|\^/|     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 ATS_MAX_TERMS;
>     local iii;
>     iii  := 1;
>     while (iii <= ATS_MAX_TERMS) do # do number 1
>         arr_a [iii] := glob__0;
>         iii  :=  iii + 1;
>     od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
    iii := 1;
    while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
    end do
end proc

# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
>     global ATS_MAX_TERMS;
>     local iii_ats, lll_ats,ma_ats, ret_ats;
>     ret_ats  := glob__0;
>     if (jjj_ats <=  mmm_ats)  then # if number 6
>         ma_ats  :=  mmm_ats + 1;
>         iii_ats  :=  jjj_ats;
>         while (iii_ats <= mmm_ats) do # do number 1
>             lll_ats  :=  ma_ats - iii_ats;
>             if ((lll_ats <= ATS_MAX_TERMS  and (iii_ats <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_ats  :=  ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
>             fi;# end if 7;
>             iii_ats  :=  iii_ats + 1;
>         od;# end do number 1
>     fi;# end if 6;
>     ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
    ret_ats := glob__0;
    if jjj_ats <= mmm_ats then
        ma_ats := mmm_ats + 1;
        iii_ats := jjj_ats;
        while iii_ats <= mmm_ats do
            lll_ats := ma_ats - iii_ats;
            if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
                ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
            end if;
            iii_ats := iii_ats + 1
        end do
    end if;
    ret_ats
end proc

# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
>     global ATS_MAX_TERMS;
>     local al_att, iii_att,lll_att, ma_att, ret_att;
>     ret_att  := glob__0;
>     if (jjj_att < mmm_att)  then # if number 6
>         ma_att  :=  mmm_att + 2;
>         iii_att  :=  jjj_att;
>         while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) )   do # do number 1
>             lll_att  :=  ma_att - iii_att;
>             al_att  :=  (lll_att - 1);
>             if ((lll_att <= ATS_MAX_TERMS  and (iii_att <= ATS_MAX_TERMS) ))  then # if number 7
>                 ret_att  :=   ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
>             fi;# end if 7;
>             iii_att  :=  iii_att + 1;
>         od;# end do number 1;
>         ret_att  :=  ret_att / c(mmm_att) ;
>     fi;# end if 6;
>     ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
    ret_att := glob__0;
    if jjj_att < mmm_att then
        ma_att := mmm_att + 2;
        iii_att := jjj_att;
        while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
            lll_att := ma_att - iii_att;
            al_att := lll_att - 1;
            if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
                ret_att :=
                ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
            end if;
            iii_att := iii_att + 1
        end do;
        ret_att := ret_att/c(mmm_att)
    end if;
    ret_att
end proc

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

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

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

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

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

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

# End Function number 26
# Begin Function number 27
> c := proc(in_val)
>     #To Force Conversion when needed
>     local ret;
>     ret := evalf(in_val);
>     ret;
>     #End Conversion
> end;
        c := proc(in_val) local ret; ret := evalf(in_val); ret end proc

# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float;
>     local ret,temp;
>     temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
>     if (float_abs(temp) > glob__0)  then # if number 12
>         ret := float_abs((term2*glob_h*term1)/(temp));
>     else
>         ret := glob_larger_float;
>     fi;# end if 12;
>     ret;
>     #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
    temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
         - term1*term3*c(last_no) + term1*term3);
    if glob__0 < float_abs(temp) then
        ret := float_abs(term2*glob_h*term1/temp)
    else ret := glob_larger_float
    end if;
    ret
end proc

# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
>     #TOP THREE TERM ORDER ANALYSIS
>     local ret;
>     ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
>     ret;
>     #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
    ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
         - glob__4*term2*term2*c(last_no) + glob__4*term2*term2
         + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
        /(term2*term2*c(last_no) - glob__2*term2*term2
         - term1*term3*c(last_no) + term1*term3));
    ret
end proc

# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
>     #TOP SIX TERM RADIUS ANALYSIS
>     global glob_h,glob_larger_float,glob_six_term_ord_save;
>     local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
>     if ((term5  <> glob__0) and (term4  <> glob__0) and (term3  <> glob__0) and  (term2  <> glob__0) and (term1  <> glob__0)) then # if number 12
>         rm0 := term6/term5;
>         rm1 := term5/term4;
>         rm2 := term4/term3;
>         rm3 := term3/term2;
>         rm4 := term2/term1;
>         nr1 :=  c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
>         nr2 :=  c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
>         dr1 :=  glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
>         dr2 :=  glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
>         ds1 :=  glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
>         ds2 :=  glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
>         if ((float_abs(nr1 * dr2 - nr2 * dr1)  =  glob__0)  or  (float_abs(dr1) = glob__0))  then # if number 13
>             rad_c :=  glob_larger_float;
>             ord_no :=  glob_larger_float;
>         else
>             if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0)  then # if number 14
>                 rcs :=  ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
>                 #(Manuels)  rcs  :=  (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
>                 ord_no :=  (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
>                 if (float_abs(rcs)  <> glob__0)  then # if number 15
>                     if (rcs > glob__0)  then # if number 16
>                         rad_c  :=  sqrt(rcs) * float_abs(glob_h);
>                     else
>                         rad_c  :=  glob_larger_float;
>                         ord_no :=  glob_larger_float;
>                     fi;# end if 16
>                 else
>                     rad_c :=  glob_larger_float;
>                     ord_no :=  glob_larger_float;
>                 fi;# end if 15
>             else
>                 rad_c :=  glob_larger_float;
>                 ord_no :=  glob_larger_float;
>             fi;# end if 14
>         fi;# end if 13
>     else
>         rad_c :=  glob_larger_float;
>         ord_no :=  glob_larger_float;
>     fi;# end if 12;
>     glob_six_term_ord_save :=  ord_no;
>     rad_c;
>     #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
    if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
    term2 <> glob__0 and term1 <> glob__0 then
        rm0 := term6/term5;
        rm1 := term5/term4;
        rm2 := term4/term3;
        rm3 := term3/term2;
        rm4 := term2/term1;
        nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
             + c(last_no - 3)*rm2;
        nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
             + c(last_no - 4)*rm3;
        dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
        dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
        ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
        ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
        if
        float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
        then rad_c := glob_larger_float; ord_no := glob_larger_float
        else
            if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
                rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
                ord_no :=
                    (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
                if float_abs(rcs) <> glob__0 then
                    if glob__0 < rcs then
                        rad_c := sqrt(rcs)*float_abs(glob_h)
                    else
                        rad_c := glob_larger_float;
                        ord_no := glob_larger_float
                    end if
                else
                    rad_c := glob_larger_float; ord_no := glob_larger_float
                end if
            else rad_c := glob_larger_float; ord_no := glob_larger_float
            end if
        end if
    else rad_c := glob_larger_float; ord_no := glob_larger_float
    end if;
    glob_six_term_ord_save := ord_no;
    rad_c
end proc

# End Function number 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> factorial_1 := proc(nnn)
>     global ATS_MAX_TERMS,array_fact_1;
>     local ret;
>     if (nnn <= ATS_MAX_TERMS) then # if number 12
>         if (array_fact_1[nnn] = 0) then # if number 13
>             ret := factorial_2(nnn);
>             array_fact_1[nnn] := ret;
>         else
>             ret := array_fact_1[nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
    if nnn <= ATS_MAX_TERMS then
        if array_fact_1[nnn] = 0 then
            ret := factorial_2(nnn); array_fact_1[nnn] := ret
        else ret := array_fact_1[nnn]
        end if
    else ret := factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
>     global ATS_MAX_TERMS,array_fact_2;
>     local ret;
>     if ((nnn <= ATS_MAX_TERMS)  and  (mmm <= ATS_MAX_TERMS)) then # if number 12
>         if (array_fact_2[mmm,nnn] = 0) then # if number 13
>             ret := factorial_1(mmm)/factorial_1(nnn);
>             array_fact_2[mmm,nnn] := ret;
>         else
>             ret := array_fact_2[mmm,nnn];
>         fi;# end if 13;
>     else
>         ret := factorial_2(mmm)/factorial_2(nnn);
>     fi;# end if 12;
>     ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
    if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
        if array_fact_2[mmm, nnn] = 0 then
            ret := factorial_1(mmm)/factorial_1(nnn);
            array_fact_2[mmm, nnn] := ret
        else ret := array_fact_2[mmm, nnn]
        end if
    else ret := factorial_2(mmm)/factorial_2(nnn)
    end if;
    ret
end proc

# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
>     (mmm);
> end;
                      convfloat := proc(mmm) mmm end proc

# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
>     time();
> end;
                 elapsed_time_seconds := proc() time() end proc

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

# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
>     trunc(x);
> end;
                     int_trunc := proc(x) trunc(x) end proc

# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
>     local desired_abs_gbl_error,range,estimated_steps,step_error;
>     global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
>     omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
>     desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
>     omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
>     omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
>     omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
>     range := (x_end - x_start);
>     omniout_float(ALWAYS,"range",32,range,32,"");
>     estimated_steps := range / estimated_h;
>     omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
>     step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
>     omniout_float(ALWAYS,"step_error",32,step_error,32,"");
>     (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
    omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
        glob_desired_digits_correct, 32, "");
    desired_abs_gbl_error :=
        expt(glob__10, c(-glob_desired_digits_correct))*
        c(float_abs(c(estimated_answer)));
    omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
    omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
        ;
    omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
        desired_abs_gbl_error, 32, "");
    range := x_end - x_start;
    omniout_float(ALWAYS, "range", 32, range, 32, "");
    estimated_steps := range/estimated_h;
    omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
    step_error := c(float_abs(desired_abs_gbl_error)/(
        sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
    omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
    step_error
end proc

# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y2 := proc(x)
> return(sin(c(x)));
> end;
               exact_soln_y2 := proc(x) return sin(c(x)) end proc

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

> exact_soln_y2pp := proc(x)
> return( neg( sin(c(x))));
> end;
           exact_soln_y2pp := proc(x) return neg(sin(c(x))) end proc

> exact_soln_y1 := proc(x)
> return( cos(c(x)));
> end;
               exact_soln_y1 := proc(x) return cos(c(x)) end proc

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

# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
>     local ret;
>     if (xf > x0) then # if number 5
>         ret := glob__1;
>     else
>         ret := glob__m1;
>     fi;# end if 5;
>     ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
    if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc

# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local min_size;
>     min_size := glob_estimated_size_answer;
>     if (float_abs(array_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 (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 (min_size < glob__1) then # if number 5
>         min_size := glob__1;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 5;
>     min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    min_size := glob_estimated_size_answer;
    if float_abs(array_y2[1]) < min_size then
        min_size := float_abs(array_y2[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    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 min_size < glob__1 then
        min_size := glob__1;
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    min_size
end proc

# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     max_estimated_step_error  := glob__small;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
>     est_tmp := float_abs(array_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;
>     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;
>     omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
>     max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    max_estimated_step_error := glob__small;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
    est_tmp := float_abs(array_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;
    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;
    omniout_float(ALWAYS, "max_estimated_step_error", 32,
        max_estimated_step_error, 32, "");
    max_estimated_step_error
end proc

# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
>     fi;# end if 5;
>     if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
>         array_max_est_error[1] := c(est_tmp);
>     fi;# end if 5
>     ;
>     est_tmp := c(float_abs(array_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
>         est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
>     fi;# end if 5;
>     if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
>         array_max_est_error[2] := c(est_tmp);
>     fi;# end if 5
>     ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    est_tmp := c(float_abs(array_y2[no_terms - 3]))
         + c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
    end if;
    if c(array_max_est_error[1]) <= c(est_tmp) then
        array_max_est_error[1] := c(est_tmp)
    end if;
    est_tmp := c(float_abs(array_y1[no_terms - 3]))
         + c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
    end if;
    if c(array_max_est_error[2]) <= c(est_tmp) then
        array_max_est_error[2] := c(est_tmp)
    end if
end proc

# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local ret;
>     if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 5
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 5;
>     return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    if glob_check_sign*glob_next_display - glob_h/glob__10 <=
    glob_check_sign*array_x[1] then ret := true
    else ret := false
    end if;
    return ret
end proc

# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
>     #TOP DISPLAY ALOT
>     if (reached_interval())  then # if number 5
>         if (iter >= 0)  then # if number 6
>             ind_var := array_x[1];
>             omniout_float(ALWAYS,"x[1]                             ",33,ind_var,20," ");
>             closed_form_val_y := evalf(exact_soln_y2(ind_var));
>             omniout_float(ALWAYS,"y2[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y2[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y2[1] (numeric)                  ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 7
>                 relerr := abserr*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 8
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 7;
>             if (glob_good_digits < glob_min_good_digits) then # if number 7
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 7;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 7;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 7
>                 est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 8
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[1] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 7
>                 array_1st_rel_error[1] := relerr;
>             else
>                 array_last_rel_error[1] := relerr;
>             fi;# end if 7;
>             array_est_rel_error[1] := est_rel_err;
>             omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>             omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>             omniout_int(INFO,"Desired digits                   ",32,glob_desired_digits_correct,4," ");
>             omniout_int(INFO,"Estimated correct digits         ",32,glob_est_digits,4," ");
>             omniout_int(INFO,"Correct digits                   ",32,glob_good_digits,4," ")
>             ;
>             omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>             ;
>             closed_form_val_y := evalf(exact_soln_y1(ind_var));
>             omniout_float(ALWAYS,"y1[1] (closed_form)              ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y1[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y1[1] (numeric)                  ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 7
>                 relerr := abserr*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 8
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 7;
>             if (glob_good_digits < glob_min_good_digits) then # if number 7
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 7;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 7;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 7
>                 est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 8
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 8;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 7;
>             array_est_digits[2] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 7
>                 array_1st_rel_error[2] := relerr;
>             else
>                 array_last_rel_error[2] := relerr;
>             fi;# end if 7;
>             array_est_rel_error[2] := est_rel_err;
>             omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>             omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>             omniout_int(INFO,"Desired digits                   ",32,glob_desired_digits_correct,4," ");
>             omniout_int(INFO,"Estimated correct digits         ",32,glob_est_digits,4," ");
>             omniout_int(INFO,"Correct digits                   ",32,glob_good_digits,4," ")
>             ;
>             omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>         fi;# end if 6;
>         #BOTTOM DISPLAY ALOT
>     fi;# end if 5;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    if reached_interval() then
        if 0 <= iter then
            ind_var := array_x[1];
            omniout_float(ALWAYS, "x[1]                             ", 33,
                ind_var, 20, " ");
            closed_form_val_y := evalf(exact_soln_y2(ind_var));
            omniout_float(ALWAYS, "y2[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y2[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y2[1] (numeric)                  ", 33,
                numeric_val, 20, " ");
            if c(glob_prec) < c(float_abs(closed_form_val_y)) then
                relerr := abserr*glob__100/float_abs(closed_form_val_y);
                if c(glob_prec) < c(relerr) then
                    glob_good_digits := -int_trunc(log10(c(relerr))) + 3
                else glob_good_digits := Digits
                end if
            else relerr := glob__m1; glob_good_digits := -16
            end if;
            if glob_good_digits < glob_min_good_digits then
                glob_min_good_digits := glob_good_digits
            end if;
            if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
            then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
            end if;
            if glob_prec < evalf(float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[1]*100.0*
                    sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val))
                    ;
                if glob_prec < evalf(est_rel_err) then
                    glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
                else glob_est_digits := Digits
                end if
            else relerr := glob__m1; glob_est_digits := -16
            end if;
            array_est_digits[1] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[1] := relerr
            else array_last_rel_error[1] := relerr
            end if;
            array_est_rel_error[1] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ");
            closed_form_val_y := evalf(exact_soln_y1(ind_var));
            omniout_float(ALWAYS, "y1[1] (closed_form)              ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y1[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y1[1] (numeric)                  ", 33,
                numeric_val, 20, " ");
            if c(glob_prec) < c(float_abs(closed_form_val_y)) then
                relerr := abserr*glob__100/float_abs(closed_form_val_y);
                if c(glob_prec) < c(relerr) then
                    glob_good_digits := -int_trunc(log10(c(relerr))) + 3
                else glob_good_digits := Digits
                end if
            else relerr := glob__m1; glob_good_digits := -16
            end if;
            if glob_good_digits < glob_min_good_digits then
                glob_min_good_digits := glob_good_digits
            end if;
            if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
            then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
            end if;
            if glob_prec < evalf(float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[2]*100.0*
                    sqrt(glob_iter)*35*ATS_MAX_TERMS/float_abs(numeric_val))
                    ;
                if glob_prec < evalf(est_rel_err) then
                    glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
                else glob_est_digits := Digits
                end if
            else relerr := glob__m1; glob_est_digits := -16
            end if;
            array_est_digits[2] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[2] := relerr
            else array_last_rel_error[2] := relerr
            end if;
            array_est_rel_error[2] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ")
        end if
    end if
end proc

# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>     #TOP PROGRESS REPORT
>     clock_sec1   := elapsed_time_seconds();
>     total_clock_sec   :=  (clock_sec1) - (glob_orig_start_sec);
>     glob_clock_sec   :=  (clock_sec1) - (glob_clock_start_sec);
>     left_sec   :=  (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
>     expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h)  ,( clock_sec1) - (glob_orig_start_sec));
>     opt_clock_sec   := ( clock_sec1) - (glob_optimal_clock_start_sec);
>     glob_optimal_expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
>     glob_total_exp_sec   := glob_optimal_expect_sec + c(total_clock_sec);
>     percent_done   :=  comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
>     glob_percent_done := percent_done;
>     omniout_str_noeol(INFO,"Total Elapsed Time              ");
>     omniout_timestr((total_clock_sec));
>     omniout_str_noeol(INFO,"Elapsed Time(since restart)     ");
>     omniout_timestr((glob_clock_sec));
>     if (c(percent_done) < glob__100)  then # if number 5
>         omniout_str_noeol(INFO,"Expected Time Remaining         ");
>         omniout_timestr((expect_sec));
>         omniout_str_noeol(INFO,"Optimized Time Remaining        ");
>         omniout_timestr((glob_optimal_expect_sec));
>         omniout_str_noeol(INFO,"Expected Total Time             ");
>         omniout_timestr((glob_total_exp_sec));
>     fi;# end if 5;
>     omniout_str_noeol(INFO,"Time to Timeout                 ");
>     omniout_timestr((left_sec));
>     omniout_float(INFO,    "Percent Done                    ",33,percent_done,4,"%");
>     #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    clock_sec1 := elapsed_time_seconds();
    total_clock_sec := clock_sec1 - glob_orig_start_sec;
    glob_clock_sec := clock_sec1 - glob_clock_start_sec;
    left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
    expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
        clock_sec1 - glob_orig_start_sec);
    opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
    glob_optimal_expect_sec :=
        comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
        ;
    glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
    percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
    glob_percent_done := percent_done;
    omniout_str_noeol(INFO, "Total Elapsed Time              ");
    omniout_timestr(total_clock_sec);
    omniout_str_noeol(INFO, "Elapsed Time(since restart)     ");
    omniout_timestr(glob_clock_sec);
    if c(percent_done) < glob__100 then
        omniout_str_noeol(INFO, "Expected Time Remaining         ");
        omniout_timestr(expect_sec);
        omniout_str_noeol(INFO, "Optimized Time Remaining        ");
        omniout_timestr(glob_optimal_expect_sec);
        omniout_str_noeol(INFO, "Expected Total Time             ");
        omniout_timestr(glob_total_exp_sec)
    end if;
    omniout_str_noeol(INFO, "Time to Timeout                 ");
    omniout_timestr(left_sec);
    omniout_float(INFO, "Percent Done                    ", 33,
        percent_done, 4, "%")
end proc

# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14,  rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
>     #TOP CHECK FOR POLE
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,1] :=  glob_larger_float;
>     array_ord_test_poles[1,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 3 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 5;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 6
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 7
>             found_sing := 0;
>         fi;# end if 7;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 7
>         if (rad_c  < array_rad_test_poles[1,1]) then # if number 8
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>             array_rad_test_poles[1,1] := rad_c;
>             array_ord_test_poles[1,1] := tmp_ord;
>         fi;# end if 8;
>     fi;# end if 7;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,1] :=  glob_larger_float;
>     array_ord_test_poles[2,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 7;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 8
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 9
>             found_sing := 0;
>         fi;# end if 9;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 9
>         if (rad_c  < array_rad_test_poles[2,1]) then # if number 10
>             array_rad_test_poles[2,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>             array_rad_test_poles[2,1] := rad_c;
>             array_ord_test_poles[2,1] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test2
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,2] :=  glob_larger_float;
>     array_ord_test_poles[1,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 3 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 9;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 10
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 11
>             found_sing := 0;
>         fi;# end if 11;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 11
>         if (rad_c  < array_rad_test_poles[1,2]) then # if number 12
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_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[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 13
>                 glob_min_pole_est := rad_c;
>             fi;# end if 13;
>             array_ord_test_poles[1,2] := tmp_ord;
>         fi;# end if 12;
>     fi;# end if 11;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,2] :=  glob_larger_float;
>     array_ord_test_poles[2,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 11;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 12
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 13
>             found_sing := 0;
>         fi;# end if 13;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 13
>         if (rad_c  < array_rad_test_poles[2,2]) then # if number 14
>             array_rad_test_poles[2,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_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[2,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 15
>                 glob_min_pole_est := rad_c;
>             fi;# end if 15;
>             array_ord_test_poles[2,2] := tmp_ord;
>         fi;# end if 14;
>     fi;# end if 13;
>     #BOTTOM general radius test2
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,3] :=  glob_larger_float;
>     array_ord_test_poles[1,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 3 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 13;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 14
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 15
>             found_sing := 0;
>         fi;# end if 15;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 15
>         if (rad_c  < array_rad_test_poles[1,3]) then # if number 16
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_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[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 17
>                 glob_min_pole_est := rad_c;
>             fi;# end if 17;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 16;
>     fi;# end if 15;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[2,3] :=  glob_larger_float;
>     array_ord_test_poles[2,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 15;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 16
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 17
>             found_sing := 0;
>         fi;# end if 17;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 17
>         if (rad_c  < array_rad_test_poles[2,3]) then # if number 18
>             array_rad_test_poles[2,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_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[2,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 19
>                 glob_min_pole_est := rad_c;
>             fi;# end if 19;
>             array_ord_test_poles[2,3] := tmp_ord;
>         fi;# end if 18;
>     fi;# end if 17;
>     #BOTTOM general radius test2
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
>         h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
>         omniout_str(ALWAYS,"SETTING H FOR POLE");
>         glob_h_reason := 6;
>         if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 18;
>         term := 1;
>         ratio := c(1.0);
>         while (term <= ATS_MAX_TERMS)  do # do number 1
>             array_y2[term] := array_y2[term]* ratio;
>             array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             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;
>             ratio := ratio * h_new / float_abs(glob_h);
>             term := term + 1;
>         od;# end do number 1;
>         glob_h := h_new;
>     fi;# end if 17;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 17
>         display_poles();
>     fi;# end if 17
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 1] := glob_larger_float;
    array_ord_test_poles[1, 1] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 13;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
            array_y2_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 1] then
            array_rad_test_poles[1, 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[1, 1] := rad_c;
            array_ord_test_poles[1, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 1] := glob_larger_float;
    array_ord_test_poles[2, 1] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y1_higher[1, last_no - 1],
            array_y1_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 1] then
            array_rad_test_poles[2, 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[2, 1] := rad_c;
            array_ord_test_poles[2, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 2] := glob_larger_float;
    array_ord_test_poles[1, 2] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 13;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 2] then
            array_rad_test_poles[1, 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[1, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 2] := glob_larger_float;
    array_ord_test_poles[2, 2] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 2] then
            array_rad_test_poles[2, 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[2, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 3] := glob_larger_float;
    array_ord_test_poles[1, 3] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 13;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
            array_y2_higher[1, last_no - 4],
            array_y2_higher[1, last_no - 3],
            array_y2_higher[1, last_no - 2],
            array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 3] then
            array_rad_test_poles[1, 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[1, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 3] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[2, 3] := glob_larger_float;
    array_ord_test_poles[2, 3] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y1_higher[1, last_no - 5],
            array_y1_higher[1, last_no - 4],
            array_y1_higher[1, last_no - 3],
            array_y1_higher[1, last_no - 2],
            array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
            last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[2, 3] then
            array_rad_test_poles[2, 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[2, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[2, 3] := tmp_ord
        end if
    end if;
    if
    float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
    then
        h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
        omniout_str(ALWAYS, "SETTING H FOR POLE");
        glob_h_reason := 6;
        if glob_check_sign*h_new < glob_check_sign*glob_min_h then
            omniout_str(ALWAYS, "SETTING H FOR MIN H");
            h_new := glob_min_h;
            glob_h_reason := 5
        end if;
        term := 1;
        ratio := c(1.0);
        while term <= ATS_MAX_TERMS do
            array_y2[term] := array_y2[term]*ratio;
            array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            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;
            ratio := ratio*h_new/float_abs(glob_h);
            term := term + 1
        end do;
        glob_h := h_new
    end if;
    if reached_interval() then display_poles() end if
end proc

# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre cos 1 $eq_no = 1
>     array_tmp1[1] :=  cos(array_x[1]);
>     array_tmp1_g[1] :=  sin(array_x[1]);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[1] :=  neg(array_tmp1[1]);
>     #emit pre add CONST FULL $eq_no = 1 i = 1
>     array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,4]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[1]) * (expt((glob_h) , c(3))) * c(factorial_3(0,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[4] := temporary;
>                 array_y2_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[2,3] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y2_higher[3,2] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y2_higher[4,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[1] :=  neg(array_y2[1]);
>     #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,2]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[2] := temporary;
>                 array_y1_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y1_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
>     array_tmp1[2] := neg(array_tmp1_g[1]) * array_x[2] / c(1);
>     array_tmp1_g[2] := array_tmp1[1] * array_x[2] / c(1);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[2] :=  neg(array_tmp1[2]);
>     #emit pre add CONST FULL $eq_no = 1 i = 2
>     array_tmp3[2] := array_tmp2[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,5]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[2]) * (expt((glob_h) , c(3))) * c(factorial_3(1,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[5] := temporary;
>                 array_y2_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[2,4] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[3,3] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y2_higher[4,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[2] :=  neg(array_y2[2]);
>     #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,3]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[3] := temporary;
>                 array_y1_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y1_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
>     array_tmp1[3] := neg(array_tmp1_g[2]) * array_x[2] / c(2);
>     array_tmp1_g[3] := array_tmp1[2] * array_x[2] / c(2);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[3] :=  neg(array_tmp1[3]);
>     #emit pre add CONST FULL $eq_no = 1 i = 3
>     array_tmp3[3] := array_tmp2[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,6]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[3]) * (expt((glob_h) , c(3))) * c(factorial_3(2,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[6] := temporary;
>                 array_y2_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_higher[2,5] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[3,4] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y2_higher[4,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[3] :=  neg(array_y2[3]);
>     #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[4] := temporary;
>                 array_y1_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y1_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
>     array_tmp1[4] := neg(array_tmp1_g[3]) * array_x[2] / c(3);
>     array_tmp1_g[4] := array_tmp1[3] * array_x[2] / c(3);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[4] :=  neg(array_tmp1[4]);
>     #emit pre add CONST FULL $eq_no = 1 i = 4
>     array_tmp3[4] := array_tmp2[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,7]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[4]) * (expt((glob_h) , c(3))) * c(factorial_3(3,6));
>             if (7 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[7] := temporary;
>                 array_y2_higher[1,7] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(6);
>             array_y2_higher[2,6] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_higher[3,5] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y2_higher[4,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[4] :=  neg(array_y2[4]);
>     #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[5] := temporary;
>                 array_y1_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y1_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
>     array_tmp1[5] := neg(array_tmp1_g[4]) * array_x[2] / c(4);
>     array_tmp1_g[5] := array_tmp1[4] * array_x[2] / c(4);
>     #emit pre neg FULL $eq_no = 1
>     array_tmp2[5] :=  neg(array_tmp1[5]);
>     #emit pre add CONST FULL $eq_no = 1 i = 5
>     array_tmp3[5] := array_tmp2[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if ( not  array_y2_set_initial[1,8]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[5]) * (expt((glob_h) , c(3))) * c(factorial_3(4,7));
>             if (8 <= ATS_MAX_TERMS) then # if number 3
>                 array_y2[8] := temporary;
>                 array_y2_higher[1,8] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(7);
>             array_y2_higher[2,7] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(6);
>             array_y2_higher[3,6] := c(temporary);
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y2_higher[4,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #emit pre neg FULL $eq_no = 2
>     array_tmp5[5] :=  neg(array_y2[5]);
>     #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
>     if ( not  array_y1_set_initial[2,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y1[6] := temporary;
>                 array_y1_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y1_higher[2,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #END ATOMHDR5
>     #BEGIN OUTFILE3
>     #Top Atomall While Loop-- outfile3
>     while (kkk <= ATS_MAX_TERMS) do # do number 1
>         #END OUTFILE3
>         #BEGIN OUTFILE4
>         #emit cos LINEAR $eq_no = 1
>         array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1]) * array_x[2] / c(kkk - 1);
>         array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1);
>         #emit neg FULL $eq_no = 1
>         array_tmp2[kkk] := neg(array_tmp1[kkk]);
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp3[kkk] := array_tmp2[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 3;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y2_set_initial[1,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y2[kkk + order_d] := c(temporary);
>                 array_y2_higher[1,kkk + order_d] := c(temporary);
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
>                     if (adj3 <= order_d + 1) then # if number 3
>                         if (adj2 > 0) then # if number 4
>                             temporary := c(temporary) / c(glob_h) * c(adj2);
>                         else
>                             temporary := c(temporary);
>                         fi;# end if 4;
>                         array_y2_higher[adj3,term] := c(temporary);
>                     fi;# end if 3;
>                     term  := term - 1;
>                     adj2 := adj2 - 1;
>                     adj3 := adj3 + 1;
>                 od;# end do number 1
>             fi;# end if 2
>         fi;# end if 1;
>         #emit neg FULL $eq_no = 2
>         array_tmp5[kkk] := neg(array_y2[kkk]);
>         #emit assign $eq_no = 2
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y1_set_initial[2,kkk + order_d]) then # if number 2
>                 temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d))  * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
>                 array_y1[kkk + order_d] := c(temporary);
>                 array_y1_higher[1,kkk + order_d] := c(temporary);
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
>                     if (adj3 <= order_d + 1) then # if number 3
>                         if (adj2 > 0) then # if number 4
>                             temporary := c(temporary) / c(glob_h) * c(adj2);
>                         else
>                             temporary := c(temporary);
>                         fi;# end if 4;
>                         array_y1_higher[adj3,term] := c(temporary);
>                     fi;# end if 3;
>                     term  := term - 1;
>                     adj2 := adj2 - 1;
>                     adj3 := adj3 + 1;
>                 od;# end do number 1
>             fi;# end if 2
>         fi;# end if 1;
>         kkk   :=  kkk + 1;
>     od;# end do number 1;
>     #BOTTOM ATOMALL
>     #END OUTFILE4
>     #BEGIN OUTFILE5
>     #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    array_tmp1[1] := cos(array_x[1]);
    array_tmp1_g[1] := sin(array_x[1]);
    array_tmp2[1] := neg(array_tmp1[1]);
    array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
    if not array_y2_set_initial[1, 4] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[1])*expt(glob_h, c(3))*c(factorial_3(0, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y2[4] := temporary;
                array_y2_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[2, 3] := c(temporary);
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y2_higher[3, 2] := c(temporary);
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y2_higher[4, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp5[1] := neg(array_y2[1]);
    if not array_y1_set_initial[2, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y1[2] := temporary;
                array_y1_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y1_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := neg(array_tmp1_g[1])*array_x[2]/c(1);
    array_tmp1_g[2] := array_tmp1[1]*array_x[2]/c(1);
    array_tmp2[2] := neg(array_tmp1[2]);
    array_tmp3[2] := array_tmp2[2];
    if not array_y2_set_initial[1, 5] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[2])*expt(glob_h, c(3))*c(factorial_3(1, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y2[5] := temporary;
                array_y2_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[2, 4] := c(temporary);
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[3, 3] := c(temporary);
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y2_higher[4, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp5[2] := neg(array_y2[2]);
    if not array_y1_set_initial[2, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y1[3] := temporary;
                array_y1_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y1_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp1[3] := neg(array_tmp1_g[2])*array_x[2]/c(2);
    array_tmp1_g[3] := array_tmp1[2]*array_x[2]/c(2);
    array_tmp2[3] := neg(array_tmp1[3]);
    array_tmp3[3] := array_tmp2[3];
    if not array_y2_set_initial[1, 6] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[3])*expt(glob_h, c(3))*c(factorial_3(2, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y2[6] := temporary;
                array_y2_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[2, 5] := c(temporary);
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[3, 4] := c(temporary);
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y2_higher[4, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp5[3] := neg(array_y2[3]);
    if not array_y1_set_initial[2, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y1[4] := temporary;
                array_y1_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y1_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp1[4] := neg(array_tmp1_g[3])*array_x[2]/c(3);
    array_tmp1_g[4] := array_tmp1[3]*array_x[2]/c(3);
    array_tmp2[4] := neg(array_tmp1[4]);
    array_tmp3[4] := array_tmp2[4];
    if not array_y2_set_initial[1, 7] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[4])*expt(glob_h, c(3))*c(factorial_3(3, 6));
            if 7 <= ATS_MAX_TERMS then
                array_y2[7] := temporary;
                array_y2_higher[1, 7] := temporary
            end if;
            temporary := c(temporary)*c(6)/c(glob_h);
            array_y2_higher[2, 6] := c(temporary);
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[3, 5] := c(temporary);
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y2_higher[4, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp5[4] := neg(array_y2[4]);
    if not array_y1_set_initial[2, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y1[5] := temporary;
                array_y1_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y1_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp1[5] := neg(array_tmp1_g[4])*array_x[2]/c(4);
    array_tmp1_g[5] := array_tmp1[4]*array_x[2]/c(4);
    array_tmp2[5] := neg(array_tmp1[5]);
    array_tmp3[5] := array_tmp2[5];
    if not array_y2_set_initial[1, 8] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[5])*expt(glob_h, c(3))*c(factorial_3(4, 7));
            if 8 <= ATS_MAX_TERMS then
                array_y2[8] := temporary;
                array_y2_higher[1, 8] := temporary
            end if;
            temporary := c(temporary)*c(7)/c(glob_h);
            array_y2_higher[2, 7] := c(temporary);
            temporary := c(temporary)*c(6)/c(glob_h);
            array_y2_higher[3, 6] := c(temporary);
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y2_higher[4, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    array_tmp5[5] := neg(array_y2[5]);
    if not array_y1_set_initial[2, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y1[6] := temporary;
                array_y1_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y1_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1])*array_x[2]/c(kkk - 1)
            ;
        array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
        array_tmp2[kkk] := neg(array_tmp1[kkk]);
        array_tmp3[kkk] := array_tmp2[kkk];
        order_d := 3;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y2_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y2[kkk + order_d] := c(temporary);
                array_y2_higher[1, kkk + order_d] := c(temporary);
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
                do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then
                            temporary := c(temporary)*c(adj2)/c(glob_h)
                        else temporary := c(temporary)
                        end if;
                        array_y2_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        array_tmp5[kkk] := neg(array_y2[kkk]);
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y1_set_initial[2, kkk + order_d] then
                temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y1[kkk + order_d] := c(temporary);
                array_y1_higher[1, kkk + order_d] := c(temporary);
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
                do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then
                            temporary := c(temporary)*c(adj2)/c(glob_h)
                        else temporary := c(temporary)
                        end if;
                        array_y1_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        kkk := kkk + 1
    end do
end proc

# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
>     #BEGIN OUTFIEMAIN
>     local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
>     term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
>     rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
>     x_start,x_end
>     ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
>     global
>     ALWAYS,
>     INFO,
>     DEBUGL,
>     DEBUGMASSIVE,
>     glob_iolevel,
>     glob_yes_pole,
>     glob_no_pole,
>     glob_not_given,
>     glob_no_sing_tests,
>     glob_ratio_test,
>     glob_three_term_test,
>     glob_six_term_test,
>     glob_log_10,
>     #Top Generate Globals Decl
>     MAX_UNCHANGED,
>     glob__small,
>     glob_small_float,
>     glob_smallish_float,
>     glob_large_float,
>     glob_larger_float,
>     glob__m2,
>     glob__m1,
>     glob__0,
>     glob__1,
>     glob__2,
>     glob__3,
>     glob__4,
>     glob__5,
>     glob__8,
>     glob__10,
>     glob__100,
>     glob__pi,
>     glob__0_5,
>     glob__0_8,
>     glob__m0_8,
>     glob__0_25,
>     glob__0_125,
>     glob_prec,
>     glob_check_sign,
>     glob_desired_digits_correct,
>     glob_max_estimated_step_error,
>     glob_ratio_of_radius,
>     glob_percent_done,
>     glob_total_exp_sec,
>     glob_optimal_expect_sec,
>     glob_estimated_size_answer,
>     glob_almost_1,
>     glob_clock_sec,
>     glob_clock_start_sec,
>     glob_disp_incr,
>     glob_h,
>     glob_diff_rc_fm,
>     glob_diff_rc_fmm1,
>     glob_diff_rc_fmm2,
>     glob_diff_ord_fm,
>     glob_diff_ord_fmm1,
>     glob_diff_ord_fmm2,
>     glob_six_term_ord_save,
>     glob_guess_error_rc,
>     glob_guess_error_ord,
>     glob_least_given_sing,
>     glob_least_ratio_sing,
>     glob_least_3_sing,
>     glob_least_6_sing,
>     glob_last_good_h,
>     glob_max_h,
>     glob_min_h,
>     glob_display_interval,
>     glob_abserr,
>     glob_relerr,
>     glob_min_pole_est,
>     glob_max_rel_trunc_err,
>     glob_max_trunc_err,
>     glob_max_hours,
>     glob_optimal_clock_start_sec,
>     glob_optimal_start,
>     glob_upper_ratio_limit,
>     glob_lower_ratio_limit,
>     glob_max_sec,
>     glob_orig_start_sec,
>     glob_normmax,
>     glob_max_minutes,
>     glob_next_display,
>     glob_est_digits,
>     glob_subiter_method,
>     glob_html_log,
>     glob_min_good_digits,
>     glob_good_digits,
>     glob_min_apfp_est_good_digits,
>     glob_apfp_est_good_digits,
>     glob_max_opt_iter,
>     glob_dump,
>     glob_djd_debug,
>     glob_display_flag,
>     glob_djd_debug2,
>     glob_h_reason,
>     glob_sec_in_minute,
>     glob_min_in_hour,
>     glob_hours_in_day,
>     glob_days_in_year,
>     glob_sec_in_hour,
>     glob_sec_in_day,
>     glob_sec_in_year,
>     glob_not_yet_finished,
>     glob_initial_pass,
>     glob_not_yet_start_msg,
>     glob_reached_optimal_h,
>     glob_optimal_done,
>     glob_type_given_pole,
>     glob_optimize,
>     glob_look_poles,
>     glob_dump_closed_form,
>     glob_max_iter,
>     glob_no_eqs,
>     glob_unchanged_h_cnt,
>     glob_warned,
>     glob_warned2,
>     glob_start,
>     glob_iter,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_3,
>     array_const_0D0,
>     array_const_1,
>     #END CONST
>     array_y2_init,
>     array_y1_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_y2,
>     array_x,
>     array_y1,
>     array_tmp0,
>     array_tmp1_g,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_m1,
>     array_y2_higher,
>     array_y2_higher_work,
>     array_y2_higher_work2,
>     array_y2_set_initial,
>     array_y1_higher,
>     array_y1_higher_work,
>     array_y1_higher_work2,
>     array_y1_set_initial,
>     array_given_rad_poles,
>     array_given_ord_poles,
>     array_rad_test_poles,
>     array_ord_test_poles,
>     array_fact_2,
>     ATS_MAX_TERMS,
>     glob_last;
>     ATS_MAX_TERMS := 40;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=40;
>     #END BLOCK 1
>     #END FIRST INPUT BLOCK
>     #START OF INITS AFTER INPUT BLOCK
>     glob_html_log := true;
>     #END OF INITS AFTER INPUT BLOCK
>     # before generate arrays
>     array_y2_init:= Array(0..(40),[]);
>     array_y1_init:= Array(0..(40),[]);
>     array_norms:= Array(0..(40),[]);
>     array_fact_1:= Array(0..(40),[]);
>     array_1st_rel_error:= Array(0..(3),[]);
>     array_last_rel_error:= Array(0..(3),[]);
>     array_est_rel_error:= Array(0..(3),[]);
>     array_max_est_error:= Array(0..(3),[]);
>     array_type_pole:= Array(0..(3),[]);
>     array_type_real_pole:= Array(0..(3),[]);
>     array_type_complex_pole:= Array(0..(3),[]);
>     array_est_digits:= Array(0..(3),[]);
>     array_y2:= Array(0..(40),[]);
>     array_x:= Array(0..(40),[]);
>     array_y1:= Array(0..(40),[]);
>     array_tmp0:= Array(0..(40),[]);
>     array_tmp1_g:= Array(0..(40),[]);
>     array_tmp1:= Array(0..(40),[]);
>     array_tmp2:= Array(0..(40),[]);
>     array_tmp3:= Array(0..(40),[]);
>     array_tmp4:= Array(0..(40),[]);
>     array_tmp5:= Array(0..(40),[]);
>     array_m1:= Array(0..(40),[]);
>     array_y2_higher := Array(0..(4) ,(0..40+ 1),[]);
>     array_y2_higher_work := Array(0..(4) ,(0..40+ 1),[]);
>     array_y2_higher_work2 := Array(0..(4) ,(0..40+ 1),[]);
>     array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]);
>     array_y1_higher := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
>     array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
>     array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
>     array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
>     array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
>     array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
>     array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
>     # before generate constants
>     # before generate globals definition
>     #Top Generate Globals Definition
>     #Bottom Generate Globals Deninition
>     # before generate const definition
>     # before arrays initialized
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y2_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y1_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_fact_1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_1st_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_last_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_est_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_max_est_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_real_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_type_complex_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 3) do # do number 1
>         array_est_digits[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_y1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1_g[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp4[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_tmp5[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 40) do # do number 1
>         array_m1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=4) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=4) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=4) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_higher_work2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y2_set_initial[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_higher_work2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_y1_set_initial[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_rad_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_ord_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_rad_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=3) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_ord_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=40) do # do number 1
>         term := 1;
>         while (term <= 40) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y2);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_y1);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1_g);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_tmp4);
>     zero_ats_ar(array_tmp5);
>     zero_ats_ar(array_m1);
>     zero_ats_ar(array_const_3);
>     array_const_3[1]   := c(3);
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := c(0.0);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := c(1);
>     zero_ats_ar(array_m1);
>     array_m1[1]   := glob__m1;
>     #END SYMBOLS INITIALIZATED
>     # before generate factorials init
>     #Initing Factorial Tables
>     iiif := 0;
>     while (iiif <= ATS_MAX_TERMS) do # do number 1
>         jjjf := 0;
>         while (jjjf <= ATS_MAX_TERMS) do # do number 2
>             array_fact_1[iiif] := 0;
>             array_fact_2[iiif,jjjf] := 0;
>             jjjf := jjjf + 1;
>         od;# end do number 2;
>         iiif := iiif + 1;
>     od;# end do number 1;
>     #Done Initing Factorial Table
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     glob_iolevel := 5;
>     glob_yes_pole := 4;
>     glob_no_pole := 3;
>     glob_not_given := 0;
>     glob_no_sing_tests := 4;
>     glob_ratio_test := 1;
>     glob_three_term_test := 2;
>     glob_six_term_test := 3;
>     glob_log_10 := log(c(10.0));
>     MAX_UNCHANGED := 10;
>     glob__small := c(0.1e-50);
>     glob_small_float := c(0.1e-50);
>     glob_smallish_float := c(0.1e-60);
>     glob_large_float := c(1.0e100);
>     glob_larger_float := c(1.1e100);
>     glob__m2 := c(-2);
>     glob__m1 := c(-1);
>     glob__0 := c(0);
>     glob__1 := c(1);
>     glob__2 := c(2);
>     glob__3 := c(3);
>     glob__4 := c(4);
>     glob__5 := c(5);
>     glob__8 := c(8);
>     glob__10 := c(10);
>     glob__100 := c(100);
>     glob__pi := c(0.0);
>     glob__0_5 := c(0.5);
>     glob__0_8 := c(0.8);
>     glob__m0_8 := c(-0.8);
>     glob__0_25 := c(0.25);
>     glob__0_125 := c(0.125);
>     glob_prec := c(1.0e-16);
>     glob_check_sign := c(1.0);
>     glob_desired_digits_correct := c(8.0);
>     glob_max_estimated_step_error := c(0.0);
>     glob_ratio_of_radius := c(0.1);
>     glob_percent_done := c(0.0);
>     glob_total_exp_sec := c(0.1);
>     glob_optimal_expect_sec := c(0.1);
>     glob_estimated_size_answer := c(100.0);
>     glob_almost_1 := c(0.9990);
>     glob_clock_sec := c(0.0);
>     glob_clock_start_sec := c(0.0);
>     glob_disp_incr := c(0.1);
>     glob_h := c(0.1);
>     glob_diff_rc_fm := c(0.1);
>     glob_diff_rc_fmm1 := c(0.1);
>     glob_diff_rc_fmm2 := c(0.1);
>     glob_diff_ord_fm := c(0.1);
>     glob_diff_ord_fmm1 := c(0.1);
>     glob_diff_ord_fmm2 := c(0.1);
>     glob_six_term_ord_save := c(0.1);
>     glob_guess_error_rc := c(0.1);
>     glob_guess_error_ord := c(0.1);
>     glob_least_given_sing := c(9.9e200);
>     glob_least_ratio_sing := c(9.9e200);
>     glob_least_3_sing := c(9.9e100);
>     glob_least_6_sing := c(9.9e100);
>     glob_last_good_h := c(0.1);
>     glob_max_h := c(0.1);
>     glob_min_h := c(0.000001);
>     glob_display_interval := c(0.1);
>     glob_abserr := c(0.1e-10);
>     glob_relerr := c(0.1e-10);
>     glob_min_pole_est := c(0.1e+10);
>     glob_max_rel_trunc_err := c(0.1e-10);
>     glob_max_trunc_err := c(0.1e-10);
>     glob_max_hours := c(0.0);
>     glob_optimal_clock_start_sec := c(0.0);
>     glob_optimal_start := c(0.0);
>     glob_upper_ratio_limit := c(1.0001);
>     glob_lower_ratio_limit := c(0.9999);
>     glob_max_sec := c(10000.0);
>     glob_orig_start_sec := c(0.0);
>     glob_normmax := c(0.0);
>     glob_max_minutes := c(0.0);
>     glob_next_display := c(0.0);
>     glob_est_digits := 1;
>     glob_subiter_method := 3;
>     glob_html_log := true;
>     glob_min_good_digits := 99999;
>     glob_good_digits := 0;
>     glob_min_apfp_est_good_digits := 99999;
>     glob_apfp_est_good_digits := 0;
>     glob_max_opt_iter := 10;
>     glob_dump := false;
>     glob_djd_debug := true;
>     glob_display_flag := true;
>     glob_djd_debug2 := true;
>     glob_h_reason := 0;
>     glob_sec_in_minute := 60 ;
>     glob_min_in_hour := 60;
>     glob_hours_in_day := 24;
>     glob_days_in_year := 365;
>     glob_sec_in_hour := 3600;
>     glob_sec_in_day := 86400;
>     glob_sec_in_year := 31536000;
>     glob_not_yet_finished := true;
>     glob_initial_pass := true;
>     glob_not_yet_start_msg := true;
>     glob_reached_optimal_h := false;
>     glob_optimal_done := false;
>     glob_type_given_pole := 0;
>     glob_optimize := false;
>     glob_look_poles := false;
>     glob_dump_closed_form := false;
>     glob_max_iter := 1000;
>     glob_no_eqs := 0;
>     glob_unchanged_h_cnt := 0;
>     glob_warned := false;
>     glob_warned2 := false;
>     glob_start := 0;
>     glob_iter := 0;
>     # before generate set diff initial
>     array_y2_set_initial[1,1] := true;
>     array_y2_set_initial[1,2] := true;
>     array_y2_set_initial[1,3] := true;
>     array_y2_set_initial[1,4] := false;
>     array_y2_set_initial[1,5] := false;
>     array_y2_set_initial[1,6] := false;
>     array_y2_set_initial[1,7] := false;
>     array_y2_set_initial[1,8] := false;
>     array_y2_set_initial[1,9] := false;
>     array_y2_set_initial[1,10] := false;
>     array_y2_set_initial[1,11] := false;
>     array_y2_set_initial[1,12] := false;
>     array_y2_set_initial[1,13] := false;
>     array_y2_set_initial[1,14] := false;
>     array_y2_set_initial[1,15] := false;
>     array_y2_set_initial[1,16] := false;
>     array_y2_set_initial[1,17] := false;
>     array_y2_set_initial[1,18] := false;
>     array_y2_set_initial[1,19] := false;
>     array_y2_set_initial[1,20] := false;
>     array_y2_set_initial[1,21] := false;
>     array_y2_set_initial[1,22] := false;
>     array_y2_set_initial[1,23] := false;
>     array_y2_set_initial[1,24] := false;
>     array_y2_set_initial[1,25] := false;
>     array_y2_set_initial[1,26] := false;
>     array_y2_set_initial[1,27] := false;
>     array_y2_set_initial[1,28] := false;
>     array_y2_set_initial[1,29] := false;
>     array_y2_set_initial[1,30] := false;
>     array_y2_set_initial[1,31] := false;
>     array_y2_set_initial[1,32] := false;
>     array_y2_set_initial[1,33] := false;
>     array_y2_set_initial[1,34] := false;
>     array_y2_set_initial[1,35] := false;
>     array_y2_set_initial[1,36] := false;
>     array_y2_set_initial[1,37] := false;
>     array_y2_set_initial[1,38] := false;
>     array_y2_set_initial[1,39] := false;
>     array_y2_set_initial[1,40] := false;
>     array_y1_set_initial[2,1] := true;
>     array_y1_set_initial[2,2] := false;
>     array_y1_set_initial[2,3] := false;
>     array_y1_set_initial[2,4] := false;
>     array_y1_set_initial[2,5] := false;
>     array_y1_set_initial[2,6] := false;
>     array_y1_set_initial[2,7] := false;
>     array_y1_set_initial[2,8] := false;
>     array_y1_set_initial[2,9] := false;
>     array_y1_set_initial[2,10] := false;
>     array_y1_set_initial[2,11] := false;
>     array_y1_set_initial[2,12] := false;
>     array_y1_set_initial[2,13] := false;
>     array_y1_set_initial[2,14] := false;
>     array_y1_set_initial[2,15] := false;
>     array_y1_set_initial[2,16] := false;
>     array_y1_set_initial[2,17] := false;
>     array_y1_set_initial[2,18] := false;
>     array_y1_set_initial[2,19] := false;
>     array_y1_set_initial[2,20] := false;
>     array_y1_set_initial[2,21] := false;
>     array_y1_set_initial[2,22] := false;
>     array_y1_set_initial[2,23] := false;
>     array_y1_set_initial[2,24] := false;
>     array_y1_set_initial[2,25] := false;
>     array_y1_set_initial[2,26] := false;
>     array_y1_set_initial[2,27] := false;
>     array_y1_set_initial[2,28] := false;
>     array_y1_set_initial[2,29] := false;
>     array_y1_set_initial[2,30] := false;
>     array_y1_set_initial[2,31] := false;
>     array_y1_set_initial[2,32] := false;
>     array_y1_set_initial[2,33] := false;
>     array_y1_set_initial[2,34] := false;
>     array_y1_set_initial[2,35] := false;
>     array_y1_set_initial[2,36] := false;
>     array_y1_set_initial[2,37] := false;
>     array_y1_set_initial[2,38] := false;
>     array_y1_set_initial[2,39] := false;
>     array_y1_set_initial[2,40] := false;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 40;
>     glob_iolevel := INFO;
>     # set default block
>     #Write Set Defaults
>     glob_orig_start_sec   :=  elapsed_time_seconds();
>     glob_display_flag   :=   true;
>     glob_no_eqs   := 2;
>     glob_iter   :=  -1;
>     opt_iter   :=  -1;
>     glob_max_iter   :=  50000;
>     glob_max_hours   :=  (0.0);
>     glob_max_minutes   :=  (15.0);
>     omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
>     omniout_str(ALWAYS,"##############temp/mtest4postode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
>     omniout_str(ALWAYS,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=40;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(0.1);");
>     omniout_str(ALWAYS,"x_end := c(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,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 3;");
>     omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>     omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
>     omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
>     omniout_str(ALWAYS,"glob_subiter_method:=3;");
>     omniout_str(ALWAYS,"glob_max_iter:=100000;");
>     omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
>     omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
>     omniout_str(ALWAYS,"glob_look_poles:=true;");
>     omniout_str(ALWAYS,"glob_h:=c(0.001);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
>     omniout_str(ALWAYS,"return(sin(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
>     omniout_str(ALWAYS,"return( cos(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
>     omniout_str(ALWAYS,"return( neg( sin(c(x))));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
>     omniout_str(ALWAYS,"return( cos(c(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   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(0.1);
>     x_end := c(5.0);
>     array_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);
>     array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
>     glob_look_poles := true;
>     glob_type_given_pole := 3;
>     #END SECOND INPUT BLOCK
>     #BEGIN OVERRIDE  BLOCK
>     glob_desired_digits_correct:=8;
>     glob_max_minutes:=(3.0);
>     glob_subiter_method:=3;
>     glob_max_iter:=100000;
>     glob_upper_ratio_limit:=c(1.0000001);
>     glob_lower_ratio_limit:=c(0.9999999);
>     glob_look_poles:=true;
>     glob_h:=c(0.001);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(x_start,x_end));
>     glob__pi := arccos(glob__m1);
>     glob_prec = expt(10.0,c(-Digits));
>     if (glob_optimize)  then # if number 17
>         #BEGIN OPTIMIZE CODE
>         omniout_str(ALWAYS,"START of Optimize");
>         #Start Series -- INITIALIZE FOR OPTIMIZE
>         found_h := false;
>         glob_min_pole_est :=  glob_larger_float;
>         last_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         glob_min_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_max_h := float_abs(glob_max_h) * glob_check_sign;
>         glob_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
>         display_max := c(x_end) - c(x_start)/glob__10;
>         if ((glob_display_interval) > (display_max)) then # if number 18
>             glob_display_interval := c(display_max);
>         fi;# end if 18;
>         chk_data();
>         min_value := glob_larger_float;
>         est_answer := est_size_answer();
>         opt_iter := 1;
>         est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>         omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>         estimated_step_error  := glob_small_float;
>         while ((opt_iter <= 100) and ( not found_h)) do # do number 1
>             omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
>             array_x[1]   := c(x_start);
>             array_x[2]   :=  c(glob_h);
>             glob_next_display := c(x_start);
>             order_diff := 3;
>             #Start Series array_y2
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             rows   :=  order_diff;
>             r_order   :=  1;
>             while (r_order <= rows) do # do number 2
>                 term_no   :=  1;
>                 while (term_no <= (rows - r_order + 1)) do # do number 3
>                     it  := term_no + r_order - 1;
>                     if (term_no < ATS_MAX_TERMS) then # if number 18
>                         array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 18;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             order_diff := 1;
>             #Start Series array_y1
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             rows   :=  order_diff;
>             r_order   :=  1;
>             while (r_order <= rows) do # do number 2
>                 term_no   :=  1;
>                 while (term_no <= (rows - r_order + 1)) do # do number 3
>                     it  := term_no + r_order - 1;
>                     if (term_no < ATS_MAX_TERMS) then # if number 18
>                         array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 18;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             if (glob_subiter_method  =  1 ) then # if number 18
>                 atomall();
>             elif
>             (glob_subiter_method  =  2 ) then # if number 19
>                 subiter := 1;
>                 while (subiter <= 4) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 4 + ATS_MAX_TERMS) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             fi;# end if 19;
>             if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19
>                 omniout_str(ALWAYS,"SETTING H FOR MIN H");
>                 glob_h := glob_check_sign * float_abs(glob_min_h);
>                 glob_h_reason := 1;
>                 found_h := true;
>             fi;# end if 19;
>             if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19
>                 omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>                 glob_h_reason := 2;
>                 glob_h := glob_display_interval;
>                 found_h := true;
>             fi;# end if 19;
>             if (glob_look_poles)  then # if number 19
>                 check_for_pole();
>             fi;# end if 19;
>             if ( not found_h) then # if number 19
>                 est_answer := est_size_answer();
>                 est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>                 omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>                 estimated_step_error := test_suggested_h();
>                 omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
>                 if (estimated_step_error < est_needed_step_err) then # if number 20
>                     omniout_str(ALWAYS,"Double H and LOOP");
>                     glob_h := glob_h*glob__2;
>                 else
>                     omniout_str(ALWAYS,"Found H for OPTIMAL");
>                     found_h := true;
>                     glob_h_reason := 3;
>                     glob_h := glob_h/glob__2;
>                 fi;# end if 20;
>             fi;# end if 19;
>             opt_iter := opt_iter + 1;
>         od;# end do number 1;
>         if (( not found_h) and (opt_iter = 1)) then # if number 19
>             omniout_str(ALWAYS,"Beginning glob_h too large.");
>             found_h := false;
>         fi;# end if 19;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19
>             omniout_str(ALWAYS,"SETTING H FOR MAX H");
>             glob_h := glob_check_sign * float_abs(glob_max_h);
>             glob_h_reason := 1;
>             found_h := true;
>         fi;# end if 19;
>     else
>         found_h := true;
>         glob_h := glob_h * glob_check_sign;
>     fi;# end if 18;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 18
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 18;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 18
>         omniout_str(ALWAYS,"START of Soultion");
>         #Start Series -- INITIALIZE FOR SOLUTION
>         array_x[1]   := c(x_start);
>         array_x[2]   :=  c(glob_h);
>         glob_next_display := c(x_start);
>         glob_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         order_diff := 3;
>         #Start Series array_y2
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>             term_no   :=  term_no + 1;
>         od;# end do number 1;
>         rows   :=  order_diff;
>         r_order   :=  1;
>         while (r_order <= rows) do # do number 1
>             term_no   :=  1;
>             while (term_no <= (rows - r_order + 1)) do # do number 2
>                 it  := term_no + r_order - 1;
>                 if (term_no < ATS_MAX_TERMS) then # if number 19
>                     array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 19;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         order_diff := 1;
>         #Start Series array_y1
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>             term_no   :=  term_no + 1;
>         od;# end do number 1;
>         rows   :=  order_diff;
>         r_order   :=  1;
>         while (r_order <= rows) do # do number 1
>             term_no   :=  1;
>             while (term_no <= (rows - r_order + 1)) do # do number 2
>                 it  := term_no + r_order - 1;
>                 if (term_no < ATS_MAX_TERMS) then # if number 19
>                     array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 19;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         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 <= 4) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             else
>                 subiter := 1;
>                 while (subiter <= 4 + ATS_MAX_TERMS) do # do number 2
>                     atomall();
>                     subiter := subiter + 1;
>                 od;# end do number 2;
>             fi;# end if 20;
>             track_estimated_error();
>             display_alot(current_iter);
>             if (glob_look_poles)  then # if number 20
>                 check_for_pole();
>             fi;# end if 20;
>             if (reached_interval()) then # if number 20
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 20;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y2;
>             order_diff  := 4;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y2
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 4;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 4;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 3;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 3;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 3;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 3;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 3;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 3;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 4;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 4;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 3;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 3;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y2
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y2_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #END SUM AND ADJUST EQ =1
>             #END PART 1
>             #START PART 2  MOVE TERMS to REGULAR Array
>             term_no := ATS_MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_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
>             #Jump Series array_y1;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =2
>             #sum_and_adjust array_y1
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #BEFORE ADJUST SUBSERIES EQ =2
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =2
>             #BEFORE SUM SUBSERIES EQ =2
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y1
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y1_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =2
>             #END SUM AND ADJUST EQ =2
>             #END PART 1
>             #START PART 2  MOVE TERMS to REGULAR Array
>             term_no := ATS_MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_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
>             ;
>         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  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
>         omniout_str(INFO,"diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
>         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,"2015-05-02T17:56:53-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"mtest4.ode.txt\">mtest4</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ")
>             ;
>             logitem_float(html_log_file,x_start)
>             ;
>             logitem_float(html_log_file,x_end)
>             ;
>             logitem_float(html_log_file,array_x[1])
>             ;
>             logitem_float(html_log_file,glob_h)
>             ;
>             logitem_h_reason(html_log_file)
>             ;
>             logitem_integer(html_log_file,Digits)
>             ;
>             ;
>             logitem_float(html_log_file,glob_desired_digits_correct)
>             ;
>             if (array_est_digits[1] <> -16) then # if number 21
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             if (glob_min_good_digits <> -16) then # if number 21
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             if (glob_good_digits <> -16) then # if number 21
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 21;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_integer(html_log_file,ATS_MAX_TERMS)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 21
>                 logitem_str(html_log_file,"Not Given")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 22
>                 logitem_str(html_log_file,"No Solution")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 23
>                 logitem_str(html_log_file,"Some Pole")
>                 ;
>                 logitem_str(html_log_file,"????")
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 24
>                 logitem_str(html_log_file,"No Pole")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 25
>                 logitem_str(html_log_file,"Real Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 26
>                 logitem_str(html_log_file,"Complex Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             fi;# end if 26;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_ratio_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             if (glob_least_3_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_3_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             if (glob_least_6_sing < glob_large_float) then # if number 26
>                 logitem_float(html_log_file,glob_least_6_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 26;
>             logitem_integer(html_log_file,glob_iter)
>             ;
>             logitem_time(html_log_file,(glob_clock_sec))
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 26
>                 logitem_time(html_log_file,(glob_total_exp_sec))
>                 ;
>                 0;
>             else
>                 logitem_str(html_log_file,"Done")
>                 ;
>                 0;
>             fi;# end if 26;
>             log_revs(html_log_file,"<td> 308.maple.seems.ok </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.mtest4.mxt.txt\">mtest4 diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.mtest4.mxt.txt\">mtest4 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  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ")
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             ;
>             logditto(html_log_file)
>             ;
>             if (array_est_digits[2] <> -16) then # if number 26
>                 logitem_integer(html_log_file,array_est_digits[2])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             if (glob_min_good_digits <> -16) then # if number 26
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             if (glob_good_digits <> -16) then # if number 26
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 26;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logditto(html_log_file)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 26
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 27
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 28
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 29
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 30
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 31
>                 logditto(html_log_file)
>                 ;
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_3_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             if (glob_least_6_sing < glob_large_float) then # if number 31
>                 logditto(html_log_file)
>                 ;
>             else
>                 logditto(html_log_file)
>                 ;
>             fi;# end if 31;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 31
>                 logditto(html_log_file)
>                 ;
>                 0;
>             else
>                 logditto(html_log_file)
>                 ;
>                 0;
>             fi;# end if 31;
>             logditto(html_log_file);
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logditto(html_log_file)
>             ;
>             logend(html_log_file)
>             ;
>             ;
>         fi;# end if 30;
>         if (glob_html_log)  then # if number 30
>             fclose(html_log_file);
>         fi;# end if 30
>         ;
>         ;;
>     fi;# end if 29
>     #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
    ATS_MAX_TERMS := 40;
    Digits := 32;
    max_terms := 40;
    glob_html_log := true;
    array_y2_init := Array(0 .. 40, []);
    array_y1_init := Array(0 .. 40, []);
    array_norms := Array(0 .. 40, []);
    array_fact_1 := Array(0 .. 40, []);
    array_1st_rel_error := Array(0 .. 3, []);
    array_last_rel_error := Array(0 .. 3, []);
    array_est_rel_error := Array(0 .. 3, []);
    array_max_est_error := Array(0 .. 3, []);
    array_type_pole := Array(0 .. 3, []);
    array_type_real_pole := Array(0 .. 3, []);
    array_type_complex_pole := Array(0 .. 3, []);
    array_est_digits := Array(0 .. 3, []);
    array_y2 := Array(0 .. 40, []);
    array_x := Array(0 .. 40, []);
    array_y1 := Array(0 .. 40, []);
    array_tmp0 := Array(0 .. 40, []);
    array_tmp1_g := Array(0 .. 40, []);
    array_tmp1 := Array(0 .. 40, []);
    array_tmp2 := Array(0 .. 40, []);
    array_tmp3 := Array(0 .. 40, []);
    array_tmp4 := Array(0 .. 40, []);
    array_tmp5 := Array(0 .. 40, []);
    array_m1 := Array(0 .. 40, []);
    array_y2_higher := Array(0 .. 4, 0 .. 41, []);
    array_y2_higher_work := Array(0 .. 4, 0 .. 41, []);
    array_y2_higher_work2 := Array(0 .. 4, 0 .. 41, []);
    array_y2_set_initial := Array(0 .. 3, 0 .. 41, []);
    array_y1_higher := Array(0 .. 2, 0 .. 41, []);
    array_y1_higher_work := Array(0 .. 2, 0 .. 41, []);
    array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []);
    array_y1_set_initial := Array(0 .. 3, 0 .. 41, []);
    array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
    array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
    array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
    array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
    array_fact_2 := Array(0 .. 40, 0 .. 41, []);
    term := 1;
    while term <= 40 do array_y2_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_y1_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do
        array_last_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
    term := 1;
    while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
    ;
    term := 1;
    while term <= 40 do array_y2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_y1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 4 do
        term := 1;
        while term <= 40 do
            array_y2_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 4 do
        term := 1;
        while term <= 40 do
            array_y2_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 4 do
        term := 1;
        while term <= 40 do
            array_y2_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 40 do
            array_y2_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 40 do
            array_y1_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 40 do
            array_y1_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 3 do
            array_given_rad_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 3 do
            array_given_ord_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 4 do
            array_rad_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= 4 do
            array_ord_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 40 do
        term := 1;
        while term <= 40 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y2);
    zero_ats_ar(array_x);
    zero_ats_ar(array_y1);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1_g);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_tmp4);
    zero_ats_ar(array_tmp5);
    zero_ats_ar(array_m1);
    zero_ats_ar(array_const_3);
    array_const_3[1] := c(3);
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := c(0.);
    zero_ats_ar(array_const_1);
    array_const_1[1] := c(1);
    zero_ats_ar(array_m1);
    array_m1[1] := glob__m1;
    iiif := 0;
    while iiif <= ATS_MAX_TERMS do
        jjjf := 0;
        while jjjf <= ATS_MAX_TERMS do
            array_fact_1[iiif] := 0;
            array_fact_2[iiif, jjjf] := 0;
            jjjf := jjjf + 1
        end do;
        iiif := iiif + 1
    end do;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := 5;
    glob_yes_pole := 4;
    glob_no_pole := 3;
    glob_not_given := 0;
    glob_no_sing_tests := 4;
    glob_ratio_test := 1;
    glob_three_term_test := 2;
    glob_six_term_test := 3;
    glob_log_10 := log(c(10.0));
    MAX_UNCHANGED := 10;
    glob__small := c(0.1*10^(-50));
    glob_small_float := c(0.1*10^(-50));
    glob_smallish_float := c(0.1*10^(-60));
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob__m2 := c(-2);
    glob__m1 := c(-1);
    glob__0 := c(0);
    glob__1 := c(1);
    glob__2 := c(2);
    glob__3 := c(3);
    glob__4 := c(4);
    glob__5 := c(5);
    glob__8 := c(8);
    glob__10 := c(10);
    glob__100 := c(100);
    glob__pi := c(0.);
    glob__0_5 := c(0.5);
    glob__0_8 := c(0.8);
    glob__m0_8 := c(-0.8);
    glob__0_25 := c(0.25);
    glob__0_125 := c(0.125);
    glob_prec := c(0.10*10^(-15));
    glob_check_sign := c(1.0);
    glob_desired_digits_correct := c(8.0);
    glob_max_estimated_step_error := c(0.);
    glob_ratio_of_radius := c(0.1);
    glob_percent_done := c(0.);
    glob_total_exp_sec := c(0.1);
    glob_optimal_expect_sec := c(0.1);
    glob_estimated_size_answer := c(100.0);
    glob_almost_1 := c(0.9990);
    glob_clock_sec := c(0.);
    glob_clock_start_sec := c(0.);
    glob_disp_incr := c(0.1);
    glob_h := c(0.1);
    glob_diff_rc_fm := c(0.1);
    glob_diff_rc_fmm1 := c(0.1);
    glob_diff_rc_fmm2 := c(0.1);
    glob_diff_ord_fm := c(0.1);
    glob_diff_ord_fmm1 := c(0.1);
    glob_diff_ord_fmm2 := c(0.1);
    glob_six_term_ord_save := c(0.1);
    glob_guess_error_rc := c(0.1);
    glob_guess_error_ord := c(0.1);
    glob_least_given_sing := c(0.99*10^201);
    glob_least_ratio_sing := c(0.99*10^201);
    glob_least_3_sing := c(0.99*10^101);
    glob_least_6_sing := c(0.99*10^101);
    glob_last_good_h := c(0.1);
    glob_max_h := c(0.1);
    glob_min_h := c(0.1*10^(-5));
    glob_display_interval := c(0.1);
    glob_abserr := c(0.1*10^(-10));
    glob_relerr := c(0.1*10^(-10));
    glob_min_pole_est := c(0.1*10^10);
    glob_max_rel_trunc_err := c(0.1*10^(-10));
    glob_max_trunc_err := c(0.1*10^(-10));
    glob_max_hours := c(0.);
    glob_optimal_clock_start_sec := c(0.);
    glob_optimal_start := c(0.);
    glob_upper_ratio_limit := c(1.0001);
    glob_lower_ratio_limit := c(0.9999);
    glob_max_sec := c(10000.0);
    glob_orig_start_sec := c(0.);
    glob_normmax := c(0.);
    glob_max_minutes := c(0.);
    glob_next_display := c(0.);
    glob_est_digits := 1;
    glob_subiter_method := 3;
    glob_html_log := true;
    glob_min_good_digits := 99999;
    glob_good_digits := 0;
    glob_min_apfp_est_good_digits := 99999;
    glob_apfp_est_good_digits := 0;
    glob_max_opt_iter := 10;
    glob_dump := false;
    glob_djd_debug := true;
    glob_display_flag := true;
    glob_djd_debug2 := true;
    glob_h_reason := 0;
    glob_sec_in_minute := 60;
    glob_min_in_hour := 60;
    glob_hours_in_day := 24;
    glob_days_in_year := 365;
    glob_sec_in_hour := 3600;
    glob_sec_in_day := 86400;
    glob_sec_in_year := 31536000;
    glob_not_yet_finished := true;
    glob_initial_pass := true;
    glob_not_yet_start_msg := true;
    glob_reached_optimal_h := false;
    glob_optimal_done := false;
    glob_type_given_pole := 0;
    glob_optimize := false;
    glob_look_poles := false;
    glob_dump_closed_form := false;
    glob_max_iter := 1000;
    glob_no_eqs := 0;
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_start := 0;
    glob_iter := 0;
    array_y2_set_initial[1, 1] := true;
    array_y2_set_initial[1, 2] := true;
    array_y2_set_initial[1, 3] := true;
    array_y2_set_initial[1, 4] := false;
    array_y2_set_initial[1, 5] := false;
    array_y2_set_initial[1, 6] := false;
    array_y2_set_initial[1, 7] := false;
    array_y2_set_initial[1, 8] := false;
    array_y2_set_initial[1, 9] := false;
    array_y2_set_initial[1, 10] := false;
    array_y2_set_initial[1, 11] := false;
    array_y2_set_initial[1, 12] := false;
    array_y2_set_initial[1, 13] := false;
    array_y2_set_initial[1, 14] := false;
    array_y2_set_initial[1, 15] := false;
    array_y2_set_initial[1, 16] := false;
    array_y2_set_initial[1, 17] := false;
    array_y2_set_initial[1, 18] := false;
    array_y2_set_initial[1, 19] := false;
    array_y2_set_initial[1, 20] := false;
    array_y2_set_initial[1, 21] := false;
    array_y2_set_initial[1, 22] := false;
    array_y2_set_initial[1, 23] := false;
    array_y2_set_initial[1, 24] := false;
    array_y2_set_initial[1, 25] := false;
    array_y2_set_initial[1, 26] := false;
    array_y2_set_initial[1, 27] := false;
    array_y2_set_initial[1, 28] := false;
    array_y2_set_initial[1, 29] := false;
    array_y2_set_initial[1, 30] := false;
    array_y2_set_initial[1, 31] := false;
    array_y2_set_initial[1, 32] := false;
    array_y2_set_initial[1, 33] := false;
    array_y2_set_initial[1, 34] := false;
    array_y2_set_initial[1, 35] := false;
    array_y2_set_initial[1, 36] := false;
    array_y2_set_initial[1, 37] := false;
    array_y2_set_initial[1, 38] := false;
    array_y2_set_initial[1, 39] := false;
    array_y2_set_initial[1, 40] := false;
    array_y1_set_initial[2, 1] := true;
    array_y1_set_initial[2, 2] := false;
    array_y1_set_initial[2, 3] := false;
    array_y1_set_initial[2, 4] := false;
    array_y1_set_initial[2, 5] := false;
    array_y1_set_initial[2, 6] := false;
    array_y1_set_initial[2, 7] := false;
    array_y1_set_initial[2, 8] := false;
    array_y1_set_initial[2, 9] := false;
    array_y1_set_initial[2, 10] := false;
    array_y1_set_initial[2, 11] := false;
    array_y1_set_initial[2, 12] := false;
    array_y1_set_initial[2, 13] := false;
    array_y1_set_initial[2, 14] := false;
    array_y1_set_initial[2, 15] := false;
    array_y1_set_initial[2, 16] := false;
    array_y1_set_initial[2, 17] := false;
    array_y1_set_initial[2, 18] := false;
    array_y1_set_initial[2, 19] := false;
    array_y1_set_initial[2, 20] := false;
    array_y1_set_initial[2, 21] := false;
    array_y1_set_initial[2, 22] := false;
    array_y1_set_initial[2, 23] := false;
    array_y1_set_initial[2, 24] := false;
    array_y1_set_initial[2, 25] := false;
    array_y1_set_initial[2, 26] := false;
    array_y1_set_initial[2, 27] := false;
    array_y1_set_initial[2, 28] := false;
    array_y1_set_initial[2, 29] := false;
    array_y1_set_initial[2, 30] := false;
    array_y1_set_initial[2, 31] := false;
    array_y1_set_initial[2, 32] := false;
    array_y1_set_initial[2, 33] := false;
    array_y1_set_initial[2, 34] := false;
    array_y1_set_initial[2, 35] := false;
    array_y1_set_initial[2, 36] := false;
    array_y1_set_initial[2, 37] := false;
    array_y1_set_initial[2, 38] := false;
    array_y1_set_initial[2, 39] := false;
    array_y1_set_initial[2, 40] := false;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 40;
    glob_iolevel := INFO;
    glob_orig_start_sec := elapsed_time_seconds();
    glob_display_flag := true;
    glob_no_eqs := 2;
    glob_iter := -1;
    opt_iter := -1;
    glob_max_iter := 50000;
    glob_max_hours := 0.;
    glob_max_minutes := 15.0;
    omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
    omniout_str(ALWAYS,
        "##############temp/mtest4postode.ode#################");
    omniout_str(ALWAYS,
        "diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
    omniout_str(ALWAYS, "diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ")
        ;
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=40;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(0.1);");
    omniout_str(ALWAYS, "x_end := c(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, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
        ;
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 3;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
    omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
    omniout_str(ALWAYS, "glob_subiter_method:=3;");
    omniout_str(ALWAYS, "glob_max_iter:=100000;");
    omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
    omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
    omniout_str(ALWAYS, "glob_look_poles:=true;");
    omniout_str(ALWAYS, "glob_h:=c(0.001);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
    omniout_str(ALWAYS, "return(sin(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
    omniout_str(ALWAYS, "return( cos(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
    omniout_str(ALWAYS, "return( neg( sin(c(x))));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
    omniout_str(ALWAYS, "return( cos(c(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 := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(0.1);
    x_end := c(5.0);
    array_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);
    array_y2_init[3] := exact_soln_y2pp(x_start);
    glob_look_poles := true;
    glob_type_given_pole := 3;
    glob_desired_digits_correct := 8;
    glob_max_minutes := 3.0;
    glob_subiter_method := 3;
    glob_max_iter := 100000;
    glob_upper_ratio_limit := c(1.0000001);
    glob_lower_ratio_limit := c(0.9999999);
    glob_look_poles := true;
    glob_h := c(0.001);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(x_start, x_end));
    glob__pi := arccos(glob__m1);
    glob_prec = expt(10.0, c(-Digits));
    if glob_optimize then
        omniout_str(ALWAYS, "START of Optimize");
        found_h := false;
        glob_min_pole_est := glob_larger_float;
        last_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        glob_min_h := float_abs(glob_min_h)*glob_check_sign;
        glob_max_h := float_abs(glob_max_h)*glob_check_sign;
        glob_h := float_abs(glob_min_h)*glob_check_sign;
        glob_display_interval :=
            c(float_abs(c(glob_display_interval))*glob_check_sign);
        display_max := c(x_end) - c(x_start)/glob__10;
        if display_max < glob_display_interval then
            glob_display_interval := c(display_max)
        end if;
        chk_data();
        min_value := glob_larger_float;
        est_answer := est_size_answer();
        opt_iter := 1;
        est_needed_step_err :=
            estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
            ;
        omniout_float(ALWAYS, "est_needed_step_err", 32,
            est_needed_step_err, 16, "");
        estimated_step_error := glob_small_float;
        while opt_iter <= 100 and not found_h do
            omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
            array_x[1] := c(x_start);
            array_x[2] := c(glob_h);
            glob_next_display := c(x_start);
            order_diff := 3;
            term_no := 1;
            while term_no <= order_diff do
                array_y2[term_no] := array_y2_init[term_no]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1));
                term_no := term_no + 1
            end do;
            rows := order_diff;
            r_order := 1;
            while r_order <= rows do
                term_no := 1;
                while term_no <= rows - r_order + 1 do
                    it := term_no + r_order - 1;
                    if term_no < ATS_MAX_TERMS then
                        array_y2_higher[r_order, term_no] :=
                        array_y2_init[it]*expt(glob_h, c(term_no - 1))/
                        c(factorial_1(term_no - 1))
                    end if;
                    term_no := term_no + 1
                end do;
                r_order := r_order + 1
            end do;
            order_diff := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y1[term_no] := array_y1_init[term_no]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1));
                term_no := term_no + 1
            end do;
            rows := order_diff;
            r_order := 1;
            while r_order <= rows do
                term_no := 1;
                while term_no <= rows - r_order + 1 do
                    it := term_no + r_order - 1;
                    if term_no < ATS_MAX_TERMS then
                        array_y1_higher[r_order, term_no] :=
                        array_y1_init[it]*expt(glob_h, c(term_no - 1))/
                        c(factorial_1(term_no - 1))
                    end if;
                    term_no := term_no + 1
                end do;
                r_order := r_order + 1
            end do;
            if glob_subiter_method = 1 then atomall()
            elif glob_subiter_method = 2 then
                subiter := 1;
                while subiter <= 4 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 4 + ATS_MAX_TERMS do
                    atomall(); subiter := subiter + 1
                end do
            end if;
            if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
                omniout_str(ALWAYS, "SETTING H FOR MIN H");
                glob_h := float_abs(glob_min_h)*glob_check_sign;
                glob_h_reason := 1;
                found_h := true
            end if;
            if
            glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
            then
                omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
                glob_h_reason := 2;
                glob_h := glob_display_interval;
                found_h := true
            end if;
            if glob_look_poles then check_for_pole() end if;
            if not found_h then
                est_answer := est_size_answer();
                est_needed_step_err := estimated_needed_step_error(x_start,
                    x_end, glob_h, est_answer);
                omniout_float(ALWAYS, "est_needed_step_err", 32,
                    est_needed_step_err, 16, "");
                estimated_step_error := test_suggested_h();
                omniout_float(ALWAYS, "estimated_step_error", 32,
                    estimated_step_error, 32, "");
                if estimated_step_error < est_needed_step_err then
                    omniout_str(ALWAYS, "Double H and LOOP");
                    glob_h := glob_h*glob__2
                else
                    omniout_str(ALWAYS, "Found H for OPTIMAL");
                    found_h := true;
                    glob_h_reason := 3;
                    glob_h := glob_h/glob__2
                end if
            end if;
            opt_iter := opt_iter + 1
        end do;
        if not found_h and opt_iter = 1 then
            omniout_str(ALWAYS, "Beginning glob_h too large.");
            found_h := false
        end if;
        if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
            omniout_str(ALWAYS, "SETTING H FOR MAX H");
            glob_h := float_abs(glob_max_h)*glob_check_sign;
            glob_h_reason := 1;
            found_h := true
        end if
    else found_h := true; glob_h := glob_check_sign*glob_h
    end if;
    if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
    end if;
    if found_h then
        omniout_str(ALWAYS, "START of Soultion");
        array_x[1] := c(x_start);
        array_x[2] := c(glob_h);
        glob_next_display := c(x_start);
        glob_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        order_diff := 3;
        term_no := 1;
        while term_no <= order_diff do
            array_y2[term_no] := array_y2_init[term_no]*
                expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
            term_no := term_no + 1
        end do;
        rows := order_diff;
        r_order := 1;
        while r_order <= rows do
            term_no := 1;
            while term_no <= rows - r_order + 1 do
                it := term_no + r_order - 1;
                if term_no < ATS_MAX_TERMS then
                    array_y2_higher[r_order, term_no] := array_y2_init[it]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1))
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y1[term_no] := array_y1_init[term_no]*
                expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
            term_no := term_no + 1
        end do;
        rows := order_diff;
        r_order := 1;
        while r_order <= rows do
            term_no := 1;
            while term_no <= rows - r_order + 1 do
                it := term_no + r_order - 1;
                if term_no < ATS_MAX_TERMS then
                    array_y1_higher[r_order, term_no] := array_y1_init[it]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1))
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        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 <= 4 do atomall(); subiter := subiter + 1
                end do
            else
                subiter := 1;
                while subiter <= 4 + ATS_MAX_TERMS do
                    atomall(); subiter := subiter + 1
                end do
            end if;
            track_estimated_error();
            display_alot(current_iter);
            if glob_look_poles then check_for_pole() end if;
            if reached_interval() then glob_next_display :=
                glob_next_display + glob_display_interval
            end if;
            array_x[1] := array_x[1] + glob_h;
            array_x[2] := glob_h;
            order_diff := 4;
            ord := 4;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 4;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 3;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 3;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 3;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 3;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 4;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 4;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 3;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y2_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y2_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            term_no := ATS_MAX_TERMS;
            while 1 <= term_no do
                array_y2[term_no] := array_y2_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y2_higher[ord, term_no] :=
                        array_y2_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y1_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y1_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            term_no := ATS_MAX_TERMS;
            while 1 <= term_no do
                array_y1[term_no] := array_y1_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y1_higher[ord, term_no] :=
                        array_y1_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do
        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  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; ");
        omniout_str(INFO,
            "diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
        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, "2015-05-02T17:56:53-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"mtest4.ode.txt\">mtest4</a>");
            logitem_str(html_log_file, "diff  (  y2  ,  x  ,  3  )   =  n\
                eg (  cos  (  x  )   )  ; ");
            logitem_float(html_log_file, x_start);
            logitem_float(html_log_file, x_end);
            logitem_float(html_log_file, array_x[1]);
            logitem_float(html_log_file, glob_h);
            logitem_h_reason(html_log_file);
            logitem_integer(html_log_file, Digits);
            logitem_float(html_log_file, glob_desired_digits_correct);
            if array_est_digits[1] <> -16 then
                logitem_integer(html_log_file, array_est_digits[1])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_min_good_digits <> -16 then
                logitem_integer(html_log_file, glob_min_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_good_digits <> -16 then
                logitem_integer(html_log_file, glob_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            logitem_integer(html_log_file, ATS_MAX_TERMS);
            if glob_type_given_pole = 0 then
                logitem_str(html_log_file, "Not Given");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 4 then
                logitem_str(html_log_file, "No Solution");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 5 then
                logitem_str(html_log_file, "Some Pole");
                logitem_str(html_log_file, "????")
            elif glob_type_given_pole = 3 then
                logitem_str(html_log_file, "No Pole");
                logitem_str(html_log_file, "NA")
            elif glob_type_given_pole = 1 then
                logitem_str(html_log_file, "Real Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            elif glob_type_given_pole = 2 then
                logitem_str(html_log_file, "Complex Sing");
                logitem_float(html_log_file, glob_least_given_sing)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_ratio_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_3_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_3_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            if glob_least_6_sing < glob_large_float then
                logitem_float(html_log_file, glob_least_6_sing)
            else logitem_str(html_log_file, "NONE")
            end if;
            logitem_integer(html_log_file, glob_iter);
            logitem_time(html_log_file, glob_clock_sec);
            if c(glob_percent_done) < glob__100 then
                logitem_time(html_log_file, glob_total_exp_sec); 0
            else logitem_str(html_log_file, "Done"); 0
            end if;
            log_revs(html_log_file, "<td> 308.maple.seems.ok </td>");
            logitem_str(html_log_file,
                "<a href=\"diffeq.mtest4.mxt.txt\">mtest4 diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.mtest4.mxt.txt\\
                ">mtest4 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  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; ");
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            if array_est_digits[2] <> -16 then
                logitem_integer(html_log_file, array_est_digits[2])
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_min_good_digits <> -16 then
                logitem_integer(html_log_file, glob_min_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            if glob_good_digits <> -16 then
                logitem_integer(html_log_file, glob_good_digits)
            else logitem_str(html_log_file, "Unknown")
            end if;
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            logditto(html_log_file);
            if glob_type_given_pole = 0 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 4 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 5 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 3 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 1 then
                logditto(html_log_file); logditto(html_log_file)
            elif glob_type_given_pole = 2 then
                logditto(html_log_file); logditto(html_log_file)
            end if;
            if glob_least_ratio_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            if glob_least_3_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            if glob_least_6_sing < glob_large_float then
                logditto(html_log_file)
            else logditto(html_log_file)
            end if;
            logditto(html_log_file);
            logditto(html_log_file);
            if c(glob_percent_done) < glob__100 then
                logditto(html_log_file); 0
            else logditto(html_log_file); 0
            end if;
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logditto(html_log_file);
            logend(html_log_file)
        end if;
        if glob_html_log then fclose(html_log_file) end if
    end if
end proc

# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest4postode.ode#################
diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; 
diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(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);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
glob_look_poles := true;







glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y2 := proc(x)
return(sin(c(x)));
end;
exact_soln_y2p := proc(x)
return( cos(c(x)));
end;
exact_soln_y2pp := proc(x)
return( neg( sin(c(x))));
end;
exact_soln_y1 := proc(x)
return( cos(c(x)));
end;

#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 0.1                                          
y2[1] (closed_form)               = 0.099833416646828152306814198410622          
y2[1] (numeric)                   = 0.099833416646828152306814198410622          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.99500416527802576609556198780387           
y1[1] (numeric)                   = 0.99500416527802576609556198780387           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.09933                                      
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.09933                                      
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=42.4MB, alloc=40.3MB, time=0.53
memory used=83.7MB, alloc=40.3MB, time=0.98
 
TOP MAIN SOLVE Loop
memory used=124.8MB, alloc=40.3MB, time=1.42
x[1]                              = 0.11                                         
y2[1] (closed_form)               = 0.10977830083717480866494949008345           
y2[1] (numeric)                   = 0.10977830083717480866494949008347           
absolute error                    = 2e-32                                        
relative error                    = 1.8218536675717332517910891446314e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.99395609795669685035783961141985           
y1[1] (numeric)                   = 0.99395609795669685035783961141984           
absolute error                    = 1e-32                                        
relative error                    = 1.0060806529138739295356804682092e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1091                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1091                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=166.1MB, alloc=40.3MB, time=1.87
memory used=207.3MB, alloc=40.3MB, time=2.31
 
TOP MAIN SOLVE Loop
x[1]                              = 0.12                                         
y2[1] (closed_form)               = 0.11971220728891935996735061427097           
y2[1] (numeric)                   = 0.119712207288919359967350614271             
absolute error                    = 3e-32                                        
relative error                    = 2.5060100953277485493704713765586e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.99280863585386625224809816785763           
y1[1] (numeric)                   = 0.99280863585386625224809816785762           
absolute error                    = 1e-32                                        
relative error                    = 1.0072434544648665414102250278741e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1189                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1189                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=248.5MB, alloc=40.3MB, time=2.77
memory used=289.6MB, alloc=40.3MB, time=3.20
memory used=330.7MB, alloc=40.3MB, time=3.66
 
TOP MAIN SOLVE Loop
x[1]                              = 0.13                                         
y2[1] (closed_form)               = 0.12963414261969485954120581070831           
y2[1] (numeric)                   = 0.12963414261969485954120581070834           
absolute error                    = 3e-32                                        
relative error                    = 2.3142051464027043651080784631679e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.99156189371478803959451217115181           
y1[1] (numeric)                   = 0.99156189371478803959451217115181           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1285                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1285                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=372.0MB, alloc=40.3MB, time=4.09
memory used=413.2MB, alloc=40.3MB, time=4.53
memory used=454.4MB, alloc=40.3MB, time=4.98
 
TOP MAIN SOLVE Loop
x[1]                              = 0.14                                         
y2[1] (closed_form)               = 0.13954311464423648171798835170537           
y2[1] (numeric)                   = 0.13954311464423648171798835170541           
absolute error                    = 4e-32                                        
relative error                    = 2.8664975768943904047348344728184e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.9902159962126371718989482270114            
y1[1] (numeric)                   = 0.99021599621263717189894822701139           
absolute error                    = 1e-32                                        
relative error                    = 1.0098806763623134088645046107846e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1382                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1382                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=495.6MB, alloc=40.3MB, time=5.42
memory used=536.8MB, alloc=40.3MB, time=5.86
 
TOP MAIN SOLVE Loop
memory used=577.9MB, alloc=40.3MB, time=6.31
x[1]                              = 0.15                                         
y2[1] (closed_form)               = 0.14943813247359922149772543868764           
y2[1] (numeric)                   = 0.14943813247359922149772543868767           
absolute error                    = 3e-32                                        
relative error                    = 2.0075197343154705432671799057549e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.98877107793604228673498099865434           
y1[1] (numeric)                   = 0.98877107793604228673498099865433           
absolute error                    = 1e-32                                        
relative error                    = 1.0113564426736640909001707623026e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1478                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1478                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=619.2MB, alloc=40.3MB, time=6.75
memory used=660.2MB, alloc=40.3MB, time=7.20
 
TOP MAIN SOLVE Loop
memory used=701.4MB, alloc=40.3MB, time=7.64
x[1]                              = 0.16                                         
y2[1] (closed_form)               = 0.15931820661424596331146315968599           
y2[1] (numeric)                   = 0.15931820661424596331146315968603           
absolute error                    = 4e-32                                        
relative error                    = 2.5106986106648320739151935355573e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.98722728337562694904095252401834           
y1[1] (numeric)                   = 0.98722728337562694904095252401834           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1573                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1573                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=742.6MB, alloc=40.3MB, time=8.08
memory used=783.8MB, alloc=40.3MB, time=8.53
 
TOP MAIN SOLVE Loop
x[1]                              = 0.17                                         
y2[1] (closed_form)               = 0.16918234906699601015762437667085           
y2[1] (numeric)                   = 0.1691823490669960101576243766709            
absolute error                    = 5e-32                                        
relative error                    = 2.9553910485189006998222702989205e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.9855847669095607091719299902125            
y1[1] (numeric)                   = 0.98558476690956070917192999021251           
absolute error                    = 1e-32                                        
relative error                    = 1.0146260713176810517259565757587e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1667                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1667                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=825.1MB, alloc=40.3MB, time=8.97
memory used=866.3MB, alloc=40.3MB, time=9.41
memory used=907.5MB, alloc=40.3MB, time=9.86
 
TOP MAIN SOLVE Loop
x[1]                              = 0.18                                         
y2[1] (closed_form)               = 0.17902957342582417834180273969921           
y2[1] (numeric)                   = 0.17902957342582417834180273969926           
absolute error                    = 5e-32                                        
relative error                    = 2.7928346721284056824311567640715e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.98384369278812141459271602461153           
y1[1] (numeric)                   = 0.98384369278812141459271602461154           
absolute error                    = 1e-32                                        
relative error                    = 1.0164216199486862747130581631310e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1761                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1761                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=948.8MB, alloc=40.3MB, time=10.30
memory used=989.9MB, alloc=40.3MB, time=10.73
memory used=1031.2MB, alloc=40.3MB, time=11.19
 
TOP MAIN SOLVE Loop
x[1]                              = 0.19                                         
y2[1] (closed_form)               = 0.18885889497650057799285115298131           
y2[1] (numeric)                   = 0.18885889497650057799285115298135           
absolute error                    = 4e-32                                        
relative error                    = 2.1179833761590704274770212663126e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.98200423511727031896787750418991           
y1[1] (numeric)                   = 0.98200423511727031896787750418992           
absolute error                    = 1e-32                                        
relative error                    = 1.0183255471200494754242006144117e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1855                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1855                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1072.5MB, alloc=40.3MB, time=11.64
memory used=1113.7MB, alloc=40.3MB, time=12.08
 
TOP MAIN SOLVE Loop
memory used=1154.9MB, alloc=40.3MB, time=12.53
x[1]                              = 0.2                                          
y2[1] (closed_form)               = 0.19866933079506121545941262711839           
y2[1] (numeric)                   = 0.19866933079506121545941262711844           
absolute error                    = 5e-32                                        
relative error                    = 2.5167447738361721012130481837629e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.98006657784124163112419651674817           
y1[1] (numeric)                   = 0.98006657784124163112419651674816           
absolute error                    = 1e-32                                        
relative error                    = 1.0203388449411926897924327768492e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1947                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1947                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1196.2MB, alloc=40.3MB, time=12.97
memory used=1237.4MB, alloc=40.3MB, time=13.42
 
TOP MAIN SOLVE Loop
x[1]                              = 0.21                                         
y2[1] (closed_form)               = 0.20845989984609957060871242622764           
y2[1] (numeric)                   = 0.2084598998460995706087124262277            
absolute error                    = 6e-32                                        
relative error                    = 2.8782514068315495085983108012333e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.97803091472414824491613856809935           
y1[1] (numeric)                   = 0.97803091472414824491613856809934           
absolute error                    = 1e-32                                        
relative error                    = 1.0224625673331073524464086165795e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2039                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2039                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1278.7MB, alloc=40.3MB, time=13.86
memory used=1319.9MB, alloc=40.3MB, time=14.31
memory used=1361.1MB, alloc=40.3MB, time=14.75
 
TOP MAIN SOLVE Loop
x[1]                              = 0.22                                         
y2[1] (closed_form)               = 0.21822962308086931995179100545701           
y2[1] (numeric)                   = 0.21822962308086931995179100545707           
absolute error                    = 6e-32                                        
relative error                    = 2.7493975910761578254322454743429e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.9758974493306054894060229810447            
y1[1] (numeric)                   = 0.9758974493306054894060229810447            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.213                                        
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.213                                        
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1402.4MB, alloc=40.3MB, time=15.20
memory used=1443.6MB, alloc=40.3MB, time=15.64
memory used=1484.9MB, alloc=40.3MB, time=16.08
 
TOP MAIN SOLVE Loop
x[1]                              = 0.23                                         
y2[1] (closed_form)               = 0.22797752353518839540461721236007           
y2[1] (numeric)                   = 0.22797752353518839540461721236013           
absolute error                    = 6e-32                                        
relative error                    = 2.6318383965925914177221340142687e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.9736663950053748369677306480716            
y1[1] (numeric)                   = 0.97366639500537483696773064807161           
absolute error                    = 1e-32                                        
relative error                    = 1.0270458189064641551739991395066e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.222                                        
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.222                                        
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1526.2MB, alloc=40.3MB, time=16.53
memory used=1567.4MB, alloc=40.3MB, time=16.97
memory used=1608.6MB, alloc=40.3MB, time=17.42
 
TOP MAIN SOLVE Loop
x[1]                              = 0.24                                         
y2[1] (closed_form)               = 0.23770262642713458836079208448982           
y2[1] (numeric)                   = 0.23770262642713458836079208448987           
absolute error                    = 5e-32                                        
relative error                    = 2.1034685544514591305546015880043e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.97133797485202960492617524696338           
y1[1] (numeric)                   = 0.97133797485202960492617524696339           
absolute error                    = 1e-32                                        
relative error                    = 1.0295077778178462266084903163054e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2309                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2309                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1649.9MB, alloc=40.3MB, time=17.88
memory used=1691.1MB, alloc=40.3MB, time=18.31
 
TOP MAIN SOLVE Loop
memory used=1732.4MB, alloc=40.3MB, time=18.75
x[1]                              = 0.25                                         
y2[1] (closed_form)               = 0.24740395925452292959684870484939           
y2[1] (numeric)                   = 0.24740395925452292959684870484943           
absolute error                    = 4e-32                                        
relative error                    = 1.6167890004884284291332797332231e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.96891242171064478414459544949419           
y1[1] (numeric)                   = 0.96891242171064478414459544949419           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2397                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2397                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1773.6MB, alloc=40.3MB, time=19.20
memory used=1814.9MB, alloc=40.3MB, time=19.64
 
TOP MAIN SOLVE Loop
x[1]                              = 0.26                                         
y2[1] (closed_form)               = 0.25708055189215509735338846436522           
y2[1] (numeric)                   = 0.25708055189215509735338846436526           
absolute error                    = 4e-32                                        
relative error                    = 1.5559325552086079033359390319003e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.96638997813451322555821764645006           
y1[1] (numeric)                   = 0.96638997813451322555821764645006           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2484                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2484                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1856.1MB, alloc=40.3MB, time=20.09
memory used=1897.3MB, alloc=40.3MB, time=20.53
memory used=1938.6MB, alloc=40.3MB, time=20.98
 
TOP MAIN SOLVE Loop
x[1]                              = 0.27                                         
y2[1] (closed_form)               = 0.26673143668883112873228652102054           
y2[1] (numeric)                   = 0.26673143668883112873228652102057           
absolute error                    = 3e-32                                        
relative error                    = 1.1247268178215527492773931171829e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.9637708963658905130162327094922            
y1[1] (numeric)                   = 0.96377089636589051301623270949219           
absolute error                    = 1e-32                                        
relative error                    = 1.0375909915631601514930305045560e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2571                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2571                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=1979.8MB, alloc=40.3MB, time=21.42
memory used=2021.0MB, alloc=40.3MB, time=21.87
memory used=2062.2MB, alloc=40.3MB, time=22.31
 
TOP MAIN SOLVE Loop
x[1]                              = 0.28                                         
y2[1] (closed_form)               = 0.27635564856411373331966955845785           
y2[1] (numeric)                   = 0.27635564856411373331966955845788           
absolute error                    = 3e-32                                        
relative error                    = 1.0855576919043898016729914701780e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.96105543831077094792459005359648           
y1[1] (numeric)                   = 0.96105543831077094792459005359646           
absolute error                    = 2e-32                                        
relative error                    = 2.0810454009972227513247622478529e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2656                                       
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2656                                       
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2103.4MB, alloc=40.3MB, time=22.76
memory used=2144.6MB, alloc=40.3MB, time=23.20
 
TOP MAIN SOLVE Loop
memory used=2185.8MB, alloc=40.3MB, time=23.64
x[1]                              = 0.29                                         
y2[1] (closed_form)               = 0.28595222510483553268394020550437           
y2[1] (numeric)                   = 0.2859522251048355326839402055044            
absolute error                    = 3e-32                                        
relative error                    = 1.0491263003462004376796670684356e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.95824387551269716807012477793186           
y1[1] (numeric)                   = 0.95824387551269716807012477793186           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.274                                        
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.274                                        
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2227.2MB, alloc=40.3MB, time=24.09
memory used=2268.3MB, alloc=40.3MB, time=24.53
 
TOP MAIN SOLVE Loop
x[1]                              = 0.3                                          
y2[1] (closed_form)               = 0.29552020666133957510532074568503           
y2[1] (numeric)                   = 0.29552020666133957510532074568505           
absolute error                    = 2e-32                                        
relative error                    = 6.7677267236482451699209531029548e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.95533648912560601964231022756805           
y1[1] (numeric)                   = 0.95533648912560601964231022756806           
absolute error                    = 1e-32                                        
relative error                    = 1.0467516015380856009327908455870e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2823                                       
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2823                                       
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2309.6MB, alloc=40.3MB, time=24.98
memory used=2350.8MB, alloc=40.3MB, time=25.42
memory used=2392.0MB, alloc=40.3MB, time=25.86
 
TOP MAIN SOLVE Loop
x[1]                              = 0.31                                         
y2[1] (closed_form)               = 0.30505863644344350156564332395896           
y2[1] (numeric)                   = 0.30505863644344350156564332395898           
absolute error                    = 2e-32                                        
relative error                    = 6.5561166315997449231716170028411e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.95233356988571339784280543620221           
y1[1] (numeric)                   = 0.95233356988571339784280543620223           
absolute error                    = 2e-32                                        
relative error                    = 2.1001044836002303327454476474836e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2905                                       
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2905                                       
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2433.3MB, alloc=40.3MB, time=26.31
memory used=2474.4MB, alloc=40.3MB, time=26.75
memory used=2515.6MB, alloc=40.3MB, time=27.19
 
TOP MAIN SOLVE Loop
x[1]                              = 0.32                                         
y2[1] (closed_form)               = 0.31456656061611776666175754341715           
y2[1] (numeric)                   = 0.31456656061611776666175754341717           
absolute error                    = 2e-32                                        
relative error                    = 6.3579548826892185779101948190767e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.94923541808244086757530727376609           
y1[1] (numeric)                   = 0.94923541808244086757530727376611           
absolute error                    = 2e-32                                        
relative error                    = 2.1069588870168985639438319667824e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2986                                       
Order of pole (three term test)                    = 32.9                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2986                                       
Order of pole (three term test)                    = 32.1                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=2556.8MB, alloc=40.3MB, time=27.64
memory used=2598.0MB, alloc=40.3MB, time=28.08
memory used=2639.2MB, alloc=40.3MB, time=28.53
 
TOP MAIN SOLVE Loop
x[1]                              = 0.33                                         
y2[1] (closed_form)               = 0.32404302839486834670019569617022           
y2[1] (numeric)                   = 0.32404302839486834670019569617025           
absolute error                    = 3e-32                                        
relative error                    = 9.2580297587649288830101937482670e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.94604234352838697152941057836621           
y1[1] (numeric)                   = 0.94604234352838697152941057836622           
absolute error                    = 1e-32                                        
relative error                    = 1.0570351389033719013512246936692e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3066                                       
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3066                                       
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2680.5MB, alloc=40.3MB, time=28.97
memory used=2721.7MB, alloc=40.3MB, time=29.42
 
TOP MAIN SOLVE Loop
memory used=2762.9MB, alloc=40.3MB, time=29.86
x[1]                              = 0.34                                         
y2[1] (closed_form)               = 0.33348709214081439678177148703079           
y2[1] (numeric)                   = 0.33348709214081439678177148703082           
absolute error                    = 3e-32                                        
relative error                    = 8.9958504262985229685643473349653e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.94275466552834622850264406002658           
y1[1] (numeric)                   = 0.94275466552834622850264406002659           
absolute error                    = 1e-32                                        
relative error                    = 1.0607213483685831202937827622284e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3144                                       
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3144                                       
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2804.1MB, alloc=40.3MB, time=30.30
memory used=2845.4MB, alloc=40.3MB, time=30.75
 
TOP MAIN SOLVE Loop
x[1]                              = 0.35                                         
y2[1] (closed_form)               = 0.34289780745545134918963490691763           
y2[1] (numeric)                   = 0.34289780745545134918963490691765           
absolute error                    = 2e-32                                        
relative error                    = 5.8326415524247302509246725756321e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.93937271284737892003503235730367           
y1[1] (numeric)                   = 0.93937271284737892003503235730368           
absolute error                    = 1e-32                                        
relative error                    = 1.0645401833834950584242632965675e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3221                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3221                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=2886.6MB, alloc=40.3MB, time=31.19
memory used=2927.8MB, alloc=40.3MB, time=31.64
memory used=2969.1MB, alloc=40.3MB, time=32.08
 
TOP MAIN SOLVE Loop
x[1]                              = 0.36                                         
y2[1] (closed_form)               = 0.35227423327508997684991343592073           
y2[1] (numeric)                   = 0.35227423327508997684991343592075           
absolute error                    = 2e-32                                        
relative error                    = 5.6773950833872244012328772236860e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.93589682367793485835091236812474           
y1[1] (numeric)                   = 0.93589682367793485835091236812476           
absolute error                    = 2e-32                                        
relative error                    = 2.1369876992853746943292352547215e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3297                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3297                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3010.3MB, alloc=40.3MB, time=32.53
memory used=3051.5MB, alloc=40.3MB, time=32.97
memory used=3092.7MB, alloc=40.3MB, time=33.42
 
TOP MAIN SOLVE Loop
x[1]                              = 0.37                                         
y2[1] (closed_form)               = 0.36161543196496197803729246912715           
y2[1] (numeric)                   = 0.36161543196496197803729246912719           
absolute error                    = 4e-32                                        
relative error                    = 1.1061474833263123013366890623216e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.93232734560603442320381290449088           
y1[1] (numeric)                   = 0.9323273456060344232038129044909            
absolute error                    = 2e-32                                        
relative error                    = 2.1451693007030203111482463335611e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3371                                       
Order of pole (three term test)                    = 32.87                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3371                                       
Order of pole (three term test)                    = 32.13                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3134.0MB, alloc=40.3MB, time=33.86
memory used=3175.1MB, alloc=40.3MB, time=34.31
 
TOP MAIN SOLVE Loop
memory used=3216.4MB, alloc=40.3MB, time=34.75
x[1]                              = 0.38                                         
y2[1] (closed_form)               = 0.3709204694129826718454854663492            
y2[1] (numeric)                   = 0.37092046941298267184548546634924           
absolute error                    = 4e-32                                        
relative error                    = 1.0783982901591774726685676408678e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.92866463557651024949253080772456           
y1[1] (numeric)                   = 0.92866463557651024949253080772458           
absolute error                    = 2e-32                                        
relative error                    = 2.1536299794149157443180906061186e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3445                                       
Order of pole (three term test)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3445                                       
Order of pole (three term test)                    = 32.14                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3257.7MB, alloc=40.3MB, time=35.20
memory used=3298.8MB, alloc=40.3MB, time=35.64
 
TOP MAIN SOLVE Loop
memory used=3340.0MB, alloc=40.3MB, time=36.08
x[1]                              = 0.39                                         
y2[1] (closed_form)               = 0.38018841512316142823118209784716           
y2[1] (numeric)                   = 0.38018841512316142823118209784719           
absolute error                    = 3e-32                                        
relative error                    = 7.8908243404211956440396798999009e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.9249090598573130414506767528811            
y1[1] (numeric)                   = 0.92490905985731304145067675288112           
absolute error                    = 2e-32                                        
relative error                    = 2.1623747531552374206082103360578e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3516                                       
Order of pole (three term test)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3516                                       
Order of pole (three term test)                    = 32.14                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3381.3MB, alloc=40.3MB, time=36.53
memory used=3422.5MB, alloc=40.3MB, time=36.97
 
TOP MAIN SOLVE Loop
x[1]                              = 0.4                                          
y2[1] (closed_form)               = 0.38941834230865049166631175679571           
y2[1] (numeric)                   = 0.38941834230865049166631175679574           
absolute error                    = 3e-32                                        
relative error                    = 7.7037973666433492110340618900883e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.9210609940028850827985267320518            
y1[1] (numeric)                   = 0.92106099400288508279852673205182           
absolute error                    = 2e-32                                        
relative error                    = 2.1714088567664774062278599103175e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3587                                       
Order of pole (three term test)                    = 32.85                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3587                                       
Order of pole (three term test)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3463.8MB, alloc=40.3MB, time=37.42
memory used=3505.1MB, alloc=40.3MB, time=37.86
memory used=3546.3MB, alloc=40.3MB, time=38.30
 
TOP MAIN SOLVE Loop
x[1]                              = 0.41                                         
y2[1] (closed_form)               = 0.39860932798442289359379764005114           
y2[1] (numeric)                   = 0.39860932798442289359379764005118           
absolute error                    = 4e-32                                        
relative error                    = 1.0034888095133374599884491128482e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.91712082281660510547564205827702           
y1[1] (numeric)                   = 0.91712082281660510547564205827703           
absolute error                    = 1e-32                                        
relative error                    = 1.0903688752032272686284200446165e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3656                                       
Order of pole (three term test)                    = 32.84                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3656                                       
Order of pole (three term test)                    = 32.16                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3587.5MB, alloc=40.3MB, time=38.75
memory used=3628.8MB, alloc=40.3MB, time=39.19
memory used=3670.1MB, alloc=40.3MB, time=39.64
 
TOP MAIN SOLVE Loop
x[1]                              = 0.42                                         
y2[1] (closed_form)               = 0.40776045305957018597278715808634           
y2[1] (numeric)                   = 0.40776045305957018597278715808638           
absolute error                    = 4e-32                                        
relative error                    = 9.8096810761970471765127527641685e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.91308894031230827243608878966567           
y1[1] (numeric)                   = 0.91308894031230827243608878966567           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3723                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3723                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3711.4MB, alloc=40.3MB, time=40.08
memory used=3752.7MB, alloc=40.3MB, time=40.53
 
TOP MAIN SOLVE Loop
memory used=3793.9MB, alloc=40.3MB, time=40.97
x[1]                              = 0.43                                         
y2[1] (closed_form)               = 0.41687080242921076621691867262457           
y2[1] (numeric)                   = 0.4168708024292107662169186726246            
absolute error                    = 3e-32                                        
relative error                    = 7.1964742613736612050260047179132e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.90896574967488512247591047766345           
y1[1] (numeric)                   = 0.90896574967488512247591047766343           
absolute error                    = 2e-32                                        
relative error                    = 2.2003029274924288586094653589129e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3789                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3789                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3835.2MB, alloc=40.3MB, time=41.42
memory used=3876.5MB, alloc=40.3MB, time=41.86
 
TOP MAIN SOLVE Loop
x[1]                              = 0.44                                         
y2[1] (closed_form)               = 0.42593946506599960276972075077992           
y2[1] (numeric)                   = 0.42593946506599960276972075077994           
absolute error                    = 2e-32                                        
relative error                    = 4.6955029153969066303347553414383e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.90475166321996341716553738899837           
y1[1] (numeric)                   = 0.90475166321996341716553738899837           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3854                                       
Order of pole (three term test)                    = 32.82                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3854                                       
Order of pole (three term test)                    = 32.18                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=3917.8MB, alloc=40.3MB, time=42.31
memory used=3959.1MB, alloc=40.3MB, time=42.75
memory used=4000.2MB, alloc=40.3MB, time=43.19
 
TOP MAIN SOLVE Loop
x[1]                              = 0.45                                         
y2[1] (closed_form)               = 0.4349655341112302104208442462319            
y2[1] (numeric)                   = 0.43496553411123021042084424623192           
absolute error                    = 2e-32                                        
relative error                    = 4.5980654630179415802165551129761e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.90044710235267692166884061148645           
y1[1] (numeric)                   = 0.90044710235267692166884061148644           
absolute error                    = 1e-32                                        
relative error                    = 1.1105594069737272884444606710116e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3917                                       
Order of pole (three term test)                    = 32.81                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3917                                       
Order of pole (three term test)                    = 32.19                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4041.5MB, alloc=40.3MB, time=43.64
memory used=4082.7MB, alloc=40.3MB, time=44.08
memory used=4124.0MB, alloc=40.3MB, time=44.51
 
TOP MAIN SOLVE Loop
x[1]                              = 0.46                                         
y2[1] (closed_form)               = 0.4439481069655197652415136439289            
y2[1] (numeric)                   = 0.44394810696551976524151364392892           
absolute error                    = 2e-32                                        
relative error                    = 4.5050310354298560567933411674058e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.89605249752552524253638990350041           
y1[1] (numeric)                   = 0.89605249752552524253638990350039           
absolute error                    = 2e-32                                        
relative error                    = 2.2320120813490923284652883710187e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3978                                       
Order of pole (three term test)                    = 32.8                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3978                                       
Order of pole (three term test)                    = 32.2                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=4165.3MB, alloc=40.3MB, time=44.97
memory used=4206.5MB, alloc=40.3MB, time=45.42
 
TOP MAIN SOLVE Loop
memory used=4247.8MB, alloc=40.3MB, time=45.86
x[1]                              = 0.47                                         
y2[1] (closed_form)               = 0.45288628537906829070327480039641           
y2[1] (numeric)                   = 0.45288628537906829070327480039644           
absolute error                    = 3e-32                                        
relative error                    = 6.6241793952514672404578861362144e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.89156828819532893645401927653339           
y1[1] (numeric)                   = 0.89156828819532893645401927653339           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4038                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4038                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4289.1MB, alloc=40.3MB, time=46.30
memory used=4330.3MB, alloc=40.3MB, time=46.75
 
TOP MAIN SOLVE Loop
memory used=4371.6MB, alloc=40.3MB, time=47.19
x[1]                              = 0.48                                         
y2[1] (closed_form)               = 0.46177917554148288913664294258864           
y2[1] (numeric)                   = 0.46177917554148288913664294258869           
absolute error                    = 5e-32                                        
relative error                    = 1.0827686186015194819756811270705e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.88699492277928419439995483115874           
y1[1] (numeric)                   = 0.88699492277928419439995483115873           
absolute error                    = 1e-32                                        
relative error                    = 1.1274021691878787428048684309357e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4096                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4096                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4412.8MB, alloc=40.3MB, time=47.64
memory used=4454.1MB, alloc=40.3MB, time=48.08
 
TOP MAIN SOLVE Loop
x[1]                              = 0.49                                         
y2[1] (closed_form)               = 0.47062588817115803618135833718796           
y2[1] (numeric)                   = 0.47062588817115803618135833718801           
absolute error                    = 5e-32                                        
relative error                    = 1.0624149936651150309747700341755e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.88233285861012149570546815913666           
y1[1] (numeric)                   = 0.88233285861012149570546815913665           
absolute error                    = 1e-32                                        
relative error                    = 1.1333591288612230659188985538320e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4152                                       
Order of pole (three term test)                    = 32.78                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4152                                       
Order of pole (three term test)                    = 32.22                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4495.4MB, alloc=40.3MB, time=48.53
memory used=4536.6MB, alloc=40.3MB, time=48.97
memory used=4577.8MB, alloc=40.3MB, time=49.42
 
TOP MAIN SOLVE Loop
x[1]                              = 0.5                                          
y2[1] (closed_form)               = 0.47942553860420300027328793521557           
y2[1] (numeric)                   = 0.47942553860420300027328793521563           
absolute error                    = 6e-32                                        
relative error                    = 1.2514977857600929114635010052756e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.87758256189037271611628158260383           
y1[1] (numeric)                   = 0.87758256189037271611628158260385           
absolute error                    = 2e-32                                        
relative error                    = 2.2789878546490982446266555364099e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4207                                       
Order of pole (three term test)                    = 32.77                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4207                                       
Order of pole (three term test)                    = 32.23                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4618.9MB, alloc=40.3MB, time=49.86
memory used=4660.2MB, alloc=40.3MB, time=50.31
memory used=4701.4MB, alloc=40.3MB, time=50.75
 
TOP MAIN SOLVE Loop
x[1]                              = 0.51                                         
y2[1] (closed_form)               = 0.48817724688290749450013023767457           
y2[1] (numeric)                   = 0.48817724688290749450013023767463           
absolute error                    = 6e-32                                        
relative error                    = 1.2290617881744782017493327657050e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.87274450764575126310580847357551           
y1[1] (numeric)                   = 0.87274450764575126310580847357552           
absolute error                    = 1e-32                                        
relative error                    = 1.1458107054692597333792993299734e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4261                                       
Order of pole (three term test)                    = 32.76                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4261                                       
Order of pole (three term test)                    = 32.24                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4742.7MB, alloc=40.3MB, time=51.20
memory used=4783.9MB, alloc=40.3MB, time=51.64
 
TOP MAIN SOLVE Loop
memory used=4825.1MB, alloc=40.3MB, time=52.08
x[1]                              = 0.52                                         
y2[1] (closed_form)               = 0.49688013784373671433445894254775           
y2[1] (numeric)                   = 0.49688013784373671433445894254781           
absolute error                    = 6e-32                                        
relative error                    = 1.2075346835229975266236197928669e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.86781917967764990038784757198851           
y1[1] (numeric)                   = 0.86781917967764990038784757198854           
absolute error                    = 3e-32                                        
relative error                    = 3.4569413424514832526432563583826e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4312                                       
Order of pole (three term test)                    = 32.75                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4312                                       
Order of pole (three term test)                    = 32.25                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4866.4MB, alloc=40.3MB, time=52.53
memory used=4907.6MB, alloc=40.3MB, time=52.97
 
TOP MAIN SOLVE Loop
x[1]                              = 0.53                                         
y2[1] (closed_form)               = 0.50553334120484696181366102246608           
y2[1] (numeric)                   = 0.50553334120484696181366102246613           
absolute error                    = 5e-32                                        
relative error                    = 9.8905444853219918713510338381691e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.8628070705147610118066950185642            
y1[1] (numeric)                   = 0.86280707051476101180669501856422           
absolute error                    = 2e-32                                        
relative error                    = 2.3180153111248567922165470502791e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4362                                       
Order of pole (three term test)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4362                                       
Order of pole (three term test)                    = 32.26                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=4948.9MB, alloc=40.3MB, time=53.42
memory used=4990.1MB, alloc=40.3MB, time=53.88
memory used=5031.4MB, alloc=40.3MB, time=54.31
 
TOP MAIN SOLVE Loop
x[1]                              = 0.54                                         
y2[1] (closed_form)               = 0.51413599165311310467728068295824           
y2[1] (numeric)                   = 0.51413599165311310467728068295828           
absolute error                    = 4e-32                                        
relative error                    = 7.7800427609409513559610975078009e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.8577086813638241425379687789178            
y1[1] (numeric)                   = 0.8577086813638241425379687789178            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.441                                        
Order of pole (three term test)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.441                                        
Order of pole (three term test)                    = 32.26                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5072.7MB, alloc=40.3MB, time=54.77
memory used=5114.0MB, alloc=40.3MB, time=55.20
memory used=5155.3MB, alloc=40.3MB, time=55.66
 
TOP MAIN SOLVE Loop
x[1]                              = 0.55                                         
y2[1] (closed_form)               = 0.52268722893065916778837810775729           
y2[1] (numeric)                   = 0.52268722893065916778837810775733           
absolute error                    = 4e-32                                        
relative error                    = 7.6527601567449981793694067295567e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.85252452205950574280498179761777           
y1[1] (numeric)                   = 0.85252452205950574280498179761777           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4456                                       
Order of pole (three term test)                    = 32.73                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4456                                       
Order of pole (three term test)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5196.7MB, alloc=40.3MB, time=56.09
memory used=5237.8MB, alloc=40.3MB, time=56.55
memory used=5279.1MB, alloc=40.3MB, time=56.98
 
TOP MAIN SOLVE Loop
x[1]                              = 0.56                                         
y2[1] (closed_form)               = 0.53118619792088340385186944111203           
y2[1] (numeric)                   = 0.53118619792088340385186944111207           
absolute error                    = 4e-32                                        
relative error                    = 7.5303161408493015494038179548360e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.84725511101341612609452550386632           
y1[1] (numeric)                   = 0.84725511101341612609452550386632           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4501                                       
Order of pole (three term test)                    = 32.72                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4501                                       
Order of pole (three term test)                    = 32.28                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5320.5MB, alloc=40.3MB, time=57.44
memory used=5361.6MB, alloc=40.3MB, time=57.88
 
TOP MAIN SOLVE Loop
memory used=5402.9MB, alloc=40.3MB, time=58.33
x[1]                              = 0.57                                         
y2[1] (closed_form)               = 0.53963204873396924099446349307883           
y2[1] (numeric)                   = 0.53963204873396924099446349307887           
absolute error                    = 4e-32                                        
relative error                    = 7.4124581914369246048334158139102e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.84190097516226874013375636391601           
y1[1] (numeric)                   = 0.84190097516226874013375636391601           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4543                                       
Order of pole (three term test)                    = 32.71                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4543                                       
Order of pole (three term test)                    = 32.29                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5444.2MB, alloc=40.3MB, time=58.77
memory used=5485.4MB, alloc=40.3MB, time=59.20
 
TOP MAIN SOLVE Loop
x[1]                              = 0.58                                         
y2[1] (closed_form)               = 0.54802393679187355618269605957646           
y2[1] (numeric)                   = 0.54802393679187355618269605957649           
absolute error                    = 3e-32                                        
relative error                    = 5.4742134395843526372782926957189e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.83646264991518693465788732805002           
y1[1] (numeric)                   = 0.83646264991518693465788732805001           
absolute error                    = 1e-32                                        
relative error                    = 1.1955106424672935751964175215789e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4584                                       
Order of pole (three term test)                    = 32.7                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4584                                       
Order of pole (three term test)                    = 32.3                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=5526.8MB, alloc=40.3MB, time=59.66
memory used=5568.1MB, alloc=40.3MB, time=60.11
memory used=5609.3MB, alloc=40.3MB, time=60.55
 
TOP MAIN SOLVE Loop
x[1]                              = 0.59                                         
y2[1] (closed_form)               = 0.55636102291278377572254337887577           
y2[1] (numeric)                   = 0.55636102291278377572254337887579           
absolute error                    = 2e-32                                        
relative error                    = 3.5947881279122672250783008540811e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.83094067910016349524799652249068           
y1[1] (numeric)                   = 0.83094067910016349524799652249068           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4623                                       
Order of pole (three term test)                    = 32.69                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4623                                       
Order of pole (three term test)                    = 32.31                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5650.6MB, alloc=40.3MB, time=61.00
memory used=5691.8MB, alloc=40.3MB, time=61.44
memory used=5733.1MB, alloc=40.3MB, time=61.89
 
TOP MAIN SOLVE Loop
x[1]                              = 0.6                                          
y2[1] (closed_form)               = 0.56464247339503535720094544565866           
y2[1] (numeric)                   = 0.56464247339503535720094544565868           
absolute error                    = 2e-32                                        
relative error                    = 3.5420643933754507467492242142109e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.82533561490967829724095249895538           
y1[1] (numeric)                   = 0.82533561490967829724095249895538           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.466                                        
Order of pole (three term test)                    = 32.68                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.466                                        
Order of pole (three term test)                    = 32.32                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5774.4MB, alloc=40.3MB, time=62.34
memory used=5815.6MB, alloc=40.3MB, time=62.78
 
TOP MAIN SOLVE Loop
memory used=5856.8MB, alloc=40.3MB, time=63.23
x[1]                              = 0.61                                         
y2[1] (closed_form)               = 0.57286746010048126119097603216272           
y2[1] (numeric)                   = 0.57286746010048126119097603216273           
absolute error                    = 1e-32                                        
relative error                    = 1.7456044716252507362706331249149e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.81964801784547951790074657865482           
y1[1] (numeric)                   = 0.81964801784547951790074657865482           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4695                                       
Order of pole (three term test)                    = 32.67                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4695                                       
Order of pole (three term test)                    = 32.33                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5898.0MB, alloc=40.3MB, time=63.67
memory used=5939.3MB, alloc=40.3MB, time=64.12
 
TOP MAIN SOLVE Loop
x[1]                              = 0.62                                         
y2[1] (closed_form)               = 0.58103516053730507584296322758221           
y2[1] (numeric)                   = 0.58103516053730507584296322758222           
absolute error                    = 1e-32                                        
relative error                    = 1.7210662416285829802640352190038e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.8138784566625339286839996543607            
y1[1] (numeric)                   = 0.8138784566625339286839996543607            
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4729                                       
Order of pole (three term test)                    = 32.66                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4729                                       
Order of pole (three term test)                    = 32.34                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=5980.7MB, alloc=40.3MB, time=64.56
memory used=6021.9MB, alloc=40.3MB, time=65.00
memory used=6063.1MB, alloc=40.3MB, time=65.45
 
TOP MAIN SOLVE Loop
x[1]                              = 0.63                                         
y2[1] (closed_form)               = 0.58914475794226951311811209079462           
y2[1] (numeric)                   = 0.58914475794226951311811209079463           
absolute error                    = 1e-32                                        
relative error                    = 1.6973757069361725967914220639108e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.80802750831215187252370896577706           
y1[1] (numeric)                   = 0.80802750831215187252370896577706           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.476                                        
Order of pole (three term test)                    = 32.65                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.476                                        
Order of pole (three term test)                    = 32.35                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6104.5MB, alloc=40.3MB, time=65.91
memory used=6145.7MB, alloc=40.3MB, time=66.34
memory used=6187.0MB, alloc=40.3MB, time=66.80
 
TOP MAIN SOLVE Loop
x[1]                              = 0.64                                         
y2[1] (closed_form)               = 0.59719544136239205188354623920793           
y2[1] (numeric)                   = 0.59719544136239205188354623920794           
absolute error                    = 1e-32                                        
relative error                    = 1.6744936929168164811188136616446e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.80209575788429261358611077926032           
y1[1] (numeric)                   = 0.80209575788429261358611077926033           
absolute error                    = 1e-32                                        
relative error                    = 1.2467339344091835043765333244264e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.479                                        
Order of pole (three term test)                    = 32.64                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.479                                        
Order of pole (three term test)                    = 32.36                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6228.4MB, alloc=40.3MB, time=67.23
memory used=6269.6MB, alloc=40.3MB, time=67.69
memory used=6310.8MB, alloc=40.3MB, time=68.13
 
TOP MAIN SOLVE Loop
x[1]                              = 0.65                                         
y2[1] (closed_form)               = 0.60518640573603956037252167860594           
y2[1] (numeric)                   = 0.60518640573603956037252167860597           
absolute error                    = 3e-32                                        
relative error                    = 4.9571503450269033048518397165628e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.79608379854905582891760457067991           
y1[1] (numeric)                   = 0.79608379854905582891760457067991           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4818                                       
Order of pole (three term test)                    = 32.63                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4818                                       
Order of pole (three term test)                    = 32.37                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6352.1MB, alloc=40.3MB, time=68.58
memory used=6393.3MB, alloc=40.3MB, time=69.02
 
TOP MAIN SOLVE Loop
memory used=6434.5MB, alloc=40.3MB, time=69.47
x[1]                              = 0.66                                         
y2[1] (closed_form)               = 0.6131168519734337886151454793963            
y2[1] (numeric)                   = 0.61311685197343378861514547939633           
absolute error                    = 3e-32                                        
relative error                    = 4.8930313860138186286772799436418e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.78999223149736509278381709123024           
y1[1] (numeric)                   = 0.78999223149736509278381709123025           
absolute error                    = 1e-32                                        
relative error                    = 1.2658352324611882697842840177057e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4844                                       
Order of pole (three term test)                    = 32.62                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4844                                       
Order of pole (three term test)                    = 32.38                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6475.9MB, alloc=40.3MB, time=69.91
memory used=6517.2MB, alloc=40.3MB, time=70.36
 
TOP MAIN SOLVE Loop
x[1]                              = 0.67                                         
y2[1] (closed_form)               = 0.62098598703655968035744391412659           
y2[1] (numeric)                   = 0.62098598703655968035744391412663           
absolute error                    = 4e-32                                        
relative error                    = 6.4413691830448753775237599965938e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.78382166588084928530294214483812           
y1[1] (numeric)                   = 0.78382166588084928530294214483812           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4867                                       
Order of pole (three term test)                    = 32.61                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4867                                       
Order of pole (three term test)                    = 32.39                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6558.6MB, alloc=40.3MB, time=70.80
memory used=6599.9MB, alloc=40.3MB, time=71.23
memory used=6641.2MB, alloc=40.3MB, time=71.69
 
TOP MAIN SOLVE Loop
x[1]                              = 0.68                                         
y2[1] (closed_form)               = 0.62879302401846851370417818742025           
y2[1] (numeric)                   = 0.62879302401846851370417818742027           
absolute error                    = 2e-32                                        
relative error                    = 3.1806968646351541844819338546206e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.77757271875092793718239408404432           
y1[1] (numeric)                   = 0.77757271875092793718239408404432           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4889                                       
Order of pole (three term test)                    = 32.6                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4889                                       
Order of pole (three term test)                    = 32.4                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=6682.5MB, alloc=40.3MB, time=72.13
memory used=6723.7MB, alloc=40.3MB, time=72.58
memory used=6764.9MB, alloc=40.3MB, time=73.02
 
TOP MAIN SOLVE Loop
x[1]                              = 0.69                                         
y2[1] (closed_form)               = 0.63653718222196794023742920700872           
y2[1] (numeric)                   = 0.63653718222196794023742920700874           
absolute error                    = 2e-32                                        
relative error                    = 3.1420002725034476796470444715189e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.77124601499710660197353931549777           
y1[1] (numeric)                   = 0.77124601499710660197353931549777           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4909                                       
Order of pole (three term test)                    = 32.59                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4909                                       
Order of pole (three term test)                    = 32.41                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6806.3MB, alloc=40.3MB, time=73.47
memory used=6847.6MB, alloc=40.3MB, time=73.91
 
TOP MAIN SOLVE Loop
memory used=6888.8MB, alloc=40.3MB, time=74.36
x[1]                              = 0.7                                          
y2[1] (closed_form)               = 0.64421768723769105367261435139872           
y2[1] (numeric)                   = 0.64421768723769105367261435139875           
absolute error                    = 3e-32                                        
relative error                    = 4.6568109808713117359699209228648e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.76484218728448842625585999019186           
y1[1] (numeric)                   = 0.76484218728448842625585999019187           
absolute error                    = 1e-32                                        
relative error                    = 1.3074592597335938698746728353053e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4927                                       
Order of pole (three term test)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4927                                       
Order of pole (three term test)                    = 32.42                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=6930.0MB, alloc=40.3MB, time=74.80
memory used=6971.3MB, alloc=40.3MB, time=75.23
 
TOP MAIN SOLVE Loop
x[1]                              = 0.71                                         
y2[1] (closed_form)               = 0.65183377102153668121012797285284           
y2[1] (numeric)                   = 0.65183377102153668121012797285286           
absolute error                    = 2e-32                                        
relative error                    = 3.0682669246572677397779021813019e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.75836187599050816654145794413955           
y1[1] (numeric)                   = 0.75836187599050816654145794413957           
absolute error                    = 2e-32                                        
relative error                    = 2.6372633742799492530594693858876e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4943                                       
Order of pole (three term test)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4943                                       
Order of pole (three term test)                    = 32.42                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7012.5MB, alloc=40.3MB, time=75.67
memory used=7053.8MB, alloc=40.3MB, time=76.12
memory used=7095.1MB, alloc=40.3MB, time=76.56
 
TOP MAIN SOLVE Loop
x[1]                              = 0.72                                         
y2[1] (closed_form)               = 0.65938467197147315361800383264817           
y2[1] (numeric)                   = 0.65938467197147315361800383264818           
absolute error                    = 1e-32                                        
relative error                    = 1.5165654321477203357119039156049e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.75180572914089497944548696225195           
y1[1] (numeric)                   = 0.75180572914089497944548696225197           
absolute error                    = 2e-32                                        
relative error                    = 2.6602617171931426982201891539493e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4957                                       
Order of pole (three term test)                    = 32.57                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4957                                       
Order of pole (three term test)                    = 32.43                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7136.4MB, alloc=40.3MB, time=77.02
memory used=7177.7MB, alloc=40.3MB, time=77.45
memory used=7218.9MB, alloc=40.3MB, time=77.89
 
TOP MAIN SOLVE Loop
x[1]                              = 0.73                                         
y2[1] (closed_form)               = 0.66686963500369787373259413076153           
y2[1] (numeric)                   = 0.66686963500369787373259413076155           
absolute error                    = 2e-32                                        
relative error                    = 2.9990869204727094153192585309935e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.74517440234487038879013215855033           
y1[1] (numeric)                   = 0.74517440234487038879013215855035           
absolute error                    = 2e-32                                        
relative error                    = 2.6839354568628756191548285450706e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4969                                       
Order of pole (three term test)                    = 32.56                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4969                                       
Order of pole (three term test)                    = 32.44                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7260.2MB, alloc=40.3MB, time=78.34
memory used=7301.4MB, alloc=40.3MB, time=78.78
memory used=7342.6MB, alloc=40.3MB, time=79.23
 
TOP MAIN SOLVE Loop
x[1]                              = 0.74                                         
y2[1] (closed_form)               = 0.67428791162814506748388115760817           
y2[1] (numeric)                   = 0.6742879116281450674838811576082            
absolute error                    = 3e-32                                        
relative error                    = 4.4491380436528334605194900702897e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.73846855872958790979142456069883           
y1[1] (numeric)                   = 0.73846855872958790979142456069885           
absolute error                    = 2e-32                                        
relative error                    = 2.7083075865012678425941625899104e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4979                                       
Order of pole (three term test)                    = 32.55                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4979                                       
Order of pole (three term test)                    = 32.45                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7384.0MB, alloc=40.3MB, time=79.67
memory used=7425.2MB, alloc=40.3MB, time=80.13
 
TOP MAIN SOLVE Loop
memory used=7466.4MB, alloc=40.3MB, time=80.56
x[1]                              = 0.75                                         
y2[1] (closed_form)               = 0.68163876002333416673324195277989           
y2[1] (numeric)                   = 0.68163876002333416673324195277992           
absolute error                    = 3e-32                                        
relative error                    = 4.4011581734250303509177349886343e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.73168886887382088631183875300008           
y1[1] (numeric)                   = 0.73168886887382088631183875300011           
absolute error                    = 3e-32                                        
relative error                    = 4.1001033740166784056452059804705e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4987                                       
Order of pole (three term test)                    = 32.54                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4987                                       
Order of pole (three term test)                    = 32.46                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7507.8MB, alloc=40.3MB, time=81.02
memory used=7549.0MB, alloc=40.3MB, time=81.45
 
TOP MAIN SOLVE Loop
x[1]                              = 0.76                                         
y2[1] (closed_form)               = 0.68892144511055133914775563876973           
y2[1] (numeric)                   = 0.68892144511055133914775563876975           
absolute error                    = 2e-32                                        
relative error                    = 2.9030886092957371454415397095206e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.72483601074090517233968836666701           
y1[1] (numeric)                   = 0.72483601074090517233968836666702           
absolute error                    = 1e-32                                        
relative error                    = 1.3796224044909559951870120177153e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4994                                       
Order of pole (three term test)                    = 32.53                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4994                                       
Order of pole (three term test)                    = 32.47                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7590.4MB, alloc=40.3MB, time=81.89
memory used=7631.6MB, alloc=40.3MB, time=82.34
memory used=7672.8MB, alloc=40.3MB, time=82.78
 
TOP MAIN SOLVE Loop
x[1]                              = 0.77                                         
y2[1] (closed_form)               = 0.69613523862735674701988373445221           
y2[1] (numeric)                   = 0.69613523862735674701988373445225           
absolute error                    = 4e-32                                        
relative error                    = 5.7460099389412059849812174760497e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.71791066961094336337129056532434           
y1[1] (numeric)                   = 0.71791066961094336337129056532436           
absolute error                    = 2e-32                                        
relative error                    = 2.7858619249716097277693846674882e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4998                                       
Order of pole (three term test)                    = 32.52                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4998                                       
Order of pole (three term test)                    = 32.48                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7714.1MB, alloc=40.3MB, time=83.23
memory used=7755.3MB, alloc=40.3MB, time=83.67
memory used=7796.6MB, alloc=40.3MB, time=84.12
 
TOP MAIN SOLVE Loop
x[1]                              = 0.78                                         
y2[1] (closed_form)               = 0.70327941920041018436789732511792           
y2[1] (numeric)                   = 0.70327941920041018436789732511795           
absolute error                    = 3e-32                                        
relative error                    = 4.2657298338274055159561119486760e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.71091353801227735721626502376456           
y1[1] (numeric)                   = 0.71091353801227735721626502376458           
absolute error                    = 2e-32                                        
relative error                    = 2.8132816342083224421967142135470e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.5                                          
Order of pole (three term test)                    = 32.51                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.5                                          
Order of pole (three term test)                    = 32.49                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=7837.9MB, alloc=40.3MB, time=84.56
memory used=7879.1MB, alloc=40.3MB, time=85.01
 
TOP MAIN SOLVE Loop
memory used=7920.4MB, alloc=40.3MB, time=85.45
x[1]                              = 0.79                                         
y2[1] (closed_form)               = 0.7103532724176078098140288749692            
y2[1] (numeric)                   = 0.71035327241760780981402887496923           
absolute error                    = 3e-32                                        
relative error                    = 4.2232507633699440444242117090390e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.70384531565223609691278086108495           
y1[1] (numeric)                   = 0.70384531565223609691278086108496           
absolute error                    = 1e-32                                        
relative error                    = 1.4207667192802507471305291751001e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.5                                          
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.5                                          
Order of pole (three term test)                    = 32.5                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=7961.7MB, alloc=40.3MB, time=85.91
memory used=8002.9MB, alloc=40.3MB, time=86.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.8                                          
y2[1] (closed_form)               = 0.71735609089952276162717461058139           
y2[1] (numeric)                   = 0.71735609089952276162717461058141           
absolute error                    = 2e-32                                        
relative error                    = 2.7880156387772723490049644522139e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.69670670934716542092074998164232           
y1[1] (numeric)                   = 0.69670670934716542092074998164232           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4998                                       
Order of pole (three term test)                    = 32.49                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4998                                       
Order of pole (three term test)                    = 32.51                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8044.2MB, alloc=40.3MB, time=86.80
memory used=8085.5MB, alloc=40.3MB, time=87.23
memory used=8126.6MB, alloc=40.3MB, time=87.69
 
TOP MAIN SOLVE Loop
x[1]                              = 0.81                                         
y2[1] (closed_form)               = 0.72428717437014251092817685251454           
y2[1] (numeric)                   = 0.72428717437014251092817685251457           
absolute error                    = 3e-32                                        
relative error                    = 4.1420034844726774493234715007737e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.6894984329517470175496392406801            
y1[1] (numeric)                   = 0.68949843295174701754963924068009           
absolute error                    = 1e-32                                        
relative error                    = 1.4503296196323374815898349922412e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4994                                       
Order of pole (three term test)                    = 32.48                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4994                                       
Order of pole (three term test)                    = 32.52                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8167.9MB, alloc=40.3MB, time=88.13
memory used=8209.2MB, alloc=40.3MB, time=88.58
memory used=8250.4MB, alloc=40.3MB, time=89.01
 
TOP MAIN SOLVE Loop
x[1]                              = 0.82                                         
y2[1] (closed_form)               = 0.73114582972689587938131336468772           
y2[1] (numeric)                   = 0.73114582972689587938131336468776           
absolute error                    = 4e-32                                        
relative error                    = 5.4708648225404167679977161808652e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.68222120728761355166655797843693           
y1[1] (numeric)                   = 0.68222120728761355166655797843691           
absolute error                    = 2e-32                                        
relative error                    = 2.9316004525154433989688989109211e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4988                                       
Order of pole (three term test)                    = 32.47                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4988                                       
Order of pole (three term test)                    = 32.53                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8291.8MB, alloc=40.3MB, time=89.45
memory used=8332.9MB, alloc=40.3MB, time=89.91
memory used=8374.1MB, alloc=40.3MB, time=90.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.83                                         
y2[1] (closed_form)               = 0.73793137110996271872858022613808           
y2[1] (numeric)                   = 0.73793137110996271872858022613811           
absolute error                    = 3e-32                                        
relative error                    = 4.0654187061969418647964719051794e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.67487576007126710211246291786445           
y1[1] (numeric)                   = 0.67487576007126710211246291786442           
absolute error                    = 3e-32                                        
relative error                    = 4.4452626357230536977994424954309e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.498                                        
Order of pole (three term test)                    = 32.46                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.498                                        
Order of pole (three term test)                    = 32.54                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8415.5MB, alloc=40.3MB, time=90.78
memory used=8456.7MB, alloc=40.3MB, time=91.23
 
TOP MAIN SOLVE Loop
memory used=8498.1MB, alloc=40.3MB, time=91.67
x[1]                              = 0.84                                         
y2[1] (closed_form)               = 0.74464311997085932125657267062965           
y2[1] (numeric)                   = 0.74464311997085932125657267062967           
absolute error                    = 2e-32                                        
relative error                    = 2.6858503709512115049324626494095e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.66746282584130811792267103687086           
y1[1] (numeric)                   = 0.66746282584130811792267103687083           
absolute error                    = 3e-32                                        
relative error                    = 4.4946323358437667727440878712148e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.497                                        
Order of pole (three term test)                    = 32.45                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.497                                        
Order of pole (three term test)                    = 32.55                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8539.3MB, alloc=40.3MB, time=92.12
memory used=8580.6MB, alloc=40.3MB, time=92.56
 
TOP MAIN SOLVE Loop
x[1]                              = 0.85                                         
y2[1] (closed_form)               = 0.75128040514029270271207152423547           
y2[1] (numeric)                   = 0.7512804051402927027120715242355            
absolute error                    = 3e-32                                        
relative error                    = 3.9931828109369970737227756632712e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.65998314588498217039541602946147           
y1[1] (numeric)                   = 0.65998314588498217039541602946144           
absolute error                    = 3e-32                                        
relative error                    = 4.5455706235910782901110646614476e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4958                                       
Order of pole (three term test)                    = 32.44                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4958                                       
Order of pole (three term test)                    = 32.56                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8621.9MB, alloc=40.3MB, time=93.02
memory used=8663.1MB, alloc=40.3MB, time=93.47
memory used=8704.4MB, alloc=40.3MB, time=93.91
 
TOP MAIN SOLVE Loop
x[1]                              = 0.86                                         
y2[1] (closed_form)               = 0.75784256289527697229458872952865           
y2[1] (numeric)                   = 0.75784256289527697229458872952867           
absolute error                    = 2e-32                                        
relative error                    = 2.6390705641540635661109487598376e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.65243746816405184627203066422386           
y1[1] (numeric)                   = 0.65243746816405184627203066422385           
absolute error                    = 1e-32                                        
relative error                    = 1.5327139362703728856785609726008e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4944                                       
Order of pole (three term test)                    = 32.43                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4944                                       
Order of pole (three term test)                    = 32.57                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8745.6MB, alloc=40.3MB, time=94.36
memory used=8786.9MB, alloc=40.3MB, time=94.80
memory used=8828.1MB, alloc=40.3MB, time=95.25
 
TOP MAIN SOLVE Loop
x[1]                              = 0.87                                         
y2[1] (closed_form)               = 0.76432893702550507814480282372285           
y2[1] (numeric)                   = 0.76432893702550507814480282372289           
absolute error                    = 4e-32                                        
relative error                    = 5.2333488976180461258752970927359e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.64482654724000119477766380548283           
y1[1] (numeric)                   = 0.64482654724000119477766380548281           
absolute error                    = 2e-32                                        
relative error                    = 3.1016092754872421034948142280779e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4929                                       
Order of pole (three term test)                    = 32.42                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4929                                       
Order of pole (three term test)                    = 32.58                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8869.4MB, alloc=40.3MB, time=95.69
memory used=8910.7MB, alloc=40.3MB, time=96.13
 
TOP MAIN SOLVE Loop
memory used=8951.8MB, alloc=40.3MB, time=96.58
x[1]                              = 0.88                                         
y2[1] (closed_form)               = 0.77073887889896929120964513075599           
y2[1] (numeric)                   = 0.77073887889896929120964513075603           
absolute error                    = 4e-32                                        
relative error                    = 5.1898251269147818752636115922543e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.63715114419858020801549860572209           
y1[1] (numeric)                   = 0.63715114419858020801549860572209           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4911                                       
Order of pole (three term test)                    = 32.41                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4911                                       
Order of pole (three term test)                    = 32.59                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=8993.1MB, alloc=40.3MB, time=97.02
memory used=9034.4MB, alloc=40.3MB, time=97.45
 
TOP MAIN SOLVE Loop
x[1]                              = 0.89                                         
y2[1] (closed_form)               = 0.77707174752682386549033371297318           
y2[1] (numeric)                   = 0.77707174752682386549033371297325           
absolute error                    = 7e-32                                        
relative error                    = 9.0081772014988434081936613612776e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.62941202657369688020355305738025           
y1[1] (numeric)                   = 0.62941202657369688020355305738025           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4891                                       
Order of pole (three term test)                    = 32.4                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4891                                       
Order of pole (three term test)                    = 32.6                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=9075.7MB, alloc=40.3MB, time=97.91
memory used=9117.0MB, alloc=40.3MB, time=98.34
memory used=9158.1MB, alloc=40.3MB, time=98.80
 
TOP MAIN SOLVE Loop
x[1]                              = 0.9                                          
y2[1] (closed_form)               = 0.78332690962748338846138231571355           
y2[1] (numeric)                   = 0.78332690962748338846138231571362           
absolute error                    = 7e-32                                        
relative error                    = 8.9362434942122684721095195656241e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.62160996827066445648471615140713           
y1[1] (numeric)                   = 0.62160996827066445648471615140713           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4869                                       
Order of pole (three term test)                    = 32.39                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4869                                       
Order of pole (three term test)                    = 32.61                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9199.5MB, alloc=40.3MB, time=99.23
memory used=9240.7MB, alloc=40.3MB, time=99.69
memory used=9282.0MB, alloc=40.3MB, time=100.13
 
TOP MAIN SOLVE Loop
x[1]                              = 0.91                                         
y2[1] (closed_form)               = 0.78950373968995041187895751787155           
y2[1] (numeric)                   = 0.78950373968995041187895751787163           
absolute error                    = 8e-32                                        
relative error                    = 1.0132947569243581063081589588558e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.61374574948881154652117822617468           
y1[1] (numeric)                   = 0.61374574948881154652117822617467           
absolute error                    = 1e-32                                        
relative error                    = 1.6293391861905347267678537725338e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4846                                       
Order of pole (three term test)                    = 32.38                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4846                                       
Order of pole (three term test)                    = 32.62                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9323.3MB, alloc=40.3MB, time=100.56
memory used=9364.5MB, alloc=40.3MB, time=101.02
memory used=9405.8MB, alloc=40.3MB, time=101.45
 
TOP MAIN SOLVE Loop
x[1]                              = 0.92                                         
y2[1] (closed_form)               = 0.79560162003636603026827610248162           
y2[1] (numeric)                   = 0.7956016200363660302682761024817            
absolute error                    = 8e-32                                        
relative error                    = 1.0055283697932049520820357089439e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.60582015664346284179740470667438           
y1[1] (numeric)                   = 0.60582015664346284179740470667438           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.482                                        
Order of pole (three term test)                    = 32.37                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.482                                        
Order of pole (three term test)                    = 32.63                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9447.1MB, alloc=40.3MB, time=101.89
memory used=9488.2MB, alloc=40.3MB, time=102.34
 
TOP MAIN SOLVE Loop
memory used=9529.5MB, alloc=40.3MB, time=102.78
x[1]                              = 0.93                                         
y2[1] (closed_form)               = 0.80161994088377715208431921591065           
y2[1] (numeric)                   = 0.80161994088377715208431921591074           
absolute error                    = 9e-32                                        
relative error                    = 1.1227265616767965087693065789178e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.59783398228729823849490708443298           
y1[1] (numeric)                   = 0.59783398228729823849490708443299           
absolute error                    = 1e-32                                        
relative error                    = 1.6727051817530083924888988545676e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4792                                       
Order of pole (three term test)                    = 32.36                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4792                                       
Order of pole (three term test)                    = 32.64                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9570.8MB, alloc=40.3MB, time=103.23
memory used=9612.1MB, alloc=40.3MB, time=103.67
 
TOP MAIN SOLVE Loop
x[1]                              = 0.94                                         
y2[1] (closed_form)               = 0.80755810040511428687021979863415           
y2[1] (numeric)                   = 0.80755810040511428687021979863423           
absolute error                    = 8e-32                                        
relative error                    = 9.9064079674103604444523412160134e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.58978802503109822996098981522402           
y1[1] (numeric)                   = 0.58978802503109822996098981522403           
absolute error                    = 1e-32                                        
relative error                    = 1.6955244215873528317788450478026e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4763                                       
Order of pole (three term test)                    = 32.35                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4763                                       
Order of pole (three term test)                    = 32.65                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9653.4MB, alloc=40.3MB, time=104.11
memory used=9694.7MB, alloc=40.3MB, time=104.56
memory used=9736.0MB, alloc=40.3MB, time=105.00
 
TOP MAIN SOLVE Loop
x[1]                              = 0.95                                         
y2[1] (closed_form)               = 0.81341550478937375068542210210256           
y2[1] (numeric)                   = 0.81341550478937375068542210210263           
absolute error                    = 7e-32                                        
relative error                    = 8.6056879402767024629462614977729e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.58168308946388349416618097376046           
y1[1] (numeric)                   = 0.58168308946388349416618097376047           
absolute error                    = 1e-32                                        
relative error                    = 1.7191491692180088054618740078576e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4732                                       
Order of pole (three term test)                    = 32.34                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4732                                       
Order of pole (three term test)                    = 32.66                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9777.3MB, alloc=40.3MB, time=105.45
memory used=9818.6MB, alloc=40.3MB, time=105.89
memory used=9859.9MB, alloc=40.3MB, time=106.34
 
TOP MAIN SOLVE Loop
x[1]                              = 0.96                                         
y2[1] (closed_form)               = 0.81919156830099827163322214643043           
y2[1] (numeric)                   = 0.81919156830099827163322214643052           
absolute error                    = 9e-32                                        
relative error                    = 1.0986441204059244157379011799345e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.57351998607245666212505080035186           
y1[1] (numeric)                   = 0.57351998607245666212505080035187           
absolute error                    = 1e-32                                        
relative error                    = 1.7436183991566481011479254485116e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4698                                       
Order of pole (three term test)                    = 32.33                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4698                                       
Order of pole (three term test)                    = 32.67                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=9901.1MB, alloc=40.3MB, time=106.78
memory used=9942.4MB, alloc=40.3MB, time=107.23
 
TOP MAIN SOLVE Loop
memory used=9983.7MB, alloc=40.3MB, time=107.67
x[1]                              = 0.97                                         
y2[1] (closed_form)               = 0.82488571333845005747662003785634           
y2[1] (numeric)                   = 0.82488571333845005747662003785643           
absolute error                    = 9e-32                                        
relative error                    = 1.0910602347051810325796937774813e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.56529953116035431303652775484986           
y1[1] (numeric)                   = 0.56529953116035431303652775484988           
absolute error                    = 2e-32                                        
relative error                    = 3.5379473885193704095866285017291e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4663                                       
Order of pole (three term test)                    = 32.32                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4663                                       
Order of pole (three term test)                    = 32.68                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10025.1MB, alloc=40.3MB, time=108.13
memory used=10066.3MB, alloc=40.3MB, time=108.56
 
TOP MAIN SOLVE Loop
x[1]                              = 0.98                                         
y2[1] (closed_form)               = 0.83049737049197046808453328771915           
y2[1] (numeric)                   = 0.83049737049197046808453328771923           
absolute error                    = 8e-32                                        
relative error                    = 9.6327818536751727491818872618845e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.55702254676621730087665826735994           
y1[1] (numeric)                   = 0.55702254676621730087665826735997           
absolute error                    = 3e-32                                        
relative error                    = 5.3857783987675849159909778565776e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4626                                       
Order of pole (three term test)                    = 32.31                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4626                                       
Order of pole (three term test)                    = 32.69                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10107.5MB, alloc=40.3MB, time=109.00
memory used=10148.8MB, alloc=40.3MB, time=109.45
memory used=10190.0MB, alloc=40.3MB, time=109.89
 
TOP MAIN SOLVE Loop
x[1]                              = 0.99                                         
y2[1] (closed_form)               = 0.83602597860052051678925941154711           
y2[1] (numeric)                   = 0.8360259786005205167892594115472            
absolute error                    = 9e-32                                        
relative error                    = 1.0765215711437219355903634507875e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.54868986058158757534312640865361           
y1[1] (numeric)                   = 0.54868986058158757534312640865363           
absolute error                    = 2e-32                                        
relative error                    = 3.6450463981238623642542740957079e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4587                                       
Order of pole (three term test)                    = 32.3                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4587                                       
Order of pole (three term test)                    = 32.7                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=10231.4MB, alloc=40.3MB, time=110.34
memory used=10272.7MB, alloc=40.3MB, time=110.78
memory used=10314.0MB, alloc=40.3MB, time=111.23
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y2[1] (closed_form)               = 0.8414709848078965066525023216303            
y2[1] (numeric)                   = 0.84147098480789650665250232163038           
absolute error                    = 8e-32                                        
relative error                    = 9.5071608462249697300927956189964e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.54030230586813971740093660744298           
y1[1] (numeric)                   = 0.54030230586813971740093660744299           
absolute error                    = 1e-32                                        
relative error                    = 1.8508157176809256179117532413986e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4546                                       
Order of pole (three term test)                    = 32.29                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4546                                       
Order of pole (three term test)                    = 32.71                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10355.4MB, alloc=40.3MB, time=111.69
memory used=10396.5MB, alloc=40.3MB, time=112.14
memory used=10437.7MB, alloc=40.3MB, time=112.58
 
TOP MAIN SOLVE Loop
x[1]                              = 1.01                                         
y2[1] (closed_form)               = 0.84683184461801519012309878478201           
y2[1] (numeric)                   = 0.8468318446180151901230987847821            
absolute error                    = 9e-32                                        
relative error                    = 1.0627847851021328137197078576002e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.53186072137435546620673135577918           
y1[1] (numeric)                   = 0.53186072137435546620673135577919           
absolute error                    = 1e-32                                        
relative error                    = 1.8801914858761304160058742988838e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4504                                       
Order of pole (three term test)                    = 32.28                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4504                                       
Order of pole (three term test)                    = 32.72                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10479.0MB, alloc=40.3MB, time=113.03
memory used=10520.3MB, alloc=40.3MB, time=113.47
 
TOP MAIN SOLVE Loop
memory used=10561.7MB, alloc=40.3MB, time=113.92
x[1]                              = 1.02                                         
y2[1] (closed_form)               = 0.85210802194936292361654998545538           
y2[1] (numeric)                   = 0.85210802194936292361654998545548           
absolute error                    = 1.0e-31                                      
relative error                    = 1.1735601288112572819824797672248e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.52336595125164956988961380803381           
y1[1] (numeric)                   = 0.52336595125164956988961380803383           
absolute error                    = 2e-32                                        
relative error                    = 3.8214178725553772908756845559987e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.446                                        
Order of pole (three term test)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.446                                        
Order of pole (three term test)                    = 32.73                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10602.9MB, alloc=40.3MB, time=114.36
memory used=10644.1MB, alloc=40.3MB, time=114.81
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y2[1] (closed_form)               = 0.85729898918860337214627438529442           
y2[1] (numeric)                   = 0.85729898918860337214627438529452           
absolute error                    = 1.0e-31                                      
relative error                    = 1.1664541923074667312790368212473e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.51481884496995534753350229983735           
y1[1] (numeric)                   = 0.51481884496995534753350229983736           
absolute error                    = 1e-32                                        
relative error                    = 1.9424308371197244332449996487096e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4414                                       
Order of pole (three term test)                    = 32.27                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4414                                       
Order of pole (three term test)                    = 32.73                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10685.4MB, alloc=40.3MB, time=115.25
memory used=10726.2MB, alloc=40.3MB, time=115.69
memory used=10767.3MB, alloc=40.3MB, time=116.14
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y2[1] (closed_form)               = 0.86240422724333840328079169211617           
y2[1] (numeric)                   = 0.86240422724333840328079169211625           
absolute error                    = 8e-32                                        
relative error                    = 9.2763923775882623203232111975617e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.50622025723277840373447342099217           
y1[1] (numeric)                   = 0.50622025723277840373447342099219           
absolute error                    = 2e-32                                        
relative error                    = 3.9508494008771513524566758570049e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4366                                       
Order of pole (three term test)                    = 32.26                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4366                                       
Order of pole (three term test)                    = 32.74                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10808.4MB, alloc=40.3MB, time=116.58
memory used=10849.3MB, alloc=40.3MB, time=117.02
memory used=10890.3MB, alloc=40.3MB, time=117.47
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y2[1] (closed_form)               = 0.86742322559401689438140948500027           
y2[1] (numeric)                   = 0.86742322559401689438140948500035           
absolute error                    = 8e-32                                        
relative error                    = 9.2227182348288513446157392090060e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.4975710478917269902908495728121            
y1[1] (numeric)                   = 0.49757104789172699029084957281211           
absolute error                    = 1e-32                                        
relative error                    = 2.0097632373047619814603684257021e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4316                                       
Order of pole (three term test)                    = 32.25                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4316                                       
Order of pole (three term test)                    = 32.75                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=10931.3MB, alloc=40.3MB, time=117.91
memory used=10972.3MB, alloc=40.3MB, time=118.34
 
TOP MAIN SOLVE Loop
memory used=11013.2MB, alloc=40.3MB, time=118.78
x[1]                              = 1.06                                         
y2[1] (closed_form)               = 0.87235548234498626228294592199742           
y2[1] (numeric)                   = 0.8723554823449862622829459219975            
absolute error                    = 8e-32                                        
relative error                    = 9.1705734209351574322086407674450e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.48887208186052756191863753995641           
y1[1] (numeric)                   = 0.48887208186052756191863753995641           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4265                                       
Order of pole (three term test)                    = 32.24                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4265                                       
Order of pole (three term test)                    = 32.76                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11054.4MB, alloc=40.3MB, time=119.23
memory used=11095.3MB, alloc=40.3MB, time=119.67
 
TOP MAIN SOLVE Loop
memory used=11136.2MB, alloc=40.3MB, time=120.11
x[1]                              = 1.07                                         
y2[1] (closed_form)               = 0.87720050427468161030706325777682           
y2[1] (numeric)                   = 0.87720050427468161030706325777689           
absolute error                    = 7e-32                                        
relative error                    = 7.9799315730991184489344042478960e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.48012422902853412436509306817592           
y1[1] (numeric)                   = 0.48012422902853412436509306817592           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4212                                       
Order of pole (three term test)                    = 32.23                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4212                                       
Order of pole (three term test)                    = 32.77                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11177.3MB, alloc=40.3MB, time=120.56
memory used=11218.3MB, alloc=40.3MB, time=121.00
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y2[1] (closed_form)               = 0.88195780688494747373533498762476           
y2[1] (numeric)                   = 0.88195780688494747373533498762484           
absolute error                    = 8e-32                                        
relative error                    = 9.0707287100907881108618287765710e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.47132836417374002391352478852603           
y1[1] (numeric)                   = 0.47132836417374002391352478852604           
absolute error                    = 1e-32                                        
relative error                    = 2.1216631037112423847777714573716e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4157                                       
Order of pole (three term test)                    = 32.22                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4157                                       
Order of pole (three term test)                    = 32.78                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11259.4MB, alloc=40.3MB, time=121.44
memory used=11300.3MB, alloc=40.3MB, time=121.88
memory used=11341.3MB, alloc=40.3MB, time=122.31
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y2[1] (closed_form)               = 0.88662691444948723160860062863605           
y2[1] (numeric)                   = 0.88662691444948723160860062863613           
absolute error                    = 8e-32                                        
relative error                    = 9.0229609203407221123488899107590e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.46248536687530087702789707387514           
y1[1] (numeric)                   = 0.46248536687530087702789707387515           
absolute error                    = 1e-32                                        
relative error                    = 2.1622305733829374458118142722034e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4101                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4101                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11382.4MB, alloc=40.3MB, time=122.76
memory used=11423.4MB, alloc=40.3MB, time=123.20
memory used=11464.4MB, alloc=40.3MB, time=123.66
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y2[1] (closed_form)               = 0.8912073600614353399518025778717            
y2[1] (numeric)                   = 0.89120736006143533995180257787179           
absolute error                    = 9e-32                                        
relative error                    = 1.0098659866744800444678674852928e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.45359612142557738777137005178472           
y1[1] (numeric)                   = 0.45359612142557738777137005178472           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.4042                                       
Order of pole (three term test)                    = 32.21                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.4042                                       
Order of pole (three term test)                    = 32.79                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11505.4MB, alloc=40.3MB, time=124.09
memory used=11546.3MB, alloc=40.3MB, time=124.53
 
TOP MAIN SOLVE Loop
memory used=11587.3MB, alloc=40.3MB, time=124.97
x[1]                              = 1.11                                         
y2[1] (closed_form)               = 0.89569868568004762924062595933937           
y2[1] (numeric)                   = 0.89569868568004762924062595933946           
absolute error                    = 9e-32                                        
relative error                    = 1.0048021889377750437995502497241e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.44466151674170684864373751193357           
y1[1] (numeric)                   = 0.44466151674170684864373751193357           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3983                                       
Order of pole (three term test)                    = 32.2                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3983                                       
Order of pole (three term test)                    = 32.8                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=11628.4MB, alloc=40.3MB, time=125.42
memory used=11669.3MB, alloc=40.3MB, time=125.86
 
TOP MAIN SOLVE Loop
memory used=11710.3MB, alloc=40.3MB, time=126.30
x[1]                              = 1.12                                         
y2[1] (closed_form)               = 0.90010044217650499711910324733915           
y2[1] (numeric)                   = 0.90010044217650499711910324733923           
absolute error                    = 8e-32                                        
relative error                    = 8.8878969780921869267196205739329e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.43568244627671216761398879396113           
y1[1] (numeric)                   = 0.43568244627671216761398879396112           
absolute error                    = 1e-32                                        
relative error                    = 2.2952496905621863932273286161367e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3922                                       
Order of pole (three term test)                    = 32.19                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3922                                       
Order of pole (three term test)                    = 32.81                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11751.3MB, alloc=40.3MB, time=126.75
memory used=11792.2MB, alloc=40.3MB, time=127.19
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y2[1] (closed_form)               = 0.9044121893788259160370815224114            
y2[1] (numeric)                   = 0.90441218937882591603708152241149           
absolute error                    = 9e-32                                        
relative error                    = 9.9512148395317811475587861626794e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.42665980793015731037121583565354           
y1[1] (numeric)                   = 0.42665980793015731037121583565353           
absolute error                    = 1e-32                                        
relative error                    = 2.3437876767705676070253513391040e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3859                                       
Order of pole (three term test)                    = 32.18                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3859                                       
Order of pole (three term test)                    = 32.82                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11833.2MB, alloc=40.3MB, time=127.63
memory used=11874.2MB, alloc=40.3MB, time=128.06
memory used=11915.2MB, alloc=40.3MB, time=128.51
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y2[1] (closed_form)               = 0.9086334961158832645942155781022            
y2[1] (numeric)                   = 0.90863349611588326459421557810229           
absolute error                    = 9e-32                                        
relative error                    = 9.9049837348855320529025029946894e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.41759450395835809217518674082258           
y1[1] (numeric)                   = 0.41759450395835809217518674082257           
absolute error                    = 1e-32                                        
relative error                    = 2.3946675315911689408191841299543e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3794                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3794                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=11956.2MB, alloc=40.3MB, time=128.95
memory used=11997.1MB, alloc=40.3MB, time=129.39
memory used=12038.2MB, alloc=40.3MB, time=129.83
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y2[1] (closed_form)               = 0.91276394026052108094403304975368           
y2[1] (numeric)                   = 0.91276394026052108094403304975376           
absolute error                    = 8e-32                                        
relative error                    = 8.7645881340542879304444600032112e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.40848744088415729815257671880992           
y1[1] (numeric)                   = 0.40848744088415729815257671880992           
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3729                                       
Order of pole (three term test)                    = 32.17                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3729                                       
Order of pole (three term test)                    = 32.83                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12079.2MB, alloc=40.3MB, time=130.26
memory used=12120.2MB, alloc=40.3MB, time=130.72
 
TOP MAIN SOLVE Loop
memory used=12161.1MB, alloc=40.3MB, time=131.16
x[1]                              = 1.16                                         
y2[1] (closed_form)               = 0.91680310877176692661866166687433           
y2[1] (numeric)                   = 0.91680310877176692661866166687443           
absolute error                    = 1.0e-31                                      
relative error                    = 1.0907467376934304006864358212757e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.39933952940627315445163962339401           
y1[1] (numeric)                   = 0.39933952940627315445163962339402           
absolute error                    = 1e-32                                        
relative error                    = 2.5041347684432143166386845864530e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3661                                       
Order of pole (three term test)                    = 32.16                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3661                                       
Order of pole (three term test)                    = 32.84                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12202.2MB, alloc=40.3MB, time=131.59
memory used=12243.2MB, alloc=40.3MB, time=132.05
 
TOP MAIN SOLVE Loop
memory used=12284.2MB, alloc=40.3MB, time=132.48
x[1]                              = 1.17                                         
y2[1] (closed_form)               = 0.92075059773613563957301300896203           
y2[1] (numeric)                   = 0.92075059773613563957301300896213           
absolute error                    = 1.0e-31                                      
relative error                    = 1.0860704326000071520742710060653e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.3901516843082302153326619350505            
y1[1] (numeric)                   = 0.39015168430823021533266193505051           
absolute error                    = 1e-32                                        
relative error                    = 2.5631056848391647153358290323670e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3592                                       
Order of pole (three term test)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3592                                       
Order of pole (three term test)                    = 32.85                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12325.2MB, alloc=40.3MB, time=132.92
memory used=12366.2MB, alloc=40.3MB, time=133.36
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y2[1] (closed_form)               = 0.92460601240802034610753802587476           
y2[1] (numeric)                   = 0.92460601240802034610753802587487           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1896959193842878227035551928199e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.38092482436688177302959946671276           
y1[1] (numeric)                   = 0.38092482436688177302959946671278           
absolute error                    = 2e-32                                        
relative error                    = 5.2503797916665345836180073297707e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3522                                       
Order of pole (three term test)                    = 32.15                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3522                                       
Order of pole (three term test)                    = 32.85                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12407.3MB, alloc=40.3MB, time=133.81
memory used=12448.3MB, alloc=40.3MB, time=134.25
memory used=12489.2MB, alloc=40.3MB, time=134.69
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y2[1] (closed_form)               = 0.92836896724916669260202111160267           
y2[1] (numeric)                   = 0.92836896724916669260202111160279           
absolute error                    = 1.2e-31                                      
relative error                    = 1.2925895224133765598050553158072e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.37165987226053293806567955835047           
y1[1] (numeric)                   = 0.37165987226053293806567955835049           
absolute error                    = 2e-32                                        
relative error                    = 5.3812642937088548613935325903777e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.345                                        
Order of pole (three term test)                    = 32.14                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.345                                        
Order of pole (three term test)                    = 32.86                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12530.3MB, alloc=40.3MB, time=135.13
memory used=12571.3MB, alloc=40.3MB, time=135.58
memory used=12612.2MB, alloc=40.3MB, time=136.02
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y2[1] (closed_form)               = 0.93203908596722634967013443549483           
y2[1] (numeric)                   = 0.93203908596722634967013443549494           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1802080154808869515756286146788e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.36235775447667357763837335562308           
y1[1] (numeric)                   = 0.36235775447667357763837335562311           
absolute error                    = 3e-32                                        
relative error                    = 8.2791108039972193706502988177133e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3377                                       
Order of pole (three term test)                    = 32.13                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3377                                       
Order of pole (three term test)                    = 32.87                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12653.2MB, alloc=40.3MB, time=136.45
memory used=12694.2MB, alloc=40.3MB, time=136.89
 
TOP MAIN SOLVE Loop
memory used=12735.1MB, alloc=40.3MB, time=137.33
x[1]                              = 1.21                                         
y2[1] (closed_form)               = 0.93561600155338593341646488854361           
y2[1] (numeric)                   = 0.93561600155338593341646488854372           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1756960100871408312350079741769e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.35301940121933033870301071366479           
y1[1] (numeric)                   = 0.35301940121933033870301071366483           
absolute error                    = 4e-32                                        
relative error                    = 1.1330822006337286180955577608168e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3303                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3303                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12776.3MB, alloc=40.3MB, time=137.78
memory used=12817.2MB, alloc=40.3MB, time=138.22
 
TOP MAIN SOLVE Loop
memory used=12858.1MB, alloc=40.3MB, time=138.66
x[1]                              = 1.22                                         
y2[1] (closed_form)               = 0.93909935631906758093524527188837           
y2[1] (numeric)                   = 0.93909935631906758093524527188848           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1713350590629783758899019479540e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.3436457463160470204755229744352            
y1[1] (numeric)                   = 0.34364574631604702047552297443524           
absolute error                    = 4e-32                                        
relative error                    = 1.1639893823452847975735699500606e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3227                                       
Order of pole (three term test)                    = 32.12                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3227                                       
Order of pole (three term test)                    = 32.88                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12899.2MB, alloc=40.3MB, time=139.11
memory used=12940.1MB, alloc=40.3MB, time=139.55
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y2[1] (closed_form)               = 0.94248880193169751002382356538924           
y2[1] (numeric)                   = 0.94248880193169751002382356538934           
absolute error                    = 1.0e-31                                      
relative error                    = 1.0610205637991976337809176067095e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.33423772712450259823954724549766           
y1[1] (numeric)                   = 0.3342377271245025982395472454977            
absolute error                    = 4e-32                                        
relative error                    = 1.1967529920732172255226357687978e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.315                                        
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.315                                        
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=12981.1MB, alloc=40.3MB, time=139.98
memory used=13022.0MB, alloc=40.3MB, time=140.42
memory used=13063.1MB, alloc=40.3MB, time=140.88
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y2[1] (closed_form)               = 0.94578399944953898628470596308179           
y2[1] (numeric)                   = 0.94578399944953898628470596308188           
absolute error                    = 9e-32                                        
relative error                    = 9.5159148444445456168653298709188e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.32479628443877623657769341569738           
y1[1] (numeric)                   = 0.32479628443877623657769341569743           
absolute error                    = 5e-32                                        
relative error                    = 1.5394264773193533328532731450800e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.3072                                       
Order of pole (three term test)                    = 32.11                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.3072                                       
Order of pole (three term test)                    = 32.89                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13104.1MB, alloc=40.3MB, time=141.31
memory used=13145.2MB, alloc=40.3MB, time=141.75
memory used=13186.1MB, alloc=40.3MB, time=142.20
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y2[1] (closed_form)               = 0.94898461935558621434849084703605           
y2[1] (numeric)                   = 0.94898461935558621434849084703615           
absolute error                    = 1.0e-31                                      
relative error                    = 1.0537578582454329877253077296853e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.31532236239526866544753855243804           
y1[1] (numeric)                   = 0.3153223623952686654475385524381            
absolute error                    = 6e-32                                        
relative error                    = 1.9028146162620620165087579727933e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2992                                       
Order of pole (three term test)                    = 32.1                                         
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2992                                       
Order of pole (three term test)                    = 32.9                                         
NO COMPLEX POLE (six term test) for Equation 2
memory used=13227.1MB, alloc=40.3MB, time=142.64
memory used=13268.2MB, alloc=40.3MB, time=143.09
 
TOP MAIN SOLVE Loop
memory used=13309.1MB, alloc=40.3MB, time=143.53
x[1]                              = 1.26                                         
y2[1] (closed_form)               = 0.95209034159051576385681622142542           
y2[1] (numeric)                   = 0.95209034159051576385681622142553           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1553525458124000744228465106062e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.30581690837828932688634248917648           
y1[1] (numeric)                   = 0.30581690837828932688634248917653           
absolute error                    = 5e-32                                        
relative error                    = 1.6349651909419936926311241884046e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2912                                       
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2912                                       
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13350.2MB, alloc=40.3MB, time=143.97
memory used=13391.2MB, alloc=40.3MB, time=144.41
 
TOP MAIN SOLVE Loop
memory used=13432.1MB, alloc=40.3MB, time=144.86
x[1]                              = 1.27                                         
y2[1] (closed_form)               = 0.95510085558469223509018174218289           
y2[1] (numeric)                   = 0.955100855584692235090181742183             
absolute error                    = 1.1e-31                                      
relative error                    = 1.1517108309222523102971129643005e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.29628087292531873355113701608796           
y1[1] (numeric)                   = 0.296280872925318733551137016088             
absolute error                    = 4e-32                                        
relative error                    = 1.3500702763921751980119693012842e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.283                                        
Order of pole (three term test)                    = 32.09                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.283                                        
Order of pole (three term test)                    = 32.91                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13473.1MB, alloc=40.3MB, time=145.30
memory used=13514.1MB, alloc=40.3MB, time=145.73
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y2[1] (closed_form)               = 0.95801586028922496370075385916029           
y2[1] (numeric)                   = 0.95801586028922496370075385916039           
absolute error                    = 1.0e-31                                      
relative error                    = 1.0438240549567728717927004514947e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.28671520963195551277938689359259           
y1[1] (numeric)                   = 0.28671520963195551277938689359264           
absolute error                    = 5e-32                                        
relative error                    = 1.7438907431587929162692549603174e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2747                                       
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2747                                       
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13555.2MB, alloc=40.3MB, time=146.17
memory used=13596.1MB, alloc=40.3MB, time=146.62
memory used=13637.2MB, alloc=40.3MB, time=147.06
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y2[1] (closed_form)               = 0.96083506420607265890556129128537           
y2[1] (numeric)                   = 0.96083506420607265890556129128548           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1448374866595004854124647987321e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.27712087505655764138660609006118           
y1[1] (numeric)                   = 0.27712087505655764138660609006124           
absolute error                    = 6e-32                                        
relative error                    = 2.1651201840263600101325262745046e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2663                                       
Order of pole (three term test)                    = 32.08                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2663                                       
Order of pole (three term test)                    = 32.92                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13678.2MB, alloc=40.3MB, time=147.50
memory used=13719.3MB, alloc=40.3MB, time=147.95
memory used=13760.2MB, alloc=40.3MB, time=148.39
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y2[1] (closed_form)               = 0.96355818541719296470134863003955           
y2[1] (numeric)                   = 0.96355818541719296470134863003969           
absolute error                    = 1.4e-31                                      
relative error                    = 1.4529480639447220197146856827052e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.26749882862458740699798410929287           
y1[1] (numeric)                   = 0.26749882862458740699798410929293           
absolute error                    = 6e-32                                        
relative error                    = 2.2430004762452647031662010378488e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2578                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2578                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13801.3MB, alloc=40.3MB, time=148.83
memory used=13842.3MB, alloc=40.3MB, time=149.26
 
TOP MAIN SOLVE Loop
memory used=13883.3MB, alloc=40.3MB, time=149.72
x[1]                              = 1.31                                         
y2[1] (closed_form)               = 0.9661849516127340291692578059375            
y2[1] (numeric)                   = 0.96618495161273402916925780593762           
absolute error                    = 1.2e-31                                      
relative error                    = 1.2419982302529005341090772913190e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.2578500325326696613381769786162            
y1[1] (numeric)                   = 0.25785003253266966133817697861625           
absolute error                    = 5e-32                                        
relative error                    = 1.9391116421001415982201674906100e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2491                                       
Order of pole (three term test)                    = 32.07                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2491                                       
Order of pole (three term test)                    = 32.93                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=13924.3MB, alloc=40.3MB, time=150.16
memory used=13965.2MB, alloc=40.3MB, time=150.59
 
TOP MAIN SOLVE Loop
memory used=14006.2MB, alloc=40.3MB, time=151.03
x[1]                              = 1.32                                         
y2[1] (closed_form)               = 0.96871510011826526273589984597277           
y2[1] (numeric)                   = 0.9687151001182652627358998459729            
absolute error                    = 1.3e-31                                      
relative error                    = 1.3419838297568500065565996071124e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.24817545165237295957398272942735           
y1[1] (numeric)                   = 0.24817545165237295957398272942741           
absolute error                    = 6e-32                                        
relative error                    = 2.4176444366481443149116142792461e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2404                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2404                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14047.2MB, alloc=40.3MB, time=151.48
memory used=14088.1MB, alloc=40.3MB, time=151.92
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y2[1] (closed_form)               = 0.9711483779210445623376830377638            
y2[1] (numeric)                   = 0.97114837792104456233768303776392           
absolute error                    = 1.2e-31                                      
relative error                    = 1.2356505218789144986376325445111e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.23847605343372320751578498601058           
y1[1] (numeric)                   = 0.23847605343372320751578498601063           
absolute error                    = 5e-32                                        
relative error                    = 2.0966465722687708339780876237170e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2316                                       
Order of pole (three term test)                    = 32.06                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2316                                       
Order of pole (three term test)                    = 32.94                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14129.2MB, alloc=40.3MB, time=152.36
memory used=14170.1MB, alloc=40.3MB, time=152.80
memory used=14211.1MB, alloc=40.3MB, time=153.25
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y2[1] (closed_form)               = 0.97348454169531937478787034808955           
y2[1] (numeric)                   = 0.97348454169531937478787034808966           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1299614455966136539947011034401e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.22875280780845946523263949230014           
y1[1] (numeric)                   = 0.22875280780845946523263949230019           
absolute error                    = 5e-32                                        
relative error                    = 2.1857655203894270738370516051356e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2227                                       
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2227                                       
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14252.1MB, alloc=40.3MB, time=153.69
memory used=14293.0MB, alloc=40.3MB, time=154.13
memory used=14334.0MB, alloc=40.3MB, time=154.58
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y2[1] (closed_form)               = 0.97572335782665906926111353926522           
y2[1] (numeric)                   = 0.97572335782665906926111353926532           
absolute error                    = 1.0e-31                                      
relative error                    = 1.0248806610794017372368662156356e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.21900668709304158142002217301063           
y1[1] (numeric)                   = 0.21900668709304158142002217301067           
absolute error                    = 4e-32                                        
relative error                    = 1.8264282488783834594701364724300e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2137                                       
Order of pole (three term test)                    = 32.05                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2137                                       
Order of pole (three term test)                    = 32.95                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14375.1MB, alloc=40.3MB, time=155.01
memory used=14416.1MB, alloc=40.3MB, time=155.45
 
TOP MAIN SOLVE Loop
memory used=14457.0MB, alloc=40.3MB, time=155.89
x[1]                              = 1.36                                         
y2[1] (closed_form)               = 0.97786460243531618567849243942663           
y2[1] (numeric)                   = 0.97786460243531618567849243942673           
absolute error                    = 1.0e-31                                      
relative error                    = 1.0226364647105098859550318372739e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.20923866589141935767597525239186           
y1[1] (numeric)                   = 0.20923866589141935767597525239189           
absolute error                    = 3e-32                                        
relative error                    = 1.4337694169569959131632634099302e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.2046                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.2046                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14498.1MB, alloc=40.3MB, time=156.34
memory used=14539.0MB, alloc=40.3MB, time=156.78
 
TOP MAIN SOLVE Loop
memory used=14580.0MB, alloc=40.3MB, time=157.22
x[1]                              = 1.37                                         
y2[1] (closed_form)               = 0.97990806139861422288768850489193           
y2[1] (numeric)                   = 0.97990806139861422288768850489204           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1225542919097732509429232058675e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.19944972099757296568819838964531           
y1[1] (numeric)                   = 0.19944972099757296568819838964535           
absolute error                    = 4e-32                                        
relative error                    = 2.0055179721453080444837095002736e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1954                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1954                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14621.1MB, alloc=40.3MB, time=157.67
memory used=14662.0MB, alloc=40.3MB, time=158.11
 
TOP MAIN SOLVE Loop
x[1]                              = 1.38                                         
y2[1] (closed_form)               = 0.98185353037235972787813108520605           
y2[1] (numeric)                   = 0.98185353037235972787813108520617           
absolute error                    = 1.2e-31                                      
relative error                    = 1.2221782199478470588190898782452e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.1896408312978343632091500735982            
y1[1] (numeric)                   = 0.18964083129783436320915007359825           
absolute error                    = 5e-32                                        
relative error                    = 2.6365630048032268768302730981699e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1862                                       
Order of pole (three term test)                    = 32.04                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1862                                       
Order of pole (three term test)                    = 32.96                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14703.1MB, alloc=40.3MB, time=158.55
memory used=14744.1MB, alloc=40.3MB, time=158.98
memory used=14785.0MB, alloc=40.3MB, time=159.44
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y2[1] (closed_form)               = 0.98370081481127654484003822444291           
y2[1] (numeric)                   = 0.98370081481127654484003822444302           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1182261755176399924950747116541e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.17981297767299947659616321780405           
y1[1] (numeric)                   = 0.17981297767299947659616321780409           
absolute error                    = 4e-32                                        
relative error                    = 2.2245335413299457859169812246486e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1769                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1769                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14826.1MB, alloc=40.3MB, time=159.88
memory used=14867.1MB, alloc=40.3MB, time=160.31
memory used=14908.0MB, alloc=40.3MB, time=160.75
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y2[1] (closed_form)               = 0.9854497299884601806594745788061            
y2[1] (numeric)                   = 0.98544972998846018065947457880621           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1162416169243673409902737327472e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.16996714290024093861674803520365           
y1[1] (numeric)                   = 0.16996714290024093861674803520367           
absolute error                    = 2e-32                                        
relative error                    = 1.1766980169654689653988540619690e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1675                                       
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1675                                       
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=14949.0MB, alloc=40.3MB, time=161.20
memory used=14990.0MB, alloc=40.3MB, time=161.64
 
TOP MAIN SOLVE Loop
memory used=15031.0MB, alloc=40.3MB, time=162.08
x[1]                              = 1.41                                         
y2[1] (closed_form)               = 0.98710010101385034142908886194224           
y2[1] (numeric)                   = 0.98710010101385034142908886194236           
absolute error                    = 1.2e-31                                      
relative error                    = 1.2156821772862551725899653507496e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.16010431155483119016356254936092           
y1[1] (numeric)                   = 0.16010431155483119016356254936095           
absolute error                    = 3e-32                                        
relative error                    = 1.8737783953885495486989139863589e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.158                                        
Order of pole (three term test)                    = 32.03                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.158                                        
Order of pole (three term test)                    = 32.97                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15072.1MB, alloc=40.3MB, time=162.53
memory used=15113.0MB, alloc=40.3MB, time=162.97
 
TOP MAIN SOLVE Loop
memory used=15154.0MB, alloc=40.3MB, time=163.41
x[1]                              = 1.42                                         
y2[1] (closed_form)               = 0.9886517628517197927362734733357            
y2[1] (numeric)                   = 0.98865176285171979273627347333582           
absolute error                    = 1.2e-31                                      
relative error                    = 1.2137741974369783120159352477734e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.15022546991168577348698210297591           
y1[1] (numeric)                   = 0.15022546991168577348698210297594           
absolute error                    = 3e-32                                        
relative error                    = 1.9969982465447660472718376492287e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1485                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1485                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15195.0MB, alloc=40.3MB, time=163.84
memory used=15235.9MB, alloc=40.3MB, time=164.28
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y2[1] (closed_form)               = 0.99010456033717779485729149548183           
y2[1] (numeric)                   = 0.99010456033717779485729149548195           
absolute error                    = 1.2e-31                                      
relative error                    = 1.2119932056381427064035653085188e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.14033160584673666253389762457492           
y1[1] (numeric)                   = 0.14033160584673666253389762457495           
absolute error                    = 3e-32                                        
relative error                    = 2.1377935368860908801729634797422e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1389                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1389                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15276.9MB, alloc=40.3MB, time=164.73
memory used=15317.9MB, alloc=40.3MB, time=165.17
memory used=15358.9MB, alloc=40.3MB, time=165.61
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y2[1] (closed_form)               = 0.99145834819168646252760446395798           
y2[1] (numeric)                   = 0.9914583481916864625276044639581            
absolute error                    = 1.2e-31                                      
relative error                    = 1.2103382882283165112527731482405e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.13042370873814549297752015612917           
y1[1] (numeric)                   = 0.1304237087381454929775201561292            
absolute error                    = 3e-32                                        
relative error                    = 2.3001952858304045212098108052567e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1293                                       
Order of pole (three term test)                    = 32.02                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1293                                       
Order of pole (three term test)                    = 32.98                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15400.0MB, alloc=40.3MB, time=166.06
memory used=15441.0MB, alloc=40.3MB, time=166.50
memory used=15482.0MB, alloc=40.3MB, time=166.94
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y2[1] (closed_form)               = 0.99271299103758849766535413432301           
y2[1] (numeric)                   = 0.99271299103758849766535413432312           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1080745491708279078977561201952e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.12050276936736657053286662724802           
y1[1] (numeric)                   = 0.12050276936736657053286662724804           
absolute error                    = 2e-32                                        
relative error                    = 1.6597128933217872056632451020372e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1196                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1196                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15523.0MB, alloc=40.3MB, time=167.38
memory used=15564.0MB, alloc=40.3MB, time=167.83
 
TOP MAIN SOLVE Loop
memory used=15605.0MB, alloc=40.3MB, time=168.27
x[1]                              = 1.46                                         
y2[1] (closed_form)               = 0.99386836341164484228683230125003           
y2[1] (numeric)                   = 0.99386836341164484228683230125014           
absolute error                    = 1.1e-31                                      
relative error                    = 1.1067864120596794587398333969033e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.11056977982006955117464810912337           
y1[1] (numeric)                   = 0.11056977982006955117464810912339           
absolute error                    = 2e-32                                        
relative error                    = 1.8088125012590279658008208398940e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1099                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1099                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15646.1MB, alloc=40.3MB, time=168.70
memory used=15687.0MB, alloc=40.3MB, time=169.14
 
TOP MAIN SOLVE Loop
memory used=15728.0MB, alloc=40.3MB, time=169.59
x[1]                              = 1.47                                         
y2[1] (closed_form)               = 0.99492434977758089785992846273557           
y2[1] (numeric)                   = 0.99492434977758089785992846273566           
absolute error                    = 9e-32                                        
relative error                    = 9.0459138948724936187700476929769e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.10062573338693170090697460146241           
y1[1] (numeric)                   = 0.10062573338693170090697460146243           
absolute error                    = 2e-32                                        
relative error                    = 1.9875631537605674709012349381457e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.1001                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.1001                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15769.0MB, alloc=40.3MB, time=170.03
memory used=15810.0MB, alloc=40.3MB, time=170.47
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y2[1] (closed_form)               = 0.99588084453764005648407513256269           
y2[1] (numeric)                   = 0.99588084453764005648407513256278           
absolute error                    = 9e-32                                        
relative error                    = 9.0372257377622833800487766002822e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.090671624464309655776226540647838          
y1[1] (numeric)                   = 0.090671624464309655776226540647863          
absolute error                    = 2.5e-32                                      
relative error                    = 2.7572021729731498816142627996907e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.0903                                       
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.0903                                       
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15851.2MB, alloc=40.3MB, time=170.92
memory used=15892.0MB, alloc=40.3MB, time=171.36
memory used=15933.0MB, alloc=40.3MB, time=171.80
 
TOP MAIN SOLVE Loop
x[1]                              = 1.49                                         
y2[1] (closed_form)               = 0.9967377520431433885532007170437            
y2[1] (numeric)                   = 0.99673775204314338855320071704379           
absolute error                    = 9e-32                                        
relative error                    = 9.0294563254492227332902187450867e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.080708448454800614868318484563714          
y1[1] (numeric)                   = 0.080708448454800614868318484563738          
absolute error                    = 2.4e-32                                      
relative error                    = 2.9736663830727447585817409075188e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.08045                                      
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.08045                                      
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=15974.1MB, alloc=40.3MB, time=172.23
memory used=16015.0MB, alloc=40.3MB, time=172.69
memory used=16056.0MB, alloc=40.3MB, time=173.13
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y2[1] (closed_form)               = 0.99749498660405443094172337114149           
y2[1] (numeric)                   = 0.99749498660405443094172337114156           
absolute error                    = 7e-32                                        
relative error                    = 7.0175791297270743696792855465612e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.070737201667702910088189851434269          
y1[1] (numeric)                   = 0.070737201667702910088189851434292          
absolute error                    = 2.3e-32                                      
relative error                    = 3.2514715676830777088423425398626e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.07056                                      
Order of pole (three term test)                    = 32.01                                        
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.07056                                      
Order of pole (three term test)                    = 32.99                                        
NO COMPLEX POLE (six term test) for Equation 2
memory used=16097.1MB, alloc=40.3MB, time=173.58
memory used=16138.1MB, alloc=40.3MB, time=174.01
 
TOP MAIN SOLVE Loop
memory used=16179.0MB, alloc=40.3MB, time=174.45
x[1]                              = 1.51                                         
y2[1] (closed_form)               = 0.99815247249754811924273786483671           
y2[1] (numeric)                   = 0.99815247249754811924273786483679           
absolute error                    = 8e-32                                        
relative error                    = 8.0148075774261545522267390254129e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.060758881219385906581595514916193          
y1[1] (numeric)                   = 0.060758881219385906581595514916216          
absolute error                    = 2.3e-32                                      
relative error                    = 3.7854548237898680467664619680148e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.06065                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.06065                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
memory used=16220.1MB, alloc=40.3MB, time=174.89
memory used=16260.9MB, alloc=40.3MB, time=175.34
 
TOP MAIN SOLVE Loop
memory used=16302.0MB, alloc=40.3MB, time=175.78
x[1]                              = 1.52                                         
y2[1] (closed_form)               = 0.99871014397558300717231239411685           
y2[1] (numeric)                   = 0.99871014397558300717231239411693           
absolute error                    = 8e-32                                        
relative error                    = 8.0103321752137807696780439868792e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.050774484933579196726129270152727          
y1[1] (numeric)                   = 0.050774484933579196726129270152749          
absolute error                    = 2.2e-32                                      
relative error                    = 4.3328849182378451846945838457867e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.05071                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.05071                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
memory used=16343.0MB, alloc=40.3MB, time=176.22
memory used=16383.9MB, alloc=40.3MB, time=176.66
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y2[1] (closed_form)               = 0.99916794527147601592426506870898           
y2[1] (numeric)                   = 0.99916794527147601592426506870906           
absolute error                    = 8e-32                                        
relative error                    = 8.0066619809609517692808259147125e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.040785011241591058688989007076121          
y1[1] (numeric)                   = 0.040785011241591058688989007076141          
absolute error                    = 2.0e-32                                      
relative error                    = 4.9037622869660345937564607594618e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.04075                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.04075                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
memory used=16425.0MB, alloc=40.3MB, time=177.11
memory used=16466.0MB, alloc=40.3MB, time=177.55
memory used=16507.0MB, alloc=40.3MB, time=177.98
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y2[1] (closed_form)               = 0.99952583060547905600596353844003           
y2[1] (numeric)                   = 0.99952583060547905600596353844011           
absolute error                    = 8e-32                                        
relative error                    = 8.0037951547023748903674666920324e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.030791459082466157622476807076397          
y1[1] (numeric)                   = 0.030791459082466157622476807076416          
absolute error                    = 1.9e-32                                      
relative error                    = 6.1705422757375377396982542539992e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.03078                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.03078                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
memory used=16548.0MB, alloc=40.3MB, time=178.42
memory used=16588.9MB, alloc=40.3MB, time=178.87
memory used=16629.9MB, alloc=40.3MB, time=179.31
 
TOP MAIN SOLVE Loop
x[1]                              = 1.55                                         
y2[1] (closed_form)               = 0.99978376418935696389761134763447           
y2[1] (numeric)                   = 0.99978376418935696389761134763453           
absolute error                    = 6e-32                                        
relative error                    = 6.0012976954720905919209077716776e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
y1[1] (closed_form)               = 0.020794827803092473643912774695556          
y1[1] (numeric)                   = 0.020794827803092473643912774695575          
absolute error                    = 1.9e-32                                      
relative error                    = 9.1368873933038491691096837140113e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 10                                  
Correct digits                    = 32                                  
h                                 = 0.001                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1   = 0.02079                                      
Order of pole (three term test)                    = 32                                           
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2   = 0.02079                                      
Order of pole (three term test)                    = 33                                           
NO COMPLEX POLE (six term test) for Equation 2
memory used=16670.9MB, alloc=40.3MB, time=179.75
memory used=16712.0MB, alloc=40.3MB, time=180.19
Finished!
Maximum Time Reached before Solution Completed!
diff  (  y2  ,  x  ,  3  )   =  neg (  cos  (  x  )   )  ; 
diff  (  y1  ,  x  ,  1  )   =  neg (  y2  )  ; 
Iterations                       = 1457                                
Total Elapsed Time               = 3 Minutes 0 Seconds
Elapsed Time(since restart)      = 3 Minutes 0 Seconds
Expected Time Remaining          = 7 Minutes 5 Seconds
Optimized Time Remaining         = 7 Minutes 5 Seconds
Expected Total Time              = 10 Minutes 5 Seconds
Time to Timeout                  0.0 Seconds
Percent Done                     = 29.76                                      % 
> quit
memory used=16717.3MB, alloc=40.3MB, time=180.25