y1_set_initial[1, 15] := false;
    array_y1_set_initial[1, 16] := false;
    array_y1_set_initial[1, 17] := false;
    array_y1_set_initial[1, 18] := false;
    array_y1_set_initial[1, 19] := false;
    array_y1_set_initial[1, 20] := false;
    array_y1_set_initial[1, 21] := false;
    array_y1_set_initial[1, 22] := false;
    array_y1_set_initial[1, 23] := false;
    array_y1_set_initial[1, 24] := false;
    array_y1_set_initial[1, 25] := false;
    array_y1_set_initial[1, 26] := false;
    array_y1_set_initial[1, 27] := false;
    array_y1_set_initial[1, 28] := false;
    array_y1_set_initial[1, 29] := false;
    array_y1_set_initial[1, 30] := false;
    array_y2_set_initial[2, 1] := true;
    array_y2_set_initial[2, 2] := true;
    array_y2_set_initial[2, 3] := false;
    array_y2_set_initial[2, 4] := false;
    array_y2_set_initial[2, 5] := false;
    array_y2_set_initial[2, 6] := false;
    array_y2_set_initial[2, 7] := false;
    array_y2_set_initial[2, 8] := false;
    array_y2_set_initial[2, 9] := false;
    array_y2_set_initial[2, 10] := false;
    array_y2_set_initial[2, 11] := false;
    array_y2_set_initial[2, 12] := false;
    array_y2_set_initial[2, 13] := false;
    array_y2_set_initial[2, 14] := false;
    array_y2_set_initial[2, 15] := false;
    array_y2_set_initial[2, 16] := false;
    array_y2_set_initial[2, 17] := false;
    array_y2_set_initial[2, 18] := false;
    array_y2_set_initial[2, 19] := false;
    array_y2_set_initial[2, 20] := false;
    array_y2_set_initial[2, 21] := false;
    array_y2_set_initial[2, 22] := false;
    array_y2_set_initial[2, 23] := false;
    array_y2_set_initial[2, 24] := false;
    array_y2_set_initial[2, 25] := false;
    array_y2_set_initial[2, 26] := false;
    array_y2_set_initial[2, 27] := false;
    array_y2_set_initial[2, 28] := false;
    array_y2_set_initial[2, 29] := false;
    array_y2_set_initial[2, 30] := false;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    MAX_TERMS := 30;
    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/mtest5postode.ode#################");
    omniout_str(ALWAYS, "diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; ");
    omniout_str(ALWAYS,
        "diff  (  y2  ,  x  ,  2  )   =  diff  (  y1 ,  x  ,  1 )   ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=30;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := 0.5;");
    omniout_str(ALWAYS, "x_end := 5.0;");
    omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
    omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
    omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
        ;
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 3;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=16;");
    omniout_str(ALWAYS, "glob_max_minutes:=3.0;");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000000;");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
    omniout_str(ALWAYS, "return(  - cos(x));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
    omniout_str(ALWAYS, "return( - sin(x));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
    omniout_str(ALWAYS, "return( - cos(x));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := 0.;
    glob_smallish_float := 0.;
    glob_large_float := 0.10*10^101;
    glob_larger_float := 0.11*10^101;
    glob_almost_1 := 0.99;
    x_start := 0.5;
    x_end := 5.0;
    array_y1_init[1] := exact_soln_y1(x_start);
    array_y2_init[1] := exact_soln_y2(x_start);
    array_y2_init[2] := exact_soln_y2p(x_start);
    glob_look_poles := true;
    glob_type_given_pole := 3;
    glob_desired_digits_correct := 16;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000000;
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    omniout_str(ALWAYS, "START of Optimize");
    glob_check_sign := my_check_sign(x_start, x_end);
    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 :=
        float_abs(glob_display_interval)*glob_check_sign;
    display_max := (x_end - x_start)/10.0;
    if display_max < glob_display_interval then
        glob_display_interval := display_max
    end if;
    chk_data();
    min_value := glob_larger_float;
    est_answer := est_size_answer();
    opt_iter := 1;
    glob_prec = expt(10.0, -Digits);
    est_needed_step_err :=
        estimated_needed_step_error(x_start, x_end, glob_h, est_answer);
    omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err,
        16, "");
    estimated_step_error := glob_small_float;
    while opt_iter <= 100 and not found_h do
        omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
        array_x[1] := x_start;
        array_x[2] := glob_h;
        glob_next_display := x_start;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y1[term_no] := array_y1_init[term_no]*
                expt(glob_h, term_no - 1)/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 < MAX_TERMS then
                    array_y1_higher[r_order, term_no] := array_y1_init[it]*
                    expt(glob_h, term_no - 1)/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_y2[term_no] := array_y2_init[term_no]*
                expt(glob_h, term_no - 1)/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 < MAX_TERMS then
                    array_y2_higher[r_order, term_no] := array_y2_init[it]*
                    expt(glob_h, term_no - 1)/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 + MAX_TERMS do
                atomall(); subiter := subiter + 1
            end do
        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;
        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();
            if 2 < opt_iter and not found_h and (
            glob_min_pole_est < 0.999*last_min_pole_est or
            1.111*last_min_pole_est < glob_min_pole_est) then
                omniout_str(ALWAYS, "SETTING H FOR POLE ACCURACY");
                glob_h_reason := 4;
                found_h := true;
                glob_h := glob_h/2.0;
                last_min_pole_est := glob_min_pole_est
            else last_min_pole_est := glob_min_pole_est
            end if
        end if;
        if not found_h then
            est_answer := est_size_answer();
            est_needed_step_err := estimated_needed_step_error(x_start,
                x_end, glob_h, est_answer);
            omniout_float(ALWAYS, "est_needed_step_err", 32,
                est_needed_step_err, 16, "");
            estimated_step_error := test_suggested_h();
            omniout_float(ALWAYS, "estimated_step_error", 32,
                estimated_step_error, 32, "");
            if estimated_step_error < est_needed_step_err then
                omniout_str(ALWAYS, "Double H and LOOP");
                glob_h := glob_h*2.0
            else
                omniout_str(ALWAYS, "Found H for OPTIMAL");
                found_h := true;
                glob_h_reason := 3;
                glob_h := glob_h/2.0
            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_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
    end if;
    if found_h then
        omniout_str(ALWAYS, "START of Soultion");
        array_x[1] := x_start;
        array_x[2] := glob_h;
        glob_next_display := x_start;
        glob_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y1[term_no] := array_y1_init[term_no]*
                expt(glob_h, term_no - 1)/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 < MAX_TERMS then
                    array_y1_higher[r_order, term_no] := array_y1_init[it]*
                    expt(glob_h, term_no - 1)/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_y2[term_no] := array_y2_init[term_no]*
                expt(glob_h, term_no - 1)/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 < MAX_TERMS then
                    array_y2_higher[r_order, term_no] := array_y2_init[it]*
                    expt(glob_h, term_no - 1)/factorial_1(term_no - 1)
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        current_iter := 1;
        glob_clock_start_sec := elapsed_time_seconds();
        glob_clock_sec := elapsed_time_seconds();
        glob_iter := 0;
        omniout_str(DEBUGL, " ");
        glob_reached_optimal_h := true;
        glob_optimal_clock_start_sec := elapsed_time_seconds();
        while glob_iter < glob_max_iter and
        glob_check_sign*array_x[1] < glob_check_sign*x_end and
        glob_clock_sec - glob_orig_start_sec < glob_max_sec do
            if reached_interval() then
                omniout_str(INFO, " ");
                omniout_str(INFO, "TOP MAIN SOLVE Loop")
            end if;
            glob_iter := glob_iter + 1;
            glob_clock_sec := elapsed_time_seconds();
            track_estimated_error();
            if glob_subiter_method = 1 then atomall()
            elif glob_subiter_method = 2 then
                subiter := 1;
                while subiter <= 3 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 3 + MAX_TERMS do
                    atomall(); subiter := subiter + 1
                end do
            end if;
            track_estimated_error();
            display_alot(current_iter);
            check_for_pole();
            if reached_interval() then glob_next_display :=
                glob_next_display + glob_display_interval
            end if;
            array_x[1] := array_x[1] + glob_h;
            array_x[2] := glob_h;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 2;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            ord := 1;
            calc_term := 2;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 1;
            calc_term := 2;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            ord := 1;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 1;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            term_no := MAX_TERMS;
            while 1 <= term_no do
                array_y1[term_no] := array_y1_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y1_higher[ord, term_no] :=
                        array_y1_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do;
            order_diff := 3;
            ord := 3;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 3;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            ord := 2;
            calc_term := 2;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 2;
            calc_term := 2;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            ord := 2;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 2;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            ord := 1;
            calc_term := 3;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 1;
            calc_term := 3;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            ord := 1;
            calc_term := 2;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 1;
            calc_term := 2;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            ord := 1;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, calc_term - 1)*
                    factorial_3(iii - calc_term, iii - 1));
                iii := iii - 1
            end do;
            temp_sum := 0.;
            ord := 1;
            calc_term := 1;
            iii := MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
            term_no := MAX_TERMS;
            while 1 <= term_no do
                array_y2[term_no] := array_y2_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y2_higher[ord, term_no] :=
                        array_y2_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do
        end do;
        omniout_str(ALWAYS, "Finished!");
        if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
            "Maximum Iterations Reached before Solution Completed!")
        end if;
        if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
        then omniout_str(ALWAYS,
            "Maximum Time Reached before Solution Completed!")
        end if;
        glob_clock_sec := elapsed_time_seconds();
        omniout_str(INFO, "diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; ");
        omniout_str(INFO,
            "diff  (  y2  ,  x  ,  2  )   =  diff  (  y1 ,  x  ,  1 )   ; ")
            ;
        omniout_int(INFO, "Iterations                      ", 32, glob_iter,
            4, " ");
        prog_report(x_start, x_end);
        if glob_html_log then
            logstart(html_log_file);
            logitem_str(html_log_file, "2014-09-23T14:50:42-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"mtest5.ode.txt\">mtest5</a>");
            logitem_str(html_log_file,
                "diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; ");
            logitem_float(html_log_file, x_start);
            logitem_float(html_log_file, x_end);
            logitem_float(html_log_file, array_x[1]);
            logitem_float(html_log_file, glob_h);
            logitem_h_reason(html_log_file);
            logitem_integer(html_log_file, Digits);
            logitem_float(html_log_file, glob_desired_digits_correct);
            if array_est_digits[1] <> -16 then
                logitem_integer(html_log_file, array_est_digits[1])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if array_good_digits[1] <> -16 then
                logitem_integer(html_log_file, array_good_digits[1])
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_integer(html_log_file, 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 glob_percent_done < 100.0 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> 269 </td>");
            logitem_str(html_log_file,
                "<a href=\"diffeq.mtest5.mxt.txt\">mtest5 diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.mtest5.mxt.txt\\
                ">mtest5 maple results</a>");
            logitem_str(html_log_file, "OK");
            logend(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logitem_str(html_log_file, "diff  (  y2  ,  x  ,  2  )   =  d\
                iff  (  y1 ,  x  ,  1 )   ; ");
            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 array_good_digits[2] <> -16 then
                logitem_integer(html_log_file, array_good_digits[2])
            else logitem_str(html_log_file, "Unknown")
            end if;
            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 glob_percent_done < 100.0 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/mtest5postode.ode#################
diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; 
diff  (  y2  ,  x  ,  2  )   =  diff  (  y1 ,  x  ,  1 )   ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.5;
x_end := 5.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
glob_look_poles := true;







glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=16;
glob_max_minutes:=3.0;
glob_subiter_method:=3;
glob_max_iter:=100000000;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(  - cos(x));
end;
exact_soln_y2 := proc(x)
return( - sin(x));
end;
exact_soln_y2p := proc(x)
return( - cos(x));
end;

#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size                       = 0                                           
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 1.00e-06                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 4500000                                     
step_error                     = 1.5713484026367722764463208046775e-21       
est_needed_step_err            = 1.5713484026367722764463208046775e-21       
opt_iter                       = 1                                  
memory used=3.7MB, alloc=40.3MB, time=0.11
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 1.00e-06                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 4500000                                     
step_error                     = 1.5713484026367722764463208046775e-21       
est_needed_step_err            = 1.5713484026367722764463208046775e-21       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 2                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 2.000e-06                                   
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 2250000                                     
step_error                     = 2.2222222222222222222222222222222e-21       
est_needed_step_err            = 2.2222222222222222222222222222222e-21       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 3                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 4.0000e-06                                  
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 1125000                                     
step_error                     = 3.1426968052735445528926416093548e-21       
est_needed_step_err            = 3.1426968052735445528926416093548e-21       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 4                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 8.00000e-06                                 
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 562500                                      
step_error                     = 4.4444444444444444444444444444443e-21       
est_needed_step_err            = 4.4444444444444444444444444444443e-21       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 5                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 1.6000000e-05                               
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 281250                                      
step_error                     = 6.2853936105470891057852832187097e-21       
est_needed_step_err            = 6.2853936105470891057852832187097e-21       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 6                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 3.20000000e-05                              
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 140625                                      
step_error                     = 8.8888888888888888888888888888890e-21       
est_needed_step_err            = 8.8888888888888888888888888888890e-21       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 7                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 6.400000000e-05                             
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 70312.5                                     
step_error                     = 1.2570787221094178211570566437419e-20       
est_needed_step_err            = 1.2570787221094178211570566437419e-20       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 8                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.000128                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 35156.25                                    
step_error                     = 1.7777777777777777777777777777778e-20       
est_needed_step_err            = 1.7777777777777777777777777777778e-20       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 9                                  
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.000256                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 17578.125                                   
step_error                     = 2.5141574442188356423141132874839e-20       
est_needed_step_err            = 2.5141574442188356423141132874839e-20       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 10                                 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.000512                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 8789.0625                                   
step_error                     = 3.5555555555555555555555555555557e-20       
est_needed_step_err            = 3.5555555555555555555555555555557e-20       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 11                                 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.001024                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 4394.53125                                  
step_error                     = 5.0283148884376712846282265749677e-20       
est_needed_step_err            = 5.0283148884376712846282265749677e-20       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 12                                 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.002048                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 2197.265625                                 
step_error                     = 7.1111111111111111111111111111110e-20       
est_needed_step_err            = 7.1111111111111111111111111111110e-20       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 13                                 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.004096                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 1098.6328125                                
step_error                     = 1.0056629776875342569256453149936e-19       
est_needed_step_err            = 1.0056629776875342569256453149936e-19       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 14                                 
memory used=42.8MB, alloc=40.3MB, time=0.67
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.008192                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 549.31640625                                
step_error                     = 1.4222222222222222222222222222222e-19       
est_needed_step_err            = 1.4222222222222222222222222222222e-19       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 15                                 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.016384                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 274.658203125                               
step_error                     = 2.0113259553750685138512906299872e-19       
est_needed_step_err            = 2.0113259553750685138512906299872e-19       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 16                                 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.032768                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 137.3291015625                              
step_error                     = 2.8444444444444444444444444444444e-19       
est_needed_step_err            = 2.8444444444444444444444444444444e-19       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 17                                 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                       = 0.87758256189037271611628158260383          
min_size                       = 0.47942553860420300027328793521557          
min_size                       = 1                                           
glob_desired_digits_correct    = 16                                          
estimated_h                    = 0.065536                                    
estimated_answer               = 1                                           
desired_abs_gbl_error          = 1.0000000000000000000000000000000e-16       
range                          = 4.5                                         
estimated_steps                = 68.66455078125                              
step_error                     = 4.0226519107501370277025812599743e-19       
est_needed_step_err            = 4.0226519107501370277025812599743e-19       
hn_div_ho                      = 0.5                                         
hn_div_ho_2                    = 0.25                                        
hn_div_ho_3                    = 0.125                                       
max_estimated_step_error       = 0                                           
estimated_step_error           = 0                                           
Double H and LOOP
opt_iter                       = 18                                 
SETTING H FOR MAX H
SETTING H FOR DISPLAY INTERVAL
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y1[1] (closed_form)               = -0.87758256189037271611628158260383          
y1[1] (numeric)                   = -0.87758256189037271611628158260383          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.47942553860420300027328793521557          
y2[1] (numeric)                   = -0.47942553860420300027328793521557          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y1[1] (closed_form)               = -0.82533561490967829724095249895538          
y1[1] (numeric)                   = -0.82533561490946198806587518597307          
absolute error                    = 2.1630917507731298231e-13                    
relative error                    = 2.6208632121247435216007896895707e-11      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 13                                  
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.56464247339503535720094544565866          
y2[1] (numeric)                   = -0.56464247341232639952414247710196          
absolute error                    = 1.729104232319703144330e-11                  
relative error                    = 3.0622992668672068875465547287378e-09      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 11                                  
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.7                                          
y1[1] (closed_form)               = -0.76484218728448842625585999019186          
y1[1] (numeric)                   = -0.76484218727630213216327995299767          
absolute error                    = 8.18629409258003719419e-12                   
relative error                    = 1.0703246014246187991416059247260e-09      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 11                                  
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.64421768723769105367261435139872          
y2[1] (numeric)                   = -0.64421768739184129348405570864642          
absolute error                    = 1.5415023981144135724770e-10                 
relative error                    = 2.3928284315262205170249284147933e-08      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y1[1] (closed_form)               = -0.69670670934716542092074998164232          
y1[1] (numeric)                   = -0.69670670931173030506002930219315          
absolute error                    = 3.543511586072067944917e-11                  
relative error                    = 5.0860879313082000009912955034119e-09      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 11                                  
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.71735609089952276162717461058139          
y2[1] (numeric)                   = -0.71735609130115350491430826790006          
absolute error                    = 4.0163074328713365731867e-10                 
relative error                    = 5.5987639664913431603399267264759e-08      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y1[1] (closed_form)               = -0.62160996827066445648471615140713          
y1[1] (numeric)                   = -0.62160996817818380142837220973709          
absolute error                    = 9.248065505634394167004e-11                  
relative error                    = 1.4877601675794806745487865854410e-08      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.78332690962748338846138231571355          
y2[1] (numeric)                   = -0.78332691037604311962658644468379          
absolute error                    = 7.4855973116520412897024e-10                 
relative error                    = 9.5561600395062000958705638803486e-08      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y1[1] (closed_form)               = -0.54030230586813971740093660744298          
y1[1] (numeric)                   = -0.54030230567951910839316702669449          
absolute error                    = 1.8862060900776958074849e-10                 
relative error                    = 3.4910198783012831990331262723975e-08      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.8414709848078965066525023216303           
y2[1] (numeric)                   = -0.84147098598963347954958662893569          
absolute error                    = 1.18173697289708430730539e-09                
relative error                    = 1.4043704349079472702260212451316e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y1[1] (closed_form)               = -0.45359612142557738777137005178472          
y1[1] (numeric)                   = -0.45359612109383639006787237498666          
absolute error                    = 3.3174099770349767679806e-10                 
relative error                    = 7.3135765945460630286295020778452e-08      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 10                                  
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.8912073600614353399518025778717           
y2[1] (numeric)                   = -0.89120736174759931848086246463907          
absolute error                    = 1.68616397852905988676737e-09                
relative error                    = 1.8919996109691287193575279175645e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y1[1] (closed_form)               = -0.36235775447667357763837335562308          
y1[1] (numeric)                   = -0.36235775394852460084154149753889          
absolute error                    = 5.2814897679683185808419e-10                 
relative error                    = 1.4575346333062424542301054170689e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.93203908596722634967013443549483          
y2[1] (numeric)                   = -0.93203908821252682269653872127288          
absolute error                    = 2.24530047302640428577805e-09                
relative error                    = 2.4090196503898084950459905648888e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=82.1MB, alloc=40.3MB, time=1.25
x[1]                              = 1.3                                          
y1[1] (closed_form)               = -0.26749882862458740699798410929287          
y1[1] (numeric)                   = -0.26749882784215489562581098669901          
absolute error                    = 7.8243251137217312259386e-10                 
relative error                    = 2.9249941593959380079695259891528e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.96355818541719296470134863003955          
y2[1] (numeric)                   = -0.9635581882585375322024406740528           
absolute error                    = 2.84134456750109204401325e-09                
relative error                    = 2.9488043488218322958919600545607e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y1[1] (closed_form)               = -0.16996714290024093861674803520365          
y1[1] (numeric)                   = -0.16996714180289185362222639990748          
absolute error                    = 1.09734908499452163529617e-09                
relative error                    = 6.4562424611596273244655939262313e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.9854497299884601806594745788061           
y2[1] (numeric)                   = -0.98544973344399286051884599744792          
absolute error                    = 3.45553267985937141864182e-09                
relative error                    = 3.5065539871829245091595996907432e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y1[1] (closed_form)               = -0.070737201667702910088189851434269         
y1[1] (numeric)                   = -0.070737200193957700113628985935246         
absolute error                    = 1.473745209974560865499023e-09               
relative error                    = 2.0834089774962660647512106992917e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.99749498660405443094172337114149          
y2[1] (numeric)                   = -0.99749499067250941961912144707771          
absolute error                    = 4.06845498867739807593622e-09                
relative error                    = 4.0786721169680727711679912326312e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y1[1] (closed_form)               = 0.029199522301288726205770462946499          
y1[1] (numeric)                   = 0.029199524211796798219641087964235          
absolute error                    = 1.910508072013870625017736e-09               
relative error                    = 6.5429429026294378973554366986930e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 11                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.99957360304150516434211382554623          
y2[1] (numeric)                   = -0.99957360770188715405864208975704          
absolute error                    = 4.66038198971652826421081e-09                
relative error                    = 4.6623700101082159436712591931466e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.7                                          
y1[1] (closed_form)               = 0.12884449429552468408764285733487           
y1[1] (numeric)                   = 0.12884449670007487510912011510366           
absolute error                    = 2.40455019102147725776879e-09                
relative error                    = 1.8662420960776726703002485684427e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.99166481045246861534613339864788          
y2[1] (numeric)                   = -0.99166481566406618248449782723228          
absolute error                    = 5.21159756713836442858440e-09                
relative error                    = 5.2554023418058565654867567672329e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y1[1] (closed_form)               = 0.22720209469308705531667430653058           
y1[1] (numeric)                   = 0.22720209764391457104263480026048           
absolute error                    = 2.95082751572596049372990e-09                
relative error                    = 1.2987677423097911206540710860723e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.97384763087819518653237317884336          
y2[1] (numeric)                   = -0.97384763658092907974160562822642          
absolute error                    = 5.70273389320923244938306e-09                
relative error                    = 5.8558790024129623815462806364177e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y1[1] (closed_form)               = 0.32328956686350342227883369508031           
y1[1] (numeric)                   = 0.32328957040589432100501867698906           
absolute error                    = 3.54239089872618498190875e-09                
relative error                    = 1.0957331327125144156038470529717e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.94630008768741448848970961163496          
y2[1] (numeric)                   = -0.94630009380251792089754315924671          
absolute error                    = 6.11510343240783354761175e-09                
relative error                    = 6.4621186365437579955672168294331e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2                                            
y1[1] (closed_form)               = 0.41614683654714238699756822950076           
y1[1] (numeric)                   = 0.41614684071761281389994300992136           
absolute error                    = 4.17047042690237478042060e-09                
relative error                    = 1.0021631935269874698136552880977e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.90929742682568169539601986591174          
y2[1] (numeric)                   = -0.9092974332567050443387185316536           
absolute error                    = 6.43102334894269866574186e-09                
relative error                    = 7.0725190231683875546037050568804e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.1                                          
y1[1] (closed_form)               = 0.50484610459985745162093852371917           
y1[1] (numeric)                   = 0.50484610942444906736272259426574           
absolute error                    = 4.82459161574178407054657e-09                
relative error                    = 9.5565590618269105340151191266295e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.86320936664887377068075931326902          
y2[1] (numeric)                   = -0.86320937328300147125614263510354          
absolute error                    = 6.63412770057538332183452e-09                
relative error                    = 7.6854213553430269287910603016528e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.2                                          
y1[1] (closed_form)               = 0.58850111725534570852414261265493           
y1[1] (numeric)                   = 0.58850112274806772968329454175277           
absolute error                    = 5.49272202115915192909784e-09                
relative error                    = 9.3334096743539499906401086157135e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.80849640381959018430403691041612          
y2[1] (numeric)                   = -0.80849641052925312971711883528244          
absolute error                    = 6.70966294541308192486632e-09                
relative error                    = 8.2989397525017218457375565220109e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.3                                          
y1[1] (closed_form)               = 0.66627602127982419331788057116602           
y1[1] (numeric)                   = 0.66627602744127057804015985872025           
absolute error                    = 6.16144638472227928755423e-09                
relative error                    = 9.2475883686868874006057117143305e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.7457052121767201773854062116435           
y2[1] (numeric)                   = -0.74570521882148266771229440671499          
absolute error                    = 6.64476249032688819507149e-09                
relative error                    = 8.9107094624305590051862799443908e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.4                                          
y1[1] (closed_form)               = 0.73739371554124549960882222733478           
y1[1] (numeric)                   = 0.7373937223574135131456756894356            
absolute error                    = 6.81616801353685346210082e-09                
relative error                    = 9.2435938493641756777390901773966e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.67546318055115092656577152534128          
y2[1] (numeric)                   = -0.67546318697984719406449263794666          
absolute error                    = 6.42869626749872111260538e-09                
relative error                    = 9.5174636495406932523027791284353e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.5                                          
y1[1] (closed_form)               = 0.80114361554693371483350279046735           
y1[1] (numeric)                   = 0.80114362298826742467319976320897           
absolute error                    = 7.44133370983969697274162e-09                
relative error                    = 9.2883892044244323913713793238067e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.59847214410395649405185470218616          
y2[1] (numeric)                   = -0.59847215015704813029253559179807          
absolute error                    = 6.05309163624068088961191e-09                
relative error                    = 1.0114241232235597303111883107856e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=121.3MB, alloc=40.3MB, time=1.83
x[1]                              = 2.6                                          
y1[1] (closed_form)               = 0.8568887533689472337977021516452            
y1[1] (numeric)                   = 0.85688876138962644649220255096473           
absolute error                    = 8.02067921269450039931953e-09                
relative error                    = 9.3602339640476853949147774850866e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.51550137182146423525772693520937          
y2[1] (numeric)                   = -0.51550137733358650220841277163292          
absolute error                    = 5.51212226695068583642355e-09                
relative error                    = 1.0692740249117556944136002087221e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.7                                          
y1[1] (closed_form)               = 0.90407214201706114798252728194333           
y1[1] (numeric)                   = 0.90407215055455294775751891797916           
absolute error                    = 8.53749179977499163603583e-09                
relative error                    = 9.4433744863846018457111133315879e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.42737988023382993455605308585788          
y2[1] (numeric)                   = -0.42737988503649200309801060258658          
absolute error                    = 4.80266206854195751672870e-09                
relative error                    = 1.1237454757847524797200574578564e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.8                                          
y1[1] (closed_form)               = 0.94222234066865815258678811736615           
y1[1] (numeric)                   = 0.9422223496435445778793338467431            
absolute error                    = 8.97488642529254572937695e-09                
relative error                    = 9.5252320369769853605587724950613e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.33498815015590491954385375271242          
y2[1] (numeric)                   = -0.33498815408030658456884074097358          
absolute error                    = 3.92440166502498698826116e-09                
relative error                    = 1.1715046228347341983822831612583e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 2.9                                          
y1[1] (closed_form)               = 0.97095816514959052178110666934553           
y1[1] (numeric)                   = 0.9709581744656820661804346671127            
absolute error                    = 9.31609154439932799776717e-09                
relative error                    = 9.5947404108435977500171765253259e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.23924932921398232818425691873958          
y2[1] (numeric)                   = -0.239249332093907733923698941824            
absolute error                    = 2.87992540573944202308442e-09                
relative error                    = 1.2037339520244439587950311861032e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3                                            
y1[1] (closed_form)               = 0.98999249660044545727157279473126           
y1[1] (numeric)                   = 0.98999250614518605530515841685317           
absolute error                    = 9.54474059803358562212191e-09                
relative error                    = 9.6412251919175716187476602176673e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.14112000805986722210074480280811          
y2[1] (numeric)                   = -0.1411200097346146233012575466456           
absolute error                    = 1.67474740120051274383749e-09                
relative error                    = 1.1867540430482657463399634713757e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.1                                          
y1[1] (closed_form)               = 0.99913515027327946449237605454147           
y1[1] (numeric)                   = 0.99913515991844447222035220502663           
absolute error                    = 9.64516500772797615048516e-09                
relative error                    = 9.6535138465400492175987983558182e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = -0.041580662433290579194698271596673         
y2[1] (numeric)                   = -0.041580662750596185633315809424845         
absolute error                    = 3.17305606438617537828172e-10                
relative error                    = 7.6310858911322747140239972649851e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 11                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.2                                          
y1[1] (closed_form)               = 0.99829477579475308466166072228358           
y1[1] (numeric)                   = 0.99829478539743754395824573103231           
absolute error                    = 9.60268445929658500874873e-09                
relative error                    = 9.6190871595534353238143163234579e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.058374143427579909137217414619095          
y2[1] (numeric)                   = 0.058374144608666389562859897918376          
absolute error                    = 1.181086480425642483299281e-09               
relative error                    = 2.0233041738606772096615960989669e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.3                                          
y1[1] (closed_form)               = 0.98747976990886488393659105110285           
y1[1] (numeric)                   = 0.98747977931275512274831275456618           
absolute error                    = 9.40389023881172170346333e-09                
relative error                    = 9.5231219163908669486966858183310e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.15774569414324838201165427760248           
y2[1] (numeric)                   = 0.15774569694957876354943891590637           
absolute error                    = 2.80633038153778463830389e-09                
relative error                    = 1.7790218596961287632076621273292e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.4                                          
y1[1] (closed_form)               = 0.96679819257946101428220153976569           
y1[1] (numeric)                   = 0.96679820161637843874039104066046           
absolute error                    = 9.03691742445818950089477e-09                
relative error                    = 9.3472634659641716956626294961778e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.25554110202683131924990242936374           
y2[1] (numeric)                   = 0.25554110656850610355432535344796           
absolute error                    = 4.54167478430442292408422e-09                
relative error                    = 1.7772776075089305575807022116170e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.5                                          
y1[1] (closed_form)               = 0.93645668729079633769865762667176           
y1[1] (numeric)                   = 0.93645669578249817129990483729202           
absolute error                    = 8.49170183360124721062026e-09                
relative error                    = 9.0679066622590449425047155844233e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.35078322768961984812036880004364           
y2[1] (numeric)                   = 0.35078323405750788294889485380913           
absolute error                    = 6.36788803482852605376549e-09                
relative error                    = 1.8153342384040559715833806225243e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.6                                          
y1[1] (closed_form)               = 0.89675841633414700587029172526594           
y1[1] (numeric)                   = 0.89675842409436478079439712751548           
absolute error                    = 7.76021777492410540224954e-09                
relative error                    = 8.6536324985351684872976556551564e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.44252044329485238426672734749269           
y2[1] (numeric)                   = 0.44252045155832158939839600521976           
absolute error                    = 8.26346920513166865772707e-09                
relative error                    = 1.8673643964569790986640777792303e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.7                                          
y1[1] (closed_form)               = 0.8481000317104081588356701063544            
y1[1] (numeric)                   = 0.84810003854710101813124815388882           
absolute error                    = 6.83669285929557804753442e-09                
relative error                    = 8.0611868926683780643366595119581e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.52983614090849321321077762570121           
y2[1] (numeric)                   = 0.52983615111338864950875899261459           
absolute error                    = 1.020489543629798136691338e-08               
relative error                    = 1.9260474415354096225569595007569e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 3.8                                          
y1[1] (closed_form)               = 0.79096771191441669999656817435073           
y1[1] (numeric)                   = 0.79096771763221307795860873148586           
absolute error                    = 5.71779637796204055713513e-09                
relative error                    = 7.2288619267694082765507658208049e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.61185789094271907573358608611888           
y2[1] (numeric)                   = 0.61185790310962183704353390723926           
absolute error                    = 1.216690276130994782112038e-08               
relative error                    = 1.9885177492054260630704097057960e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
memory used=160.5MB, alloc=40.3MB, time=2.41
x[1]                              = 3.9                                          
y1[1] (closed_form)               = 0.72593230420014012937233048461435           
y1[1] (numeric)                   = 0.7259323086029381892883401577423            
absolute error                    = 4.40279805991600967312795e-09                
relative error                    = 6.0650256703580374773017222774854e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.68776615918397381809088812537869           
y2[1] (numeric)                   = 0.68776617330677096225741420286244           
absolute error                    = 1.412279714416652607748375e-08               
relative error                    = 2.0534300729368617234444791370935e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4                                            
y1[1] (closed_form)               = 0.65364362086361191463916818309775           
y1[1] (numeric)                   = 0.6536436237573062830943826412488            
absolute error                    = 2.89369436845521445815105e-09                
relative error                    = 4.4270215084972235130956900398550e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.75680249530792825137263909451183           
y2[1] (numeric)                   = 0.75680251135272029324534379408479           
absolute error                    = 1.604479204187270469957296e-08               
relative error                    = 2.1200765247667940271651397447532e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.1                                          
y1[1] (closed_form)               = 0.57482394653326891153502867965979           
y1[1] (numeric)                   = 0.57482394772856879754571830572565           
absolute error                    = 1.19529988601068962606586e-09                
relative error                    = 2.0794190868690777767042148343899e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.81827711106441050426503702435845           
y2[1] (numeric)                   = 0.81827712896877891290784409781515           
absolute error                    = 1.790436840864280707345670e-08               
relative error                    = 2.1880568534237625303148376250837e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.2                                          
y1[1] (closed_form)               = 0.49026082134069957765554488137713           
y1[1] (numeric)                   = 0.49026082065600133941160146770083           
absolute error                    = 6.8469823824394341367630e-10                 
relative error                    = 1.3965999493321176500560956226103e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.87157577241358806001857709790882           
y2[1] (numeric)                   = 0.87157579208624078227682232312884           
absolute error                    = 1.967265272225824522522002e-08               
relative error                    = 2.2571362519382880676096204717017e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.3                                          
y1[1] (closed_form)               = 0.40079917207997529690676239633603           
y1[1] (numeric)                   = 0.4007991693442509502033005907617            
absolute error                    = 2.73572434670346180557433e-09                
relative error                    = 6.8256736472439033108764382765110e-07      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 9                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.91616593674945498403170936028464           
y2[1] (numeric)                   = 0.91616595807026330953759960166835           
absolute error                    = 2.132080832550589024138371e-08               
relative error                    = 2.3271775854439475514406435456415e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.4                                          
y1[1] (closed_form)               = 0.30733286997841968311913974221771           
y1[1] (numeric)                   = 0.30733286503408175955397332168418           
absolute error                    = 4.94433792356516642053353e-09                
relative error                    = 1.6087891685364953709795710083099e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.95160207388951595403539233338039           
y2[1] (numeric)                   = 0.95160209670995109896745736179057           
absolute error                    = 2.282043514493206502841018e-08               
relative error                    = 2.3981069158096003241323005040097e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.5                                          
y1[1] (closed_form)               = 0.21079579943077970598048182479383           
y1[1] (numeric)                   = 0.2107957921364822858004912679456            
absolute error                    = 7.29429742017999055684823e-09                
relative error                    = 3.4603618477583862870122404340123e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.97753011766509705538913501449863           
y2[1] (numeric)                   = 0.97753014180906973344920072786923           
absolute error                    = 2.414397267806006571337060e-08               
relative error                    = 2.4698955297387388089947074908879e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.6                                          
y1[1] (closed_form)               = 0.11215252693505451742990782122919           
y1[1] (numeric)                   = 0.11215251716839019553974709129842           
absolute error                    = 9.76666432189016072993077e-09                
relative error                    = 8.7083765197246584418793773008754e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.99369100363346445613810465990883           
y2[1] (numeric)                   = 0.99369102889856548745674025645051           
absolute error                    = 2.526510103131863559654168e-08               
relative error                    = 2.5425510484583182268574405698838e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.7                                          
y1[1] (closed_form)               = 0.012388663462890737150508296327111          
y1[1] (numeric)                   = 0.012388651122943738949996495820701          
absolute error                    = 1.2339946998200511800506410e-08              
relative error                    = 9.9606765775532189796148662572219e-05      % 
Desired digits                    = 16                                  
Estimated correct digits          = 11                                  
Correct digits                    = 7                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.99992325756410088417953654157497           
y2[1] (numeric)                   = 0.99992328372323563024438000234383           
absolute error                    = 2.615913474606484346076886e-08               
relative error                    = 2.6161142415859740216879067840958e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.8                                          
y1[1] (closed_form)               = -0.087498983439446569320215257649488         
y1[1] (numeric)                   = -0.087498998429729921694379792813317         
absolute error                    = 1.4990283352374164535163829e-08              
relative error                    = 1.7131951438896600294574241059924e-05      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 7                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.99616460883584067178159646650363           
y2[1] (numeric)                   = 0.9961646356392448421300889299169            
absolute error                    = 2.680340417034849246341327e-08               
relative error                    = 2.6906601512045347208546449121935e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                              = 4.9                                          
y1[1] (closed_form)               = -0.18651236942257540449432914412192          
y1[1] (numeric)                   = -0.18651238711423617058194124406873          
absolute error                    = 1.769166076608761209994681e-08               
relative error                    = 9.4855160656954361117785947257955e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 12                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
y2[1] (closed_form)               = 0.98245261262433251227637724991833           
y2[1] (numeric)                   = 0.98245263980195173204793765504964           
absolute error                    = 2.717761921977156040513131e-08               
relative error                    = 2.7663033178948512382125568323500e-06      % 
Desired digits                    = 16                                  
Estimated correct digits          = 13                                  
Correct digits                    = 8                                   
h                                 = 0.1                                          
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
Finished!
diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; 
diff  (  y2  ,  x  ,  2  )   =  diff  (  y1 ,  x  ,  1 )   ; 
Iterations                       = 45                                  
Total Elapsed Time               = 2 Seconds
Elapsed Time(since restart)      = 2 Seconds
Time to Timeout                  = 2 Minutes 57 Seconds
Percent Done                     = 102.2                                      % 
> quit
memory used=192.9MB, alloc=40.3MB, time=2.89